📝 litedoc新增类继承显示，新增变量自动获取注释，新增类方法和函数的区分，新增魔术方法的特殊展示模式

.github/workflows/deploy-docs.yml

@@ -42,9 +42,9 @@ jobs:
       - name: Setup API markdown
         run: |-
           python -m pip install pydantic
-          python -m liteyuki_autodoc mbcp -o docs/api -l zh-Hans
+          python -m litedoc mbcp -o docs/api -l zh-Hans
-          python -m liteyuki_autodoc mbcp -o docs/en/api -l en
+          python -m litedoc mbcp -o docs/en/api -l en
-          python -m liteyuki_autodoc mbcp -o docs/ja/api -l ja
+          python -m litedoc mbcp -o docs/ja/api -l ja
 
       - name: 安装 pnpm
         uses: pnpm/action-setup@v2

docs/.vitepress/config/en.ts

@@ -4,7 +4,11 @@ export const en = defineConfig({
 
     lang: "en-US",
     description: "A library made for Minecraft particle generation",
-
     themeConfig: {
+        nav: [
+            {text: 'Get Start', link: '/guide'},
+            {text: 'API Document', link: '/api/'},
+            {text: 'Demo', link: '/demo/'},
+        ],
     },
 })

docs/.vitepress/config/index.ts

@@ -3,6 +3,8 @@ import {defineConfig} from "vitepress";
 import {common} from './common'
 import {en} from './en'
 import {zh} from './zh'
+import {zht} from './zht'
+import {ja} from './ja'
 
 
 
@@ -10,6 +12,8 @@ export default defineConfig({
     ...common,
     locales:{
         root: { label: "简体中文", ...zh },
-        en: { label: "English", ...en }
+        en: { label: "English", ...en },
+        ja: { label: "日本語", ...ja },
+        zht: { label: "繁體中文", ...zht },
     }
 })

docs/.vitepress/config/ja.ts

@@ -0,0 +1,14 @@
+import {defineConfig} from 'vitepress'
+
+export const ja = defineConfig({
+
+    lang: "ja-JP",
+    description: "Minecraftのパーティクル生成用のライブラリ",
+    themeConfig: {
+        nav: [
+            {text: 'スタート', link: '/guide'},
+            {text: 'APIドキュメント', link: '/api/'},
+            {text: 'インスタンス', link: '/demo/'},
+        ],
+    },
+})

docs/.vitepress/config/zh.ts

@@ -1,21 +1,14 @@
 import {defineConfig} from 'vitepress'
 
 export const zh = defineConfig({
+
     lang: "zh-Hans",
     description: "一个用于Minecraft粒子计算和生成的库",
-
     themeConfig: {
         nav: [
-            {text: '快速开始', link: '/guide'},
+            {text: '快速开始', link: '/guide/'},
             {text: 'API文档', link: '/api/'},
             {text: '实例', link: '/demo/'},
         ],
-        // sidebar: {
-        //     '/api/': {
-        //         base: '/api/',
-        //         items: [
-        //         ]
-        //     }
-        // }
     },
 })

docs/.vitepress/config/zht.ts

@@ -0,0 +1,14 @@
+import {defineConfig} from 'vitepress'
+
+export const zht = defineConfig({
+
+    lang: "zh-Hant",
+    description: "一個用於Minecraft粒子計算和生成的軟體庫",
+    themeConfig: {
+        nav: [
+            {text: '指引', link: '/guide/'},
+            {text: 'API文檔', link: '/api/'},
+            {text: '示範', link: '/demo/'},
+        ],
+    },
+})

docs/api/mp_math/angle.md

@@ -1,16 +1,14 @@
 ---
 title: mbcp.mp_math.angle
 ---
-### ***class*** `Angle`
+### **class** `Angle`
-
+### **class** `AnyAngle(Angle)`
-### ***class*** `AnyAngle`
+### *method* `__init__(self, value: float, is_radian: bool = False)`
-
-### *def* `__init__(self, value: float, is_radian: bool = False)`
 
 
 任意角度。
 
-参数:
+**参数**:
 
 - value: 角度或弧度值  
 
@@ -19,7 +17,7 @@ title: mbcp.mp_math.angle
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, value: float, is_radian: bool=False):
@@ -37,19 +35,19 @@ def __init__(self, value: float, is_radian: bool=False):
 </details>
 
 ### `@property`
-### *def* `complementary(self) -> 'AnyAngle'`
+### *method* `complementary(self) -> AnyAngle`
 
 
 余角：两角的和为90°。
 
-返回:
+**返回**:
 
 - 余角
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -64,19 +62,19 @@ def complementary(self) -> 'AnyAngle':
 </details>
 
 ### `@property`
-### *def* `supplementary(self) -> 'AnyAngle'`
+### *method* `supplementary(self) -> AnyAngle`
 
 
 补角：两角的和为180°。
 
-返回:
+**返回**:
 
 - 补角
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -91,19 +89,19 @@ def supplementary(self) -> 'AnyAngle':
 </details>
 
 ### `@property`
-### *def* `degree(self) -> float`
+### *method* `degree(self) -> float`
 
 
 角度。
 
-返回:
+**返回**:
 
 - 弧度
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -118,19 +116,19 @@ def degree(self) -> float:
 </details>
 
 ### `@property`
-### *def* `minimum_positive(self) -> 'AnyAngle'`
+### *method* `minimum_positive(self) -> AnyAngle`
 
 
 最小正角。
 
-返回:
+**返回**:
 
 - 最小正角度
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -145,19 +143,19 @@ def minimum_positive(self) -> 'AnyAngle':
 </details>
 
 ### `@property`
-### *def* `maximum_negative(self) -> 'AnyAngle'`
+### *method* `maximum_negative(self) -> AnyAngle`
 
 
 最大负角。
 
-返回:
+**返回**:
 
 - 最大负角度
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -172,19 +170,19 @@ def maximum_negative(self) -> 'AnyAngle':
 </details>
 
 ### `@property`
-### *def* `sin(self) -> float`
+### *method* `sin(self) -> float`
 
 
 正弦值。
 
-返回:
+**返回**:
 
 - 正弦值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -199,19 +197,19 @@ def sin(self) -> float:
 </details>
 
 ### `@property`
-### *def* `cos(self) -> float`
+### *method* `cos(self) -> float`
 
 
 余弦值。
 
-返回:
+**返回**:
 
 - 余弦值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -226,19 +224,19 @@ def cos(self) -> float:
 </details>
 
 ### `@property`
-### *def* `tan(self) -> float`
+### *method* `tan(self) -> float`
 
 
 正切值。
 
-返回:
+**返回**:
 
 - 正切值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -253,19 +251,19 @@ def tan(self) -> float:
 </details>
 
 ### `@property`
-### *def* `cot(self) -> float`
+### *method* `cot(self) -> float`
 
 
 余切值。
 
-返回:
+**返回**:
 
 - 余切值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -280,19 +278,19 @@ def cot(self) -> float:
 </details>
 
 ### `@property`
-### *def* `sec(self) -> float`
+### *method* `sec(self) -> float`
 
 
 正割值。
 
-返回:
+**返回**:
 
 - 正割值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -307,19 +305,19 @@ def sec(self) -> float:
 </details>
 
 ### `@property`
-### *def* `csc(self) -> float`
+### *method* `csc(self) -> float`
 
 
 余割值。
 
-返回:
+**返回**:
 
 - 余割值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -333,11 +331,11 @@ def csc(self) -> float:
 ```
 </details>
 
-### *def* `__add__(self, other: 'AnyAngle') -> 'AnyAngle'`
+### *method* `self + other: AnyAngle => AnyAngle`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -345,11 +343,11 @@ def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
 ```
 </details>
 
-### *def* `__eq__(self, other)`
+### *method* `__eq__(self, other)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other):
@@ -357,11 +355,11 @@ def __eq__(self, other):
 ```
 </details>
 
-### *def* `__sub__(self, other: 'AnyAngle') -> 'AnyAngle'`
+### *method* `self - other: AnyAngle => AnyAngle`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -369,11 +367,11 @@ def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
 ```
 </details>
 
-### *def* `__mul__(self, other: float) -> 'AnyAngle'`
+### *method* `self * other: float => AnyAngle`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __mul__(self, other: float) -> 'AnyAngle':
@@ -381,36 +379,12 @@ def __mul__(self, other: float) -> 'AnyAngle':
 ```
 </details>
 
-### *def* `__repr__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __repr__(self):
-    return f'AnyAngle({self.radian}, is_radian=True)'
-```
-</details>
-
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    return f'AnyAngle({self.degree}° or {self.radian} rad)'
-```
-</details>
-
 ### `@overload`
-### *def* `__truediv__(self, other: float) -> 'AnyAngle'`
+### *method* `self / other: float => AnyAngle`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -420,11 +394,11 @@ def __truediv__(self, other: float) -> 'AnyAngle':
 </details>
 
 ### `@overload`
-### *def* `__truediv__(self, other: 'AnyAngle') -> float`
+### *method* `self / other: AnyAngle => float`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -433,11 +407,11 @@ def __truediv__(self, other: 'AnyAngle') -> float:
 ```
 </details>
 
-### *def* `__truediv__(self, other)`
+### *method* `self / other`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __truediv__(self, other):

docs/api/mp_math/const.md

@@ -1,15 +1,3 @@
 ---
 title: mbcp.mp_math.const
 ---
-### ***var*** `PI = math.pi`
-
-### ***var*** `E = math.e`
-
-### ***var*** `GOLDEN_RATIO = (1 + math.sqrt(5)) / 2`
-
-### ***var*** `GAMMA = 0.5772156649015329`
-
-### ***var*** `EPSILON = 0.0001`
-
-### ***var*** `APPROX = 0.001`
-

docs/api/mp_math/equation.md

@@ -1,12 +1,12 @@
 ---
 title: mbcp.mp_math.equation
 ---
-### *def* `get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc`
+### *func* `get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc`
 
 
 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
 
-参数:
+**参数**:
 
 - func: 函数  
 
@@ -14,10 +14,18 @@ title: mbcp.mp_math.equation
 
 - epsilon: 偏移量  
 
+**返回**:
+
+- 偏导函数
+
+**引发**:
+
+- ValueError  无效变量类型
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
@@ -54,11 +62,11 @@ def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...],
 ```
 </details>
 
-### *def* `partial_derivative_func() -> Var`
+### *func* `partial_derivative_func() -> Var`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def partial_derivative_func(*args: Var) -> Var:
@@ -70,11 +78,11 @@ def partial_derivative_func(*args: Var) -> Var:
 ```
 </details>
 
-### *def* `high_order_partial_derivative_func() -> Var`
+### *func* `high_order_partial_derivative_func() -> Var`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def high_order_partial_derivative_func(*args: Var) -> Var:
@@ -85,14 +93,13 @@ def high_order_partial_derivative_func(*args: Var) -> Var:
 ```
 </details>
 
-### ***class*** `CurveEquation`
+### **class** `CurveEquation`
-
+### *method* `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`
-### *def* `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`
 
 
 曲线方程。
 
-参数:
+**参数**:
 
 - x_func: x函数  
 
@@ -103,7 +110,7 @@ def high_order_partial_derivative_func(*args: Var) -> Var:
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
@@ -120,12 +127,12 @@ def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
 ```
 </details>
 
-### *def* `__call__(self) -> Point3 | tuple[Point3, ...]`
+### *method* `__call__(self) -> Point3 | tuple[Point3, ...]`
 
 
 计算曲线上的点。
 
-参数:
+**参数**:
 
 - *t:   
 
@@ -134,7 +141,7 @@ def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
@@ -153,17 +160,3 @@ def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
 ```
 </details>
 
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    return 'CurveEquation()'
-```
-</details>
-
-### ***var*** `result_func = get_partial_derivative_func(result_func, v, epsilon)`
-

docs/api/mp_math/line.md

@@ -1,14 +1,13 @@
 ---
 title: mbcp.mp_math.line
 ---
-### ***class*** `Line3`
+### **class** `Line3`
-
+### *method* `__init__(self, point: Point3, direction: Vector3)`
-### *def* `__init__(self, point: 'Point3', direction: 'Vector3')`
 
 
 三维空间中的直线。由一个点和一个方向向量确定。
 
-参数:
+**参数**:
 
 - point: 直线上的一点  
 
@@ -17,7 +16,7 @@ title: mbcp.mp_math.line
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, point: 'Point3', direction: 'Vector3'):
@@ -32,21 +31,25 @@ def __init__(self, point: 'Point3', direction: 'Vector3'):
 ```
 </details>
 
-### *def* `approx(self, other: 'Line3', epsilon: float = APPROX) -> bool`
+### *method* `approx(self, other: Line3, epsilon: float = APPROX) -> bool`
 
 
 判断两条直线是否近似相等。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
 - epsilon: 误差  
 
+**返回**:
+
+- 是否近似相等
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
@@ -62,19 +65,27 @@ def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
 ```
 </details>
 
-### *def* `cal_angle(self, other: 'Line3') -> 'AnyAngle'`
+### *method* `cal_angle(self, other: Line3) -> AnyAngle`
 
 
 计算直线和直线之间的夹角。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 夹角弧度
+
+**引发**:
+
+- TypeError  不支持的类型
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_angle(self, other: 'Line3') -> 'AnyAngle':
@@ -91,19 +102,27 @@ def cal_angle(self, other: 'Line3') -> 'AnyAngle':
 ```
 </details>
 
-### *def* `cal_distance(self, other: 'Line3 | Point3') -> float`
+### *method* `cal_distance(self, other: Line3 | Point3) -> float`
 
 
 计算直线和直线或点之间的距离。
 
-参数:
+**参数**:
 
 - other: 平行直线或点  
 
+**返回**:
+
+- 距离
+
+**引发**:
+
+- TypeError  不支持的类型
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_distance(self, other: 'Line3 | Point3') -> float:
@@ -133,19 +152,29 @@ def cal_distance(self, other: 'Line3 | Point3') -> float:
 ```
 </details>
 
-### *def* `cal_intersection(self, other: 'Line3') -> 'Point3'`
+### *method* `cal_intersection(self, other: Line3) -> Point3`
 
 
 计算两条直线的交点。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 交点
+
+**引发**:
+
+- ValueError  直线平行
+
+- ValueError  直线不共面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_intersection(self, other: 'Line3') -> 'Point3':
@@ -167,19 +196,23 @@ def cal_intersection(self, other: 'Line3') -> 'Point3':
 ```
 </details>
 
-### *def* `cal_perpendicular(self, point: 'Point3') -> 'Line3'`
+### *method* `cal_perpendicular(self, point: Point3) -> Line3`
 
 
 计算直线经过指定点p的垂线。
 
-参数:
+**参数**:
 
 - point: 指定点  
 
+**返回**:
+
+- 垂线
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_perpendicular(self, point: 'Point3') -> 'Line3':
@@ -194,19 +227,23 @@ def cal_perpendicular(self, point: 'Point3') -> 'Line3':
 ```
 </details>
 
-### *def* `get_point(self, t: RealNumber) -> 'Point3'`
+### *method* `get_point(self, t: RealNumber) -> Point3`
 
 
 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
 
-参数:
+**参数**:
 
 - t: 参数t  
 
+**返回**:
+
+- 点
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def get_point(self, t: RealNumber) -> 'Point3':
@@ -221,19 +258,19 @@ def get_point(self, t: RealNumber) -> 'Point3':
 ```
 </details>
 
-### *def* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
+### *method* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
 
 
 获取直线的参数方程。
 
-返回:
+**返回**:
 
 - x(t), y(t), z(t)
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
@@ -246,21 +283,25 @@ def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc,
 ```
 </details>
 
-### *def* `is_approx_parallel(self, other: 'Line3', epsilon: float = 1e-06) -> bool`
+### *method* `is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool`
 
 
 判断两条直线是否近似平行。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
 - epsilon: 误差  
 
+**返回**:
+
+- 是否近似平行
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
@@ -276,19 +317,23 @@ def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
 ```
 </details>
 
-### *def* `is_parallel(self, other: 'Line3') -> bool`
+### *method* `is_parallel(self, other: Line3) -> bool`
 
 
 判断两条直线是否平行。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 是否平行
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_parallel(self, other: 'Line3') -> bool:
@@ -303,19 +348,23 @@ def is_parallel(self, other: 'Line3') -> bool:
 ```
 </details>
 
-### *def* `is_collinear(self, other: 'Line3') -> bool`
+### *method* `is_collinear(self, other: Line3) -> bool`
 
 
 判断两条直线是否共线。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 是否共线
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_collinear(self, other: 'Line3') -> bool:
@@ -330,19 +379,23 @@ def is_collinear(self, other: 'Line3') -> bool:
 ```
 </details>
 
-### *def* `is_point_on(self, point: 'Point3') -> bool`
+### *method* `is_point_on(self, point: Point3) -> bool`
 
 
 判断点是否在直线上。
 
-参数:
+**参数**:
 
 - point: 点  
 
+**返回**:
+
+- 是否在直线上
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_point_on(self, point: 'Point3') -> bool:
@@ -357,20 +410,24 @@ def is_point_on(self, point: 'Point3') -> bool:
 ```
 </details>
 
-### *def* `is_coplanar(self, other: 'Line3') -> bool`
+### *method* `is_coplanar(self, other: Line3) -> bool`
 
 
 判断两条直线是否共面。
 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 是否共面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_coplanar(self, other: 'Line3') -> bool:
@@ -386,7 +443,7 @@ def is_coplanar(self, other: 'Line3') -> bool:
 ```
 </details>
 
-### *def* `simplify(self)`
+### *method* `simplify(self)`
 
 
 简化直线方程，等价相等。
@@ -397,7 +454,7 @@ def is_coplanar(self, other: 'Line3') -> bool:
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def simplify(self):
@@ -418,21 +475,25 @@ def simplify(self):
 </details>
 
 ### `@classmethod`
-### *def* `from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3'`
+### *method* `from_two_points(cls, p1: Point3, p2: Point3) -> Line3`
 
 
 工厂函数 由两点构造直线。
 
-参数:
+**参数**:
 
 - p1: 点1  
 
 - p2: 点2  
 
+**返回**:
+
+- 直线
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @classmethod
@@ -450,19 +511,23 @@ def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
 ```
 </details>
 
-### *def* `__and__(self, other: 'Line3') -> 'Line3 | Point3 | None'`
+### *method* `__and__(self, other: Line3) -> Line3 | Point3 | None`
 
 
 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
 
-参数:
+**参数**:
 
 - other: 另一条直线  
 
+**返回**:
+
+- 交点
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
@@ -482,21 +547,21 @@ def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
 ```
 </details>
 
-### *def* `__eq__(self, other) -> bool`
+### *method* `__eq__(self, other) -> bool`
 
 
 判断两条直线是否等价。
 
 v1 // v2 ∧ (p1 - p2) // v1
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other) -> bool:
@@ -514,43 +579,3 @@ def __eq__(self, other) -> bool:
 ```
 </details>
 
-### *def* `__str__(self)`
-
-
-
-
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    """
-        返回点向式（x-x0）
-        Returns:
-
-        """
-    s = 'Line3: '
-    if self.direction.x != 0:
-        s += f'(x{sign_format(-self.point.x)})/{self.direction.x}'
-    if self.direction.y != 0:
-        s += f' = (y{sign_format(-self.point.y)})/{self.direction.y}'
-    if self.direction.z != 0:
-        s += f' = (z{sign_format(-self.point.z)})/{self.direction.z}'
-    return s
-```
-</details>
-
-### *def* `__repr__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __repr__(self):
-    return f'Line3({self.point}, {self.direction})'
-```
-</details>
-

docs/api/mp_math/mp_math_typing.md

@@ -1,37 +1,63 @@
 ---
 title: mbcp.mp_math.mp_math_typing
 ---
-### ***var*** `RealNumber: TypeAlias = int | float`
+### ***var*** `RealNumber = int | float`
 
-### ***var*** `Number: TypeAlias = RealNumber | complex`
+- **类型**: `TypeAlias`
 
-### ***var*** `SingleVar = TypeVar('SingleVar', bound=Number)`
+### ***var*** `Number = RealNumber | complex`
 
-### ***var*** `ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number])`
+- **类型**: `TypeAlias`
 
-### ***var*** `Var: TypeAlias = SingleVar | ArrayVar`
+### ***var*** `Var = SingleVar | ArrayVar`
 
-### ***var*** `OneSingleVarFunc: TypeAlias = Callable[[SingleVar], SingleVar]`
+- **类型**: `TypeAlias`
 
-### ***var*** `OneArrayFunc: TypeAlias = Callable[[ArrayVar], ArrayVar]`
+### ***var*** `OneSingleVarFunc = Callable[[SingleVar], SingleVar]`
 
-### ***var*** `OneVarFunc: TypeAlias = OneSingleVarFunc | OneArrayFunc`
+- **类型**: `TypeAlias`
 
-### ***var*** `TwoSingleVarsFunc: TypeAlias = Callable[[SingleVar, SingleVar], SingleVar]`
+### ***var*** `OneArrayFunc = Callable[[ArrayVar], ArrayVar]`
 
-### ***var*** `TwoArraysFunc: TypeAlias = Callable[[ArrayVar, ArrayVar], ArrayVar]`
+- **类型**: `TypeAlias`
 
-### ***var*** `TwoVarsFunc: TypeAlias = TwoSingleVarsFunc | TwoArraysFunc`
+### ***var*** `OneVarFunc = OneSingleVarFunc | OneArrayFunc`
 
-### ***var*** `ThreeSingleVarsFunc: TypeAlias = Callable[[SingleVar, SingleVar, SingleVar], SingleVar]`
+- **类型**: `TypeAlias`
 
-### ***var*** `ThreeArraysFunc: TypeAlias = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]`
+### ***var*** `TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar]`
 
-### ***var*** `ThreeVarsFunc: TypeAlias = ThreeSingleVarsFunc | ThreeArraysFunc`
+- **类型**: `TypeAlias`
 
-### ***var*** `MultiSingleVarsFunc: TypeAlias = Callable[..., SingleVar]`
+### ***var*** `TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar]`
 
-### ***var*** `MultiArraysFunc: TypeAlias = Callable[..., ArrayVar]`
+- **类型**: `TypeAlias`
 
-### ***var*** `MultiVarsFunc: TypeAlias = MultiSingleVarsFunc | MultiArraysFunc`
+### ***var*** `TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar]`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `MultiSingleVarsFunc = Callable[..., SingleVar]`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `MultiArraysFunc = Callable[..., ArrayVar]`
+
+- **类型**: `TypeAlias`
+
+### ***var*** `MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc`
+
+- **类型**: `TypeAlias`
 

docs/api/mp_math/plane.md

@@ -1,37 +1,36 @@
 ---
 title: mbcp.mp_math.plane
 ---
-### ***class*** `Plane3`
+### **class** `Plane3`
-
+### *method* `__init__(self, a: float, b: float, c: float, d: float)`
-### *def* `__init__(self, a: float, b: float, c: float, d: float)`
 
 
 平面方程：ax + by + cz + d = 0
 
-参数:
+**参数**:
 
-- a:   
+- a: x系数  
 
-- b:   
+- b: y系数  
 
-- c:   
+- c: z系数  
 
-- d:   
+- d: 常数项  
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
-            a:
+            a: x系数
-            b:
+            b: y系数
-            c:
+            c: z系数
-            d:
+            d: 常数项
         """
     self.a = a
     self.b = b
@@ -40,31 +39,33 @@ def __init__(self, a: float, b: float, c: float, d: float):
 ```
 </details>
 
-### *def* `approx(self, other: 'Plane3') -> bool`
+### *method* `approx(self, other: Plane3) -> bool`
 
 
 判断两个平面是否近似相等。
 
-参数:
+**参数**:
 
-- other:   
+- other: 另一个平面  
+
+**返回**:
+
+- 是否近似相等
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
-            other:
+            other: 另一个平面
-
         Returns:
             是否近似相等
         """
-    a = 3
     if self.a != 0:
         k = other.a / self.a
         return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
@@ -79,19 +80,27 @@ def approx(self, other: 'Plane3') -> bool:
 ```
 </details>
 
-### *def* `cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle'`
+### *method* `cal_angle(self, other: Line3 | Plane3) -> AnyAngle`
 
 
 计算平面与平面之间的夹角。
 
-参数:
+**参数**:
 
 - other: 另一个平面  
 
+**返回**:
+
+- 夹角弧度
+
+**引发**:
+
+- TypeError  不支持的类型
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
@@ -113,19 +122,27 @@ def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
 ```
 </details>
 
-### *def* `cal_distance(self, other: 'Plane3 | Point3') -> float`
+### *method* `cal_distance(self, other: Plane3 | Point3) -> float`
 
 
 计算平面与平面或点之间的距离。
 
-参数:
+**参数**:
 
 - other: 另一个平面或点  
 
+**返回**:
+
+- 距离
+
+**引发**:
+
+- TypeError  不支持的类型
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_distance(self, other: 'Plane3 | Point3') -> float:
@@ -147,28 +164,32 @@ def cal_distance(self, other: 'Plane3 | Point3') -> float:
 ```
 </details>
 
-### *def* `cal_intersection_line3(self, other: 'Plane3') -> 'Line3'`
+### *method* `cal_intersection_line3(self, other: Plane3) -> Line3`
 
 
-计算两平面的交线。该方法有问题，待修复。
+计算两平面的交线。
 
-参数:
+**参数**:
 
 - other: 另一个平面  
 
+**返回**:
+
+- 两平面的交线
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
-        计算两平面的交线。该方法有问题，待修复。
+        计算两平面的交线。
         Args:
             other: 另一个平面
         Returns:
-            交线
+            两平面的交线
         Raises:
         """
     if self.normal.is_parallel(other.normal):
@@ -191,19 +212,27 @@ def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
 ```
 </details>
 
-### *def* `cal_intersection_point3(self, other: 'Line3') -> 'Point3'`
+### *method* `cal_intersection_point3(self, other: Line3) -> Point3`
 
 
 计算平面与直线的交点。
 
-参数:
+**参数**:
 
 - other: 不与平面平行或在平面上的直线  
 
+**返回**:
+
+- 交点
+
+**引发**:
+
+- ValueError  平面与直线平行或重合
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
@@ -224,19 +253,23 @@ def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
 ```
 </details>
 
-### *def* `cal_parallel_plane3(self, point: 'Point3') -> 'Plane3'`
+### *method* `cal_parallel_plane3(self, point: Point3) -> Plane3`
 
 
 计算平行于该平面且过指定点的平面。
 
-参数:
+**参数**:
 
 - point: 指定点  
 
+**返回**:
+
+- 所求平面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
@@ -245,25 +278,29 @@ def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
         Args:
             point: 指定点
         Returns:
-            平面
+            所求平面
         """
     return Plane3.from_point_and_normal(point, self.normal)
 ```
 </details>
 
-### *def* `is_parallel(self, other: 'Plane3') -> bool`
+### *method* `is_parallel(self, other: Plane3) -> bool`
 
 
 判断两个平面是否平行。
 
-参数:
+**参数**:
 
 - other: 另一个平面  
 
+**返回**:
+
+- 是否平行
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_parallel(self, other: 'Plane3') -> bool:
@@ -279,19 +316,19 @@ def is_parallel(self, other: 'Plane3') -> bool:
 </details>
 
 ### `@property`
-### *def* `normal(self) -> 'Vector3'`
+### *method* `normal(self) -> Vector3`
 
 
 平面的法向量。
 
-返回:
+**返回**:
 
 - 法向量
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -306,21 +343,25 @@ def normal(self) -> 'Vector3':
 </details>
 
 ### `@classmethod`
-### *def* `from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3'`
+### *method* `from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3`
 
 
 工厂函数 由点和法向量构造平面(点法式构造)。
 
-参数:
+**参数**:
 
 - point: 平面上的一点  
 
 - normal: 法向量  
 
+**返回**:
+
+- 平面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @classmethod
@@ -340,12 +381,12 @@ def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
 </details>
 
 ### `@classmethod`
-### *def* `from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3'`
+### *method* `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3`
 
 
 工厂函数 由三点构造平面。
 
-参数:
+**参数**:
 
 - p1: 点1  
 
@@ -353,10 +394,14 @@ def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
 
 - p3: 点3  
 
+**返回**:
+
+- 平面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @classmethod
@@ -378,21 +423,25 @@ def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3'
 </details>
 
 ### `@classmethod`
-### *def* `from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3'`
+### *method* `from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3`
 
 
 工厂函数 由两直线构造平面。
 
-参数:
+**参数**:
 
 - l1: 直线1  
 
 - l2: 直线2  
 
+**返回**:
+
+- 平面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @classmethod
@@ -414,21 +463,25 @@ def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
 </details>
 
 ### `@classmethod`
-### *def* `from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3'`
+### *method* `from_point_and_line(cls, point: Point3, line: Line3) -> Plane3`
 
 
 工厂函数 由点和直线构造平面。
 
-参数:
+**参数**:
 
 - point: 面上一点  
 
 - line: 面上直线，不包含点  
 
+**返回**:
+
+- 平面
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @classmethod
@@ -445,45 +498,12 @@ def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
 ```
 </details>
 
-### *def* `__repr__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __repr__(self):
-    return f'Plane3({self.a}, {self.b}, {self.c}, {self.d})'
-```
-</details>
-
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    s = 'Plane3: '
-    if self.a != 0:
-        s += f'{sign(self.a, only_neg=True)}{abs(self.a)}x'
-    if self.b != 0:
-        s += f' {sign(self.b)} {abs(self.b)}y'
-    if self.c != 0:
-        s += f' {sign(self.c)} {abs(self.c)}z'
-    if self.d != 0:
-        s += f' {sign(self.d)} {abs(self.d)}'
-    return s + ' = 0'
-```
-</details>
-
 ### `@overload`
-### *def* `__and__(self, other: 'Line3') -> 'Point3 | None'`
+### *method* `__and__(self, other: Line3) -> Point3 | None`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -493,11 +513,11 @@ def __and__(self, other: 'Line3') -> 'Point3 | None':
 </details>
 
 ### `@overload`
-### *def* `__and__(self, other: 'Plane3') -> 'Line3 | None'`
+### *method* `__and__(self, other: Plane3) -> Line3 | None`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -506,19 +526,23 @@ def __and__(self, other: 'Plane3') -> 'Line3 | None':
 ```
 </details>
 
-### *def* `__and__(self, other)`
+### *method* `__and__(self, other)`
 
 
 取两平面的交集（人话：交线）
 
-参数:
+**参数**:
 
 - other:   
 
+**返回**:
+
+- 不平行平面的交线，平面平行返回None
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __and__(self, other):
@@ -542,11 +566,11 @@ def __and__(self, other):
 ```
 </details>
 
-### *def* `__eq__(self, other) -> bool`
+### *method* `__eq__(self, other) -> bool`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other) -> bool:
@@ -554,11 +578,11 @@ def __eq__(self, other) -> bool:
 ```
 </details>
 
-### *def* `__rand__(self, other: 'Line3') -> 'Point3'`
+### *method* `__rand__(self, other: Line3) -> Point3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __rand__(self, other: 'Line3') -> 'Point3':
@@ -566,23 +590,3 @@ def __rand__(self, other: 'Line3') -> 'Point3':
 ```
 </details>
 
-### ***var*** `k = other.a / self.a`
-
-### ***var*** `A = np.array([[self.b, self.c], [other.b, other.c]])`
-
-### ***var*** `B = np.array([-self.d, -other.d])`
-
-### ***var*** `v2 = l2.get_point(1) - l1.point`
-
-### ***var*** `k = other.b / self.b`
-
-### ***var*** `A = np.array([[self.a, self.c], [other.a, other.c]])`
-
-### ***var*** `B = np.array([-self.d, -other.d])`
-
-### ***var*** `k = other.c / self.c`
-
-### ***var*** `A = np.array([[self.a, self.b], [other.a, other.b]])`
-
-### ***var*** `B = np.array([-self.d, -other.d])`
-

docs/api/mp_math/point.md

@@ -1,14 +1,13 @@
 ---
 title: mbcp.mp_math.point
 ---
-### ***class*** `Point3`
+### **class** `Point3`
-
+### *method* `__init__(self, x: float, y: float, z: float)`
-### *def* `__init__(self, x: float, y: float, z: float)`
 
 
 笛卡尔坐标系中的点。
 
-参数:
+**参数**:
 
 - x: x 坐标  
 
@@ -19,7 +18,7 @@ title: mbcp.mp_math.point
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, x: float, y: float, z: float):
@@ -36,21 +35,25 @@ def __init__(self, x: float, y: float, z: float):
 ```
 </details>
 
-### *def* `approx(self, other: 'Point3', epsilon: float = APPROX) -> bool`
+### *method* `approx(self, other: Point3, epsilon: float = APPROX) -> bool`
 
 
 判断两个点是否近似相等。
 
-参数:
+**参数**:
 
 - other:   
 
 - epsilon:   
 
+**返回**:
+
+- 是否近似相等
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
@@ -67,24 +70,12 @@ def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
 ```
 </details>
 
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    return f'Point3({self.x}, {self.y}, {self.z})'
-```
-</details>
-
 ### `@overload`
-### *def* `__add__(self, other: 'Vector3') -> 'Point3'`
+### *method* `self + other: Vector3 => Point3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -94,11 +85,11 @@ def __add__(self, other: 'Vector3') -> 'Point3':
 </details>
 
 ### `@overload`
-### *def* `__add__(self, other: 'Point3') -> 'Point3'`
+### *method* `self + other: Point3 => Point3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -107,20 +98,20 @@ def __add__(self, other: 'Point3') -> 'Point3':
 ```
 </details>
 
-### *def* `__add__(self, other)`
+### *method* `self + other`
 
 
 P + V -> P
 P + P -> P
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __add__(self, other):
@@ -135,19 +126,19 @@ def __add__(self, other):
 ```
 </details>
 
-### *def* `__eq__(self, other)`
+### *method* `__eq__(self, other)`
 
 
 判断两个点是否相等。
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other):
@@ -161,21 +152,21 @@ def __eq__(self, other):
 ```
 </details>
 
-### *def* `__sub__(self, other: 'Point3') -> 'Vector3'`
+### *method* `self - other: Point3 => Vector3`
 
 
 P - P -> V
 
 P - V -> P  已在 :class:`Vector3` 中实现
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __sub__(self, other: 'Point3') -> 'Vector3':

docs/api/mp_math/segment.md

@@ -1,9 +1,8 @@
 ---
 title: mbcp.mp_math.segment
 ---
-### ***class*** `Segment3`
+### **class** `Segment3`
-
+### *method* `__init__(self, p1: Point3, p2: Point3)`
-### *def* `__init__(self, p1: 'Point3', p2: 'Point3')`
 
 
 三维空间中的线段。
@@ -13,7 +12,7 @@ title: mbcp.mp_math.segment
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, p1: 'Point3', p2: 'Point3'):
@@ -33,27 +32,3 @@ def __init__(self, p1: 'Point3', p2: 'Point3'):
 ```
 </details>
 
-### *def* `__repr__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __repr__(self):
-    return f'Segment3({self.p1}, {self.p2})'
-```
-</details>
-
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    return f'Segment3({self.p1} -> {self.p2})'
-```
-</details>
-

docs/api/mp_math/utils.md

@@ -1,32 +1,36 @@
 ---
 title: mbcp.mp_math.utils
 ---
-### *def* `clamp() -> float`
+### *func* `clamp() -> float`
 
 
-区间截断函数。
+区间限定函数
 
-参数:
+**参数**:
 
-- x:   
+- x: 待限定的值  
 
-- min_:   
+- min_: 最小值  
 
-- max_:   
+- max_: 最大值  
+
+**返回**:
+
+- 限制后的值
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def clamp(x: float, min_: float, max_: float) -> float:
     """
-    区间截断函数。
+    区间限定函数
     Args:
-        x:
+        x: 待限定的值
-        min_:
+        min_: 最小值
-        max_:
+        max_: 最大值
 
     Returns:
         限制后的值
@@ -35,33 +39,36 @@ def clamp(x: float, min_: float, max_: float) -> float:
 ```
 </details>
 
-### *def* `approx(x: float = 0.0, y: float = APPROX) -> bool`
+### *func* `approx(x: float = 0.0, y: float = APPROX) -> bool`
 
 
 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
 
-参数:
+**参数**:
 
-- x:   
+- x: 数1  
 
-- y:   
+- y: 数2  
 
-- epsilon:   
+- epsilon: 误差  
+
+**返回**:
+
+- 是否近似相等
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
-        x:
+        x: 数1
-        y:
+        y: 数2
-        epsilon:
+        epsilon: 误差
-
     Returns:
         是否近似相等
     """
@@ -69,21 +76,25 @@ def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
 ```
 </details>
 
-### *def* `sign(x: float = False) -> str`
+### *func* `sign(x: float = False) -> str`
 
 
 获取数的符号。
 
-参数:
+**参数**:
 
 - x: 数  
 
 - only_neg: 是否只返回负数的符号  
 
+**返回**:
+
+- 符号 + - ""
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def sign(x: float, only_neg: bool=False) -> str:
@@ -103,7 +114,7 @@ def sign(x: float, only_neg: bool=False) -> str:
 ```
 </details>
 
-### *def* `sign_format(x: float = False) -> str`
+### *func* `sign_format(x: float = False) -> str`
 
 
 格式化符号数
@@ -111,16 +122,20 @@ def sign(x: float, only_neg: bool=False) -> str:
 1 -> +1
 0 -> ""
 
-参数:
+**参数**:
 
 - x: 数  
 
 - only_neg: 是否只返回负数的符号  
 
+**返回**:
+
+- 符号 + - ""
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def sign_format(x: float, only_neg: bool=False) -> str:
@@ -143,13 +158,12 @@ def sign_format(x: float, only_neg: bool=False) -> str:
 ```
 </details>
 
-### ***class*** `Approx`
+### **class** `Approx`
-
+### *method* `__init__(self, value: RealNumber)`
-### *def* `__init__(self, value: RealNumber)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, value: RealNumber):
@@ -157,11 +171,11 @@ def __init__(self, value: RealNumber):
 ```
 </details>
 
-### *def* `__eq__(self, other)`
+### *method* `__eq__(self, other)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other):
@@ -178,11 +192,11 @@ def __eq__(self, other):
 ```
 </details>
 
-### *def* `raise_type_error(self, other)`
+### *method* `raise_type_error(self, other)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def raise_type_error(self, other):
@@ -190,11 +204,11 @@ def raise_type_error(self, other):
 ```
 </details>
 
-### *def* `__ne__(self, other)`
+### *method* `__ne__(self, other)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __ne__(self, other):

docs/api/mp_math/vector.md

@@ -1,14 +1,13 @@
 ---
 title: mbcp.mp_math.vector
 ---
-### ***class*** `Vector3`
+### **class** `Vector3`
-
+### *method* `__init__(self, x: float, y: float, z: float)`
-### *def* `__init__(self, x: float, y: float, z: float)`
 
 
 3维向量
 
-参数:
+**参数**:
 
 - x: x轴分量  
 
@@ -19,7 +18,7 @@ title: mbcp.mp_math.vector
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __init__(self, x: float, y: float, z: float):
@@ -36,21 +35,25 @@ def __init__(self, x: float, y: float, z: float):
 ```
 </details>
 
-### *def* `approx(self, other: 'Vector3', epsilon: float = APPROX) -> bool`
+### *method* `approx(self, other: Vector3, epsilon: float = APPROX) -> bool`
 
 
 判断两个向量是否近似相等。
 
-参数:
+**参数**:
 
 - other:   
 
 - epsilon:   
 
+**返回**:
+
+- 是否近似相等
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
@@ -67,19 +70,23 @@ def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
 ```
 </details>
 
-### *def* `cal_angle(self, other: 'Vector3') -> 'AnyAngle'`
+### *method* `cal_angle(self, other: Vector3) -> AnyAngle`
 
 
 计算两个向量之间的夹角。
 
-参数:
+**参数**:
 
 - other: 另一个向量  
 
+**返回**:
+
+- 夹角
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
@@ -94,7 +101,7 @@ def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
 ```
 </details>
 
-### *def* `cross(self, other: 'Vector3') -> 'Vector3'`
+### *method* `cross(self, other: Vector3) -> Vector3`
 
 
 向量积 叉乘：v1 cross v2 -> v3
@@ -103,10 +110,18 @@ def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
 其余结果的模为平行四边形的面积。
 
 
+**参数**:
+
+- other:   
+
+**返回**:
+
+- 行列式的结果
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def cross(self, other: 'Vector3') -> 'Vector3':
@@ -133,21 +148,25 @@ def cross(self, other: 'Vector3') -> 'Vector3':
 ```
 </details>
 
-### *def* `is_approx_parallel(self, other: 'Vector3', epsilon: float = APPROX) -> bool`
+### *method* `is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool`
 
 
 判断两个向量是否近似平行。
 
-参数:
+**参数**:
 
 - other: 另一个向量  
 
 - epsilon: 允许的误差  
 
+**返回**:
+
+- 是否近似平行
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
@@ -163,19 +182,23 @@ def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
 ```
 </details>
 
-### *def* `is_parallel(self, other: 'Vector3') -> bool`
+### *method* `is_parallel(self, other: Vector3) -> bool`
 
 
 判断两个向量是否平行。
 
-参数:
+**参数**:
 
 - other: 另一个向量  
 
+**返回**:
+
+- 是否平行
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def is_parallel(self, other: 'Vector3') -> bool:
@@ -190,7 +213,7 @@ def is_parallel(self, other: 'Vector3') -> bool:
 ```
 </details>
 
-### *def* `normalize(self)`
+### *method* `normalize(self)`
 
 
 将向量归一化。
@@ -200,7 +223,7 @@ def is_parallel(self, other: 'Vector3') -> bool:
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def normalize(self):
@@ -217,7 +240,7 @@ def normalize(self):
 </details>
 
 ### `@property`
-### *def* `np_array(self) -> 'np.ndarray'`
+### *method* `np_array(self) -> np.ndarray`
 
 
 
@@ -225,7 +248,7 @@ def normalize(self):
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -239,19 +262,19 @@ def np_array(self) -> 'np.ndarray':
 </details>
 
 ### `@property`
-### *def* `length(self) -> float`
+### *method* `length(self) -> float`
 
 
 向量的模。
 
-返回:
+**返回**:
 
 - 模
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -266,19 +289,19 @@ def length(self) -> float:
 </details>
 
 ### `@property`
-### *def* `unit(self) -> 'Vector3'`
+### *method* `unit(self) -> Vector3`
 
 
 获取该向量的单位向量。
 
-返回:
+**返回**:
 
 - 单位向量
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @property
@@ -292,11 +315,11 @@ def unit(self) -> 'Vector3':
 ```
 </details>
 
-### *def* `__abs__(self)`
+### *method* `__abs__(self)`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __abs__(self):
@@ -305,11 +328,11 @@ def __abs__(self):
 </details>
 
 ### `@overload`
-### *def* `__add__(self, other: 'Vector3') -> 'Vector3'`
+### *method* `self + other: Vector3 => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -319,11 +342,11 @@ def __add__(self, other: 'Vector3') -> 'Vector3':
 </details>
 
 ### `@overload`
-### *def* `__add__(self, other: 'Point3') -> 'Point3'`
+### *method* `self + other: Point3 => Point3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -332,21 +355,21 @@ def __add__(self, other: 'Point3') -> 'Point3':
 ```
 </details>
 
-### *def* `__add__(self, other)`
+### *method* `self + other`
 
 
 V + P -> P
 
 V + V -> V
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __add__(self, other):
@@ -368,19 +391,23 @@ def __add__(self, other):
 ```
 </details>
 
-### *def* `__eq__(self, other)`
+### *method* `__eq__(self, other)`
 
 
 判断两个向量是否相等。
 
-参数:
+**参数**:
 
 - other:   
 
+**返回**:
+
+- 是否相等
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __eq__(self, other):
@@ -395,7 +422,7 @@ def __eq__(self, other):
 ```
 </details>
 
-### *def* `__radd__(self, other: 'Point3') -> 'Point3'`
+### *method* `self + other: Point3 => Point3`
 
 
 P + V -> P
@@ -407,7 +434,7 @@ P + V -> P
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __radd__(self, other: 'Point3') -> 'Point3':
@@ -423,11 +450,11 @@ def __radd__(self, other: 'Point3') -> 'Point3':
 </details>
 
 ### `@overload`
-### *def* `__sub__(self, other: 'Vector3') -> 'Vector3'`
+### *method* `self - other: Vector3 => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -437,11 +464,11 @@ def __sub__(self, other: 'Vector3') -> 'Vector3':
 </details>
 
 ### `@overload`
-### *def* `__sub__(self, other: 'Point3') -> 'Point3'`
+### *method* `self - other: Point3 => Point3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -450,21 +477,21 @@ def __sub__(self, other: 'Point3') -> 'Point3':
 ```
 </details>
 
-### *def* `__sub__(self, other)`
+### *method* `self - other`
 
 
 V - P -> P
 
 V - V -> V
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __sub__(self, other):
@@ -485,19 +512,19 @@ def __sub__(self, other):
 ```
 </details>
 
-### *def* `__rsub__(self, other: 'Point3')`
+### *method* `self - other: Point3`
 
 
 P - V -> P
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __rsub__(self, other: 'Point3'):
@@ -516,11 +543,11 @@ def __rsub__(self, other: 'Point3'):
 </details>
 
 ### `@overload`
-### *def* `__mul__(self, other: 'Vector3') -> 'Vector3'`
+### *method* `self * other: Vector3 => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -530,11 +557,11 @@ def __mul__(self, other: 'Vector3') -> 'Vector3':
 </details>
 
 ### `@overload`
-### *def* `__mul__(self, other: RealNumber) -> 'Vector3'`
+### *method* `self * other: RealNumber => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @overload
@@ -543,19 +570,19 @@ def __mul__(self, other: RealNumber) -> 'Vector3':
 ```
 </details>
 
-### *def* `__mul__(self, other: 'int | float | Vector3') -> 'Vector3'`
+### *method* `self * other: int | float | Vector3 => Vector3`
 
 
 数组运算 非点乘。点乘使用@，叉乘使用cross。
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
@@ -575,11 +602,11 @@ def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
 ```
 </details>
 
-### *def* `__rmul__(self, other: 'RealNumber') -> 'Vector3'`
+### *method* `self * other: RealNumber => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __rmul__(self, other: 'RealNumber') -> 'Vector3':
@@ -587,19 +614,19 @@ def __rmul__(self, other: 'RealNumber') -> 'Vector3':
 ```
 </details>
 
-### *def* `__matmul__(self, other: 'Vector3') -> 'RealNumber'`
+### *method* `self @ other: Vector3 => RealNumber`
 
 
 点乘。
 
-参数:
+**参数**:
 
 - other:   
 
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __matmul__(self, other: 'Vector3') -> 'RealNumber':
@@ -613,11 +640,11 @@ def __matmul__(self, other: 'Vector3') -> 'RealNumber':
 ```
 </details>
 
-### *def* `__truediv__(self, other: RealNumber) -> 'Vector3'`
+### *method* `self / other: RealNumber => Vector3`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __truediv__(self, other: RealNumber) -> 'Vector3':
@@ -625,11 +652,11 @@ def __truediv__(self, other: RealNumber) -> 'Vector3':
 ```
 </details>
 
-### *def* `__neg__(self)`
+### *method* `- self`
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 def __neg__(self):
@@ -637,35 +664,27 @@ def __neg__(self):
 ```
 </details>
 
-### *def* `__repr__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __repr__(self):
-    return f'Vector3({self.x}, {self.y}, {self.z})'
-```
-</details>
-
-### *def* `__str__(self)`
-
-
-<details>
-<summary>源码</summary>
-
-```python
-def __str__(self):
-    return f'Vector3({self.x}, {self.y}, {self.z})'
-```
-</details>
-
 ### ***var*** `zero_vector3 = Vector3(0, 0, 0)`
 
+- **类型**: `Vector3`
+
+- **说明**: 零向量
+
 ### ***var*** `x_axis = Vector3(1, 0, 0)`
 
+- **类型**: `Vector3`
+
+- **说明**: x轴单位向量
+
 ### ***var*** `y_axis = Vector3(0, 1, 0)`
 
+- **类型**: `Vector3`
+
+- **说明**: y轴单位向量
+
 ### ***var*** `z_axis = Vector3(0, 0, 1)`
 
+- **类型**: `Vector3`
+
+- **说明**: z轴单位向量
+

docs/api/presets/model/index.md

@@ -1,24 +1,27 @@
 ---
 title: mbcp.presets.model
 ---
-### ***class*** `GeometricModels`
+### **class** `GeometricModels`
-
 ### `@staticmethod`
-### *def* `sphere(radius: float, density: float)`
+### *method* `sphere(radius: float, density: float)`
 
 
 生成球体上的点集。
 
-参数:
+**参数**:
 
 - radius:   
 
 - density:   
 
+**返回**:
+
+- List[Point3]: 球体上的点集。
+
 
 
 <details>
-<summary>源码</summary>
+<summary> <i>源代码</i> </summary>
 
 ```python
 @staticmethod

docs/en/api/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp
+---

docs/en/api/mp_math/angle.md

@@ -0,0 +1,423 @@
+---
+title: mbcp.mp_math.angle
+---
+### **class** `Angle`
+### **class** `AnyAngle(Angle)`
+### *method* `__init__(self, value: float, is_radian: bool = False)`
+
+
+任意角度。
+
+**Arguments**:
+
+- value: 角度或弧度值  
+
+- is_radian: 是否为弧度，默认为否  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, value: float, is_radian: bool=False):
+    """
+        任意角度。
+        Args:
+            value: 角度或弧度值
+            is_radian: 是否为弧度，默认为否
+        """
+    if is_radian:
+        self.radian = value
+    else:
+        self.radian = value * PI / 180
+```
+</details>
+
+### `@property`
+### *method* `complementary(self) -> AnyAngle`
+
+
+余角：两角的和为90°。
+
+**Return**:
+
+- 余角
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def complementary(self) -> 'AnyAngle':
+    """
+        余角：两角的和为90°。
+        Returns:
+            余角
+        """
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `supplementary(self) -> AnyAngle`
+
+
+补角：两角的和为180°。
+
+**Return**:
+
+- 补角
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def supplementary(self) -> 'AnyAngle':
+    """
+        补角：两角的和为180°。
+        Returns:
+            补角
+        """
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `degree(self) -> float`
+
+
+角度。
+
+**Return**:
+
+- 弧度
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def degree(self) -> float:
+    """
+        角度。
+        Returns:
+            弧度
+        """
+    return self.radian * 180 / PI
+```
+</details>
+
+### `@property`
+### *method* `minimum_positive(self) -> AnyAngle`
+
+
+最小正角。
+
+**Return**:
+
+- 最小正角度
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def minimum_positive(self) -> 'AnyAngle':
+    """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+    return AnyAngle(self.radian % (2 * PI))
+```
+</details>
+
+### `@property`
+### *method* `maximum_negative(self) -> AnyAngle`
+
+
+最大负角。
+
+**Return**:
+
+- 最大负角度
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def maximum_negative(self) -> 'AnyAngle':
+    """
+        最大负角。
+        Returns:
+            最大负角度
+        """
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `sin(self) -> float`
+
+
+正弦值。
+
+**Return**:
+
+- 正弦值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def sin(self) -> float:
+    """
+        正弦值。
+        Returns:
+            正弦值
+        """
+    return math.sin(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cos(self) -> float`
+
+
+余弦值。
+
+**Return**:
+
+- 余弦值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def cos(self) -> float:
+    """
+        余弦值。
+        Returns:
+            余弦值
+        """
+    return math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `tan(self) -> float`
+
+
+正切值。
+
+**Return**:
+
+- 正切值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def tan(self) -> float:
+    """
+        正切值。
+        Returns:
+            正切值
+        """
+    return math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cot(self) -> float`
+
+
+余切值。
+
+**Return**:
+
+- 余切值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def cot(self) -> float:
+    """
+        余切值。
+        Returns:
+            余切值
+        """
+    return 1 / math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `sec(self) -> float`
+
+
+正割值。
+
+**Return**:
+
+- 正割值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def sec(self) -> float:
+    """
+        正割值。
+        Returns:
+            正割值
+        """
+    return 1 / math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `csc(self) -> float`
+
+
+余割值。
+
+**Return**:
+
+- 余割值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def csc(self) -> float:
+    """
+        余割值。
+        Returns:
+            余割值
+        """
+    return 1 / math.sin(self.radian)
+```
+</details>
+
+### *method* `self + other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other):
+    return approx(self.radian, other.radian)
+```
+</details>
+
+### *method* `self - other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
+```
+</details>
+
+### *method* `self * other: float => AnyAngle`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
+```
+</details>
+
+### `@overload`
+### *method* `self / other: float => AnyAngle`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: float) -> 'AnyAngle':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self / other: AnyAngle => float`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: 'AnyAngle') -> float:
+    ...
+```
+</details>
+
+### *method* `self / other`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __truediv__(self, other):
+    if isinstance(other, AnyAngle):
+        return self.radian / other.radian
+    return AnyAngle(self.radian / other, is_radian=True)
+```
+</details>
+

docs/en/api/mp_math/const.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math.const
+---

docs/en/api/mp_math/equation.md

@@ -0,0 +1,162 @@
+---
+title: mbcp.mp_math.equation
+---
+### *func* `get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc`
+
+
+求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+
+**Arguments**:
+
+- func: 函数  
+
+- var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)  
+
+- epsilon: 偏移量  
+
+**Return**:
+
+- 偏导函数
+
+**Raises**:
+
+- ValueError  无效变量类型
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    """
+    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    Args:
+        func: 函数
+        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
+        epsilon: 偏移量
+    Returns:
+        偏导函数
+    Raises:
+        ValueError: 无效变量类型
+    """
+    if isinstance(var, int):
+
+        def partial_derivative_func(*args: Var) -> Var:
+            args_list_plus = list(args)
+            args_list_plus[var] += epsilon
+            args_list_minus = list(args)
+            args_list_minus[var] -= epsilon
+            return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+        return partial_derivative_func
+    elif isinstance(var, tuple):
+
+        def high_order_partial_derivative_func(*args: Var) -> Var:
+            result_func = func
+            for v in var:
+                result_func = get_partial_derivative_func(result_func, v, epsilon)
+            return result_func(*args)
+        return high_order_partial_derivative_func
+    else:
+        raise ValueError('Invalid var type')
+```
+</details>
+
+### *func* `partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def partial_derivative_func(*args: Var) -> Var:
+    args_list_plus = list(args)
+    args_list_plus[var] += epsilon
+    args_list_minus = list(args)
+    args_list_minus[var] -= epsilon
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+```
+</details>
+
+### *func* `high_order_partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def high_order_partial_derivative_func(*args: Var) -> Var:
+    result_func = func
+    for v in var:
+        result_func = get_partial_derivative_func(result_func, v, epsilon)
+    return result_func(*args)
+```
+</details>
+
+### **class** `CurveEquation`
+### *method* `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`
+
+
+曲线方程。
+
+**Arguments**:
+
+- x_func: x函数  
+
+- y_func: y函数  
+
+- z_func: z函数  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    """
+        曲线方程。
+        Args:
+            x_func: x函数
+            y_func: y函数
+            z_func: z函数
+        """
+    self.x_func = x_func
+    self.y_func = y_func
+    self.z_func = z_func
+```
+</details>
+
+### *method* `__call__(self) -> Point3 | tuple[Point3, ...]`
+
+
+计算曲线上的点。
+
+**Arguments**:
+
+- *t:   
+
+- 参数:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    """
+        计算曲线上的点。
+        Args:
+            *t:
+                参数
+        Returns:
+
+        """
+    if len(t) == 1:
+        return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
+    else:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
+```
+</details>
+

docs/en/api/mp_math/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math
+---

docs/en/api/mp_math/line.md

@@ -0,0 +1,581 @@
+---
+title: mbcp.mp_math.line
+---
+### **class** `Line3`
+### *method* `__init__(self, point: Point3, direction: Vector3)`
+
+
+三维空间中的直线。由一个点和一个方向向量确定。
+
+**Arguments**:
+
+- point: 直线上的一点  
+
+- direction: 直线的方向向量  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, point: 'Point3', direction: 'Vector3'):
+    """
+        三维空间中的直线。由一个点和一个方向向量确定。
+        Args:
+            point: 直线上的一点
+            direction: 直线的方向向量
+        """
+    self.point = point
+    self.direction = direction
+```
+</details>
+
+### *method* `approx(self, other: Line3, epsilon: float = APPROX) -> bool`
+
+
+判断两条直线是否近似相等。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**Return**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    """
+        判断两条直线是否近似相等。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似相等
+        """
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3) -> AnyAngle`
+
+
+计算直线和直线之间的夹角。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 夹角弧度
+
+**Raises**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    """
+        计算直线和直线之间的夹角。
+        Args:
+            other: 另一条直线
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    return self.direction.cal_angle(other.direction)
+```
+</details>
+
+### *method* `cal_distance(self, other: Line3 | Point3) -> float`
+
+
+计算直线和直线或点之间的距离。
+
+**Arguments**:
+
+- other: 平行直线或点  
+
+**Return**:
+
+- 距离
+
+**Raises**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_distance(self, other: 'Line3 | Point3') -> float:
+    """
+        计算直线和直线或点之间的距离。
+        Args:
+            other: 平行直线或点
+
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    elif isinstance(other, Point3):
+        return (other - self.point).cross(self.direction).length / self.direction.length
+    else:
+        raise TypeError('Unsupported type.')
+```
+</details>
+
+### *method* `cal_intersection(self, other: Line3) -> Point3`
+
+
+计算两条直线的交点。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 交点
+
+**Raises**:
+
+- ValueError  直线平行
+
+- ValueError  直线不共面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_intersection(self, other: 'Line3') -> 'Point3':
+    """
+        计算两条直线的交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 直线平行
+            ValueError: 直线不共面
+        """
+    if self.is_parallel(other):
+        raise ValueError('Lines are parallel and do not intersect.')
+    if not self.is_coplanar(other):
+        raise ValueError('Lines are not coplanar and do not intersect.')
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
+```
+</details>
+
+### *method* `cal_perpendicular(self, point: Point3) -> Line3`
+
+
+计算直线经过指定点p的垂线。
+
+**Arguments**:
+
+- point: 指定点  
+
+**Return**:
+
+- 垂线
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    """
+        计算直线经过指定点p的垂线。
+        Args:
+            point: 指定点
+        Returns:
+            垂线
+        """
+    return Line3(point, self.direction.cross(point - self.point))
+```
+</details>
+
+### *method* `get_point(self, t: RealNumber) -> Point3`
+
+
+获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+
+**Arguments**:
+
+- t: 参数t  
+
+**Return**:
+
+- 点
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def get_point(self, t: RealNumber) -> 'Point3':
+    """
+        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+        Args:
+            t: 参数t
+        Returns:
+            点
+        """
+    return self.point + t * self.direction
+```
+</details>
+
+### *method* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
+
+
+获取直线的参数方程。
+
+**Return**:
+
+- x(t), y(t), z(t)
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    """
+        获取直线的参数方程。
+        Returns:
+            x(t), y(t), z(t)
+        """
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool`
+
+
+判断两条直线是否近似平行。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**Return**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    """
+        判断两条直线是否近似平行。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似平行
+        """
+    return self.direction.is_approx_parallel(other.direction, epsilon)
+```
+</details>
+
+### *method* `is_parallel(self, other: Line3) -> bool`
+
+
+判断两条直线是否平行。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_parallel(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否平行。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否平行
+        """
+    return self.direction.is_parallel(other.direction)
+```
+</details>
+
+### *method* `is_collinear(self, other: Line3) -> bool`
+
+
+判断两条直线是否共线。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 是否共线
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_collinear(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共线。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共线
+        """
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_point_on(self, point: Point3) -> bool`
+
+
+判断点是否在直线上。
+
+**Arguments**:
+
+- point: 点  
+
+**Return**:
+
+- 是否在直线上
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_point_on(self, point: 'Point3') -> bool:
+    """
+        判断点是否在直线上。
+        Args:
+            point: 点
+        Returns:
+            是否在直线上
+        """
+    return (point - self.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_coplanar(self, other: Line3) -> bool`
+
+
+判断两条直线是否共面。
+充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 是否共面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_coplanar(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共面。
+        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共面
+        """
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
+```
+</details>
+
+### *method* `simplify(self)`
+
+
+简化直线方程，等价相等。
+自体简化，不返回值。
+
+按照可行性一次对x y z 化 0 处理，并对向量单位化
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def simplify(self):
+    """
+        简化直线方程，等价相等。
+        自体简化，不返回值。
+
+        按照可行性一次对x y z 化 0 处理，并对向量单位化
+        """
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    if self.direction.y == 0:
+        self.point.y = 0
+    if self.direction.z == 0:
+        self.point.z = 0
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_points(cls, p1: Point3, p2: Point3) -> Line3`
+
+
+工厂函数 由两点构造直线。
+
+**Arguments**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+**Return**:
+
+- 直线
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    """
+        工厂函数 由两点构造直线。
+        Args:
+            p1: 点1
+            p2: 点2
+        Returns:
+            直线
+        """
+    direction = p2 - p1
+    return cls(p1, direction)
+```
+</details>
+
+### *method* `__and__(self, other: Line3) -> Line3 | Point3 | None`
+
+
+计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+
+**Arguments**:
+
+- other: 另一条直线  
+
+**Return**:
+
+- 交点
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    """
+        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        """
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+判断两条直线是否等价。
+
+v1 // v2 ∧ (p1 - p2) // v1
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    """
+        判断两条直线是否等价。
+
+        v1 // v2 ∧ (p1 - p2) // v1
+        Args:
+            other:
+
+        Returns:
+
+        """
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+

docs/en/api/mp_math/mp_math_typing.md

@@ -0,0 +1,63 @@
+---
+title: mbcp.mp_math.mp_math_typing
+---
+### ***var*** `RealNumber = int | float`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `Number = RealNumber | complex`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `Var = SingleVar | ArrayVar`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `OneSingleVarFunc = Callable[[SingleVar], SingleVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `OneArrayFunc = Callable[[ArrayVar], ArrayVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `OneVarFunc = OneSingleVarFunc | OneArrayFunc`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `MultiSingleVarsFunc = Callable[..., SingleVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `MultiArraysFunc = Callable[..., ArrayVar]`
+
+- **Type**: `TypeAlias`
+
+### ***var*** `MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc`
+
+- **Type**: `TypeAlias`
+

docs/en/api/mp_math/plane.md

@@ -0,0 +1,592 @@
+---
+title: mbcp.mp_math.plane
+---
+### **class** `Plane3`
+### *method* `__init__(self, a: float, b: float, c: float, d: float)`
+
+
+平面方程：ax + by + cz + d = 0
+
+**Arguments**:
+
+- a: x系数  
+
+- b: y系数  
+
+- c: z系数  
+
+- d: 常数项  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a: x系数
+            b: y系数
+            c: z系数
+            d: 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d
+```
+</details>
+
+### *method* `approx(self, other: Plane3) -> bool`
+
+
+判断两个平面是否近似相等。
+
+**Arguments**:
+
+- other: 另一个平面  
+
+**Return**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def approx(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3 | Plane3) -> AnyAngle`
+
+
+计算平面与平面之间的夹角。
+
+**Arguments**:
+
+- other: 另一个平面  
+
+**Return**:
+
+- 夹角弧度
+
+**Raises**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        Args:
+            other: 另一个平面
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_distance(self, other: Plane3 | Point3) -> float`
+
+
+计算平面与平面或点之间的距离。
+
+**Arguments**:
+
+- other: 另一个平面或点  
+
+**Return**:
+
+- 距离
+
+**Raises**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other: 另一个平面或点
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_intersection_line3(self, other: Plane3) -> Line3`
+
+
+计算两平面的交线。
+
+**Arguments**:
+
+- other: 另一个平面  
+
+**Return**:
+
+- 两平面的交线
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        Args:
+            other: 另一个平面
+        Returns:
+            两平面的交线
+        Raises:
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)
+```
+</details>
+
+### *method* `cal_intersection_point3(self, other: Line3) -> Point3`
+
+
+计算平面与直线的交点。
+
+**Arguments**:
+
+- other: 不与平面平行或在平面上的直线  
+
+**Return**:
+
+- 交点
+
+**Raises**:
+
+- ValueError  平面与直线平行或重合
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other: 不与平面平行或在平面上的直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))
+```
+</details>
+
+### *method* `cal_parallel_plane3(self, point: Point3) -> Plane3`
+
+
+计算平行于该平面且过指定点的平面。
+
+**Arguments**:
+
+- point: 指定点  
+
+**Return**:
+
+- 所求平面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point: 指定点
+        Returns:
+            所求平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)
+```
+</details>
+
+### *method* `is_parallel(self, other: Plane3) -> bool`
+
+
+判断两个平面是否平行。
+
+**Arguments**:
+
+- other: 另一个平面  
+
+**Return**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否平行
+        """
+    return self.normal.is_parallel(other.normal)
+```
+</details>
+
+### `@property`
+### *method* `normal(self) -> Vector3`
+
+
+平面的法向量。
+
+**Return**:
+
+- 法向量
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+    return Vector3(self.a, self.b, self.c)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3`
+
+
+工厂函数 由点和法向量构造平面(点法式构造)。
+
+**Arguments**:
+
+- point: 平面上的一点  
+
+- normal: 法向量  
+
+**Return**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point: 平面上的一点
+            normal: 法向量
+        Returns:
+            平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3`
+
+
+工厂函数 由三点构造平面。
+
+**Arguments**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+- p3: 点3  
+
+**Return**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1: 点1
+            p2: 点2
+            p3: 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3`
+
+
+工厂函数 由两直线构造平面。
+
+**Arguments**:
+
+- l1: 直线1  
+
+- l2: 直线2  
+
+**Return**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1: 直线1
+            l2: 直线2
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_line(cls, point: Point3, line: Line3) -> Plane3`
+
+
+工厂函数 由点和直线构造平面。
+
+**Arguments**:
+
+- point: 面上一点  
+
+- line: 面上直线，不包含点  
+
+**Return**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point: 面上一点
+            line: 面上直线，不包含点
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Line3) -> Point3 | None`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Line3') -> 'Point3 | None':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Plane3) -> Line3 | None`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Plane3') -> 'Line3 | None':
+    ...
+```
+</details>
+
+### *method* `__and__(self, other)`
+
+
+取两平面的交集（人话：交线）
+
+**Arguments**:
+
+- other:   
+
+**Return**:
+
+- 不平行平面的交线，平面平行返回None
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other:
+        Returns:
+            不平行平面的交线，平面平行返回None
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    return self.approx(other)
+```
+</details>
+
+### *method* `__rand__(self, other: Line3) -> Point3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
+```
+</details>
+

docs/en/api/mp_math/point.md

@@ -0,0 +1,186 @@
+---
+title: mbcp.mp_math.point
+---
+### **class** `Point3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+笛卡尔坐标系中的点。
+
+**Arguments**:
+
+- x: x 坐标  
+
+- y: y 坐标  
+
+- z: z 坐标  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        笛卡尔坐标系中的点。
+        Args:
+            x: x 坐标
+            y: y 坐标
+            z: z 坐标
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Point3, epsilon: float = APPROX) -> bool`
+
+
+判断两个点是否近似相等。
+
+**Arguments**:
+
+- other:   
+
+- epsilon:   
+
+**Return**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个点是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Point3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Point3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+P + V -> P
+P + P -> P
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        P + V -> P
+        P + P -> P
+        Args:
+            other:
+        Returns:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个点是否相等。
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个点是否相等。
+        Args:
+            other:
+        Returns:
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self - other: Point3 => Vector3`
+
+
+P - P -> V
+
+P - V -> P  已在 :class:`Vector3` 中实现
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __sub__(self, other: 'Point3') -> 'Vector3':
+    """
+        P - P -> V
+
+        P - V -> P  已在 :class:`Vector3` 中实现
+        Args:
+            other:
+        Returns:
+
+        """
+    from .vector import Vector3
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+```
+</details>
+

docs/en/api/mp_math/segment.md

@@ -0,0 +1,34 @@
+---
+title: mbcp.mp_math.segment
+---
+### **class** `Segment3`
+### *method* `__init__(self, p1: Point3, p2: Point3)`
+
+
+三维空间中的线段。
+:param p1:
+:param p2:
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, p1: 'Point3', p2: 'Point3'):
+    """
+        三维空间中的线段。
+        :param p1:
+        :param p2:
+        """
+    self.p1 = p1
+    self.p2 = p2
+    '方向向量'
+    self.direction = self.p2 - self.p1
+    '长度'
+    self.length = self.direction.length
+    '中心点'
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
+```
+</details>
+

docs/en/api/mp_math/utils.md

@@ -0,0 +1,218 @@
+---
+title: mbcp.mp_math.utils
+---
+### *func* `clamp() -> float`
+
+
+区间限定函数
+
+**Arguments**:
+
+- x: 待限定的值  
+
+- min_: 最小值  
+
+- max_: 最大值  
+
+**Return**:
+
+- 限制后的值
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def clamp(x: float, min_: float, max_: float) -> float:
+    """
+    区间限定函数
+    Args:
+        x: 待限定的值
+        min_: 最小值
+        max_: 最大值
+
+    Returns:
+        限制后的值
+    """
+    return max(min(x, max_), min_)
+```
+</details>
+
+### *func* `approx(x: float = 0.0, y: float = APPROX) -> bool`
+
+
+判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+
+**Arguments**:
+
+- x: 数1  
+
+- y: 数2  
+
+- epsilon: 误差  
+
+**Return**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    """
+    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+    Args:
+        x: 数1
+        y: 数2
+        epsilon: 误差
+    Returns:
+        是否近似相等
+    """
+    return abs(x - y) < epsilon
+```
+</details>
+
+### *func* `sign(x: float = False) -> str`
+
+
+获取数的符号。
+
+**Arguments**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**Return**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def sign(x: float, only_neg: bool=False) -> str:
+    """获取数的符号。
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return '+' if not only_neg else ''
+    elif x < 0:
+        return '-'
+    else:
+        return ''
+```
+</details>
+
+### *func* `sign_format(x: float = False) -> str`
+
+
+格式化符号数
+-1 -> -1
+1 -> +1
+0 -> ""
+
+**Arguments**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**Return**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def sign_format(x: float, only_neg: bool=False) -> str:
+    """格式化符号数
+    -1 -> -1
+    1 -> +1
+    0 -> ""
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return f'+{x}' if not only_neg else f'{x}'
+    elif x < 0:
+        return f'-{abs(x)}'
+    else:
+        return ''
+```
+</details>
+
+### **class** `Approx`
+### *method* `__init__(self, value: RealNumber)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, value: RealNumber):
+    self.value = value
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other):
+    if isinstance(self.value, (float, int)):
+        if isinstance(other, (float, int)):
+            return abs(self.value - other) < APPROX
+        else:
+            self.raise_type_error(other)
+    elif isinstance(self.value, Vector3):
+        if isinstance(other, (Vector3, Point3, Plane3, Line3)):
+            return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
+        else:
+            self.raise_type_error(other)
+```
+</details>
+
+### *method* `raise_type_error(self, other)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
+```
+</details>
+
+### *method* `__ne__(self, other)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __ne__(self, other):
+    return not self.__eq__(other)
+```
+</details>
+

docs/en/api/mp_math/vector.md

@@ -0,0 +1,690 @@
+---
+title: mbcp.mp_math.vector
+---
+### **class** `Vector3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+3维向量
+
+**Arguments**:
+
+- x: x轴分量  
+
+- y: y轴分量  
+
+- z: z轴分量  
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        3维向量
+        Args:
+            x: x轴分量
+            y: y轴分量
+            z: z轴分量
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似相等。
+
+**Arguments**:
+
+- other:   
+
+- epsilon:   
+
+**Return**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### *method* `cal_angle(self, other: Vector3) -> AnyAngle`
+
+
+计算两个向量之间的夹角。
+
+**Arguments**:
+
+- other: 另一个向量  
+
+**Return**:
+
+- 夹角
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    """
+        计算两个向量之间的夹角。
+        Args:
+            other: 另一个向量
+        Returns:
+            夹角
+        """
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
+```
+</details>
+
+### *method* `cross(self, other: Vector3) -> Vector3`
+
+
+向量积 叉乘：v1 cross v2 -> v3
+
+叉乘为0，则两向量平行。
+其余结果的模为平行四边形的面积。
+
+
+**Arguments**:
+
+- other:   
+
+**Return**:
+
+- 行列式的结果
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def cross(self, other: 'Vector3') -> 'Vector3':
+    """
+        向量积 叉乘：v1 cross v2 -> v3
+
+        叉乘为0，则两向量平行。
+        其余结果的模为平行四边形的面积。
+
+        返回如下行列式的结果：
+
+        ``i  j  k``
+
+        ``x1 y1 z1``
+
+        ``x2 y2 z2``
+
+        Args:
+            other:
+        Returns:
+            行列式的结果
+        """
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似平行。
+
+**Arguments**:
+
+- other: 另一个向量  
+
+- epsilon: 允许的误差  
+
+**Return**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other: 另一个向量
+            epsilon: 允许的误差
+        Returns:
+            是否近似平行
+        """
+    return self.cross(other).length < epsilon
+```
+</details>
+
+### *method* `is_parallel(self, other: Vector3) -> bool`
+
+
+判断两个向量是否平行。
+
+**Arguments**:
+
+- other: 另一个向量  
+
+**Return**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def is_parallel(self, other: 'Vector3') -> bool:
+    """
+        判断两个向量是否平行。
+        Args:
+            other: 另一个向量
+        Returns:
+            是否平行
+        """
+    return self.cross(other).approx(zero_vector3)
+```
+</details>
+
+### *method* `normalize(self)`
+
+
+将向量归一化。
+
+自体归一化，不返回值。
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def normalize(self):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length
+```
+</details>
+
+### `@property`
+### *method* `np_array(self) -> np.ndarray`
+
+
+
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def np_array(self) -> 'np.ndarray':
+    """
+        返回numpy数组
+        Returns:
+        """
+    return np.array([self.x, self.y, self.z])
+```
+</details>
+
+### `@property`
+### *method* `length(self) -> float`
+
+
+向量的模。
+
+**Return**:
+
+- 模
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            模
+        """
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
+```
+</details>
+
+### `@property`
+### *method* `unit(self) -> Vector3`
+
+
+获取该向量的单位向量。
+
+**Return**:
+
+- 单位向量
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@property
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            单位向量
+        """
+    return self / self.length
+```
+</details>
+
+### *method* `__abs__(self)`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __abs__(self):
+    return self.length
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+V + P -> P
+
+V + V -> V
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个向量是否相等。
+
+**Arguments**:
+
+- other:   
+
+**Return**:
+
+- 是否相等
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个向量是否相等。
+        Args:
+            other:
+        Returns:
+            是否相等
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self + other: Point3 => Point3`
+
+
+P + V -> P
+
+别去点那边实现了。
+:param other:
+:return:
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __radd__(self, other: 'Point3') -> 'Point3':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        :param other:
+        :return:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Point3 => Point3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self - other`
+
+
+V - P -> P
+
+V - V -> V
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __sub__(self, other):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other:
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
+```
+</details>
+
+### *method* `self - other: Point3`
+
+
+P - V -> P
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __rsub__(self, other: 'Point3'):
+    """
+        P - V -> P
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
+```
+</details>
+
+### `@overload`
+### *method* `self * other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: RealNumber) -> 'Vector3':
+    ...
+```
+</details>
+
+### *method* `self * other: int | float | Vector3 => Vector3`
+
+
+数组运算 非点乘。点乘使用@，叉乘使用cross。
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other:
+
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
+```
+</details>
+
+### *method* `self @ other: Vector3 => RealNumber`
+
+
+点乘。
+
+**Arguments**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+    """
+        点乘。
+        Args:
+            other:
+        Returns:
+        """
+    return self.x * other.x + self.y * other.y + self.z * other.z
+```
+</details>
+
+### *method* `self / other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
+```
+</details>
+
+### *method* `- self`
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
+```
+</details>
+
+### ***var*** `zero_vector3 = Vector3(0, 0, 0)`
+
+- **Type**: `Vector3`
+
+- **Description**: 零向量
+
+### ***var*** `x_axis = Vector3(1, 0, 0)`
+
+- **Type**: `Vector3`
+
+- **Description**: x轴单位向量
+
+### ***var*** `y_axis = Vector3(0, 1, 0)`
+
+- **Type**: `Vector3`
+
+- **Description**: y轴单位向量
+
+### ***var*** `z_axis = Vector3(0, 0, 1)`
+
+- **Type**: `Vector3`
+
+- **Description**: z轴单位向量
+

docs/en/api/particle/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.particle
+---

docs/en/api/presets/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.presets
+---

docs/en/api/presets/model/index.md

@@ -0,0 +1,47 @@
+---
+title: mbcp.presets.model
+---
+### **class** `GeometricModels`
+### `@staticmethod`
+### *method* `sphere(radius: float, density: float)`
+
+
+生成球体上的点集。
+
+**Arguments**:
+
+- radius:   
+
+- density:   
+
+**Return**:
+
+- List[Point3]: 球体上的点集。
+
+
+
+<details>
+<summary> <i>Source code</i> </summary>
+
+```python
+@staticmethod
+def sphere(radius: float, density: float):
+    """
+        生成球体上的点集。
+        Args:
+            radius:
+            density:
+        Returns:
+            List[Point3]: 球体上的点集。
+        """
+    area = 4 * np.pi * radius ** 2
+    num = int(area * density)
+    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
+    theta_list = np.sqrt(num * np.pi) * phi_list
+    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
+    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
+    z_array = radius * np.cos(phi_list)
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
+```
+</details>
+

docs/guide/index.md

@@ -0,0 +1 @@
+# 开始不了一点

docs/index.md

@@ -9,7 +9,7 @@ hero:
   actions:
     - theme: brand
       text: 快速开始
-      link: md-ex
+      link: guide/
     - theme: alt
       text: API文档
       link: api/

docs/ja/api/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp
+---

docs/ja/api/mp_math/angle.md

@@ -0,0 +1,423 @@
+---
+title: mbcp.mp_math.angle
+---
+### **class** `Angle`
+### **class** `AnyAngle(Angle)`
+### *method* `__init__(self, value: float, is_radian: bool = False)`
+
+
+任意角度。
+
+**引数**:
+
+- value: 角度或弧度值  
+
+- is_radian: 是否为弧度，默认为否  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, value: float, is_radian: bool=False):
+    """
+        任意角度。
+        Args:
+            value: 角度或弧度值
+            is_radian: 是否为弧度，默认为否
+        """
+    if is_radian:
+        self.radian = value
+    else:
+        self.radian = value * PI / 180
+```
+</details>
+
+### `@property`
+### *method* `complementary(self) -> AnyAngle`
+
+
+余角：两角的和为90°。
+
+**戻り値**:
+
+- 余角
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def complementary(self) -> 'AnyAngle':
+    """
+        余角：两角的和为90°。
+        Returns:
+            余角
+        """
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `supplementary(self) -> AnyAngle`
+
+
+补角：两角的和为180°。
+
+**戻り値**:
+
+- 补角
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def supplementary(self) -> 'AnyAngle':
+    """
+        补角：两角的和为180°。
+        Returns:
+            补角
+        """
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `degree(self) -> float`
+
+
+角度。
+
+**戻り値**:
+
+- 弧度
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def degree(self) -> float:
+    """
+        角度。
+        Returns:
+            弧度
+        """
+    return self.radian * 180 / PI
+```
+</details>
+
+### `@property`
+### *method* `minimum_positive(self) -> AnyAngle`
+
+
+最小正角。
+
+**戻り値**:
+
+- 最小正角度
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def minimum_positive(self) -> 'AnyAngle':
+    """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+    return AnyAngle(self.radian % (2 * PI))
+```
+</details>
+
+### `@property`
+### *method* `maximum_negative(self) -> AnyAngle`
+
+
+最大负角。
+
+**戻り値**:
+
+- 最大负角度
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def maximum_negative(self) -> 'AnyAngle':
+    """
+        最大负角。
+        Returns:
+            最大负角度
+        """
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `sin(self) -> float`
+
+
+正弦值。
+
+**戻り値**:
+
+- 正弦值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def sin(self) -> float:
+    """
+        正弦值。
+        Returns:
+            正弦值
+        """
+    return math.sin(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cos(self) -> float`
+
+
+余弦值。
+
+**戻り値**:
+
+- 余弦值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def cos(self) -> float:
+    """
+        余弦值。
+        Returns:
+            余弦值
+        """
+    return math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `tan(self) -> float`
+
+
+正切值。
+
+**戻り値**:
+
+- 正切值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def tan(self) -> float:
+    """
+        正切值。
+        Returns:
+            正切值
+        """
+    return math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cot(self) -> float`
+
+
+余切值。
+
+**戻り値**:
+
+- 余切值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def cot(self) -> float:
+    """
+        余切值。
+        Returns:
+            余切值
+        """
+    return 1 / math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `sec(self) -> float`
+
+
+正割值。
+
+**戻り値**:
+
+- 正割值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def sec(self) -> float:
+    """
+        正割值。
+        Returns:
+            正割值
+        """
+    return 1 / math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `csc(self) -> float`
+
+
+余割值。
+
+**戻り値**:
+
+- 余割值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def csc(self) -> float:
+    """
+        余割值。
+        Returns:
+            余割值
+        """
+    return 1 / math.sin(self.radian)
+```
+</details>
+
+### *method* `self + other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other):
+    return approx(self.radian, other.radian)
+```
+</details>
+
+### *method* `self - other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
+```
+</details>
+
+### *method* `self * other: float => AnyAngle`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
+```
+</details>
+
+### `@overload`
+### *method* `self / other: float => AnyAngle`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: float) -> 'AnyAngle':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self / other: AnyAngle => float`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: 'AnyAngle') -> float:
+    ...
+```
+</details>
+
+### *method* `self / other`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __truediv__(self, other):
+    if isinstance(other, AnyAngle):
+        return self.radian / other.radian
+    return AnyAngle(self.radian / other, is_radian=True)
+```
+</details>
+

docs/ja/api/mp_math/const.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math.const
+---

docs/ja/api/mp_math/equation.md

@@ -0,0 +1,162 @@
+---
+title: mbcp.mp_math.equation
+---
+### *func* `get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc`
+
+
+求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+
+**引数**:
+
+- func: 函数  
+
+- var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)  
+
+- epsilon: 偏移量  
+
+**戻り値**:
+
+- 偏导函数
+
+**例外**:
+
+- ValueError  无效变量类型
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    """
+    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    Args:
+        func: 函数
+        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
+        epsilon: 偏移量
+    Returns:
+        偏导函数
+    Raises:
+        ValueError: 无效变量类型
+    """
+    if isinstance(var, int):
+
+        def partial_derivative_func(*args: Var) -> Var:
+            args_list_plus = list(args)
+            args_list_plus[var] += epsilon
+            args_list_minus = list(args)
+            args_list_minus[var] -= epsilon
+            return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+        return partial_derivative_func
+    elif isinstance(var, tuple):
+
+        def high_order_partial_derivative_func(*args: Var) -> Var:
+            result_func = func
+            for v in var:
+                result_func = get_partial_derivative_func(result_func, v, epsilon)
+            return result_func(*args)
+        return high_order_partial_derivative_func
+    else:
+        raise ValueError('Invalid var type')
+```
+</details>
+
+### *func* `partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def partial_derivative_func(*args: Var) -> Var:
+    args_list_plus = list(args)
+    args_list_plus[var] += epsilon
+    args_list_minus = list(args)
+    args_list_minus[var] -= epsilon
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+```
+</details>
+
+### *func* `high_order_partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def high_order_partial_derivative_func(*args: Var) -> Var:
+    result_func = func
+    for v in var:
+        result_func = get_partial_derivative_func(result_func, v, epsilon)
+    return result_func(*args)
+```
+</details>
+
+### **class** `CurveEquation`
+### *method* `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`
+
+
+曲线方程。
+
+**引数**:
+
+- x_func: x函数  
+
+- y_func: y函数  
+
+- z_func: z函数  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    """
+        曲线方程。
+        Args:
+            x_func: x函数
+            y_func: y函数
+            z_func: z函数
+        """
+    self.x_func = x_func
+    self.y_func = y_func
+    self.z_func = z_func
+```
+</details>
+
+### *method* `__call__(self) -> Point3 | tuple[Point3, ...]`
+
+
+计算曲线上的点。
+
+**引数**:
+
+- *t:   
+
+- 参数:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    """
+        计算曲线上的点。
+        Args:
+            *t:
+                参数
+        Returns:
+
+        """
+    if len(t) == 1:
+        return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
+    else:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
+```
+</details>
+

docs/ja/api/mp_math/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math
+---

docs/ja/api/mp_math/line.md

@@ -0,0 +1,581 @@
+---
+title: mbcp.mp_math.line
+---
+### **class** `Line3`
+### *method* `__init__(self, point: Point3, direction: Vector3)`
+
+
+三维空间中的直线。由一个点和一个方向向量确定。
+
+**引数**:
+
+- point: 直线上的一点  
+
+- direction: 直线的方向向量  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, point: 'Point3', direction: 'Vector3'):
+    """
+        三维空间中的直线。由一个点和一个方向向量确定。
+        Args:
+            point: 直线上的一点
+            direction: 直线的方向向量
+        """
+    self.point = point
+    self.direction = direction
+```
+</details>
+
+### *method* `approx(self, other: Line3, epsilon: float = APPROX) -> bool`
+
+
+判断两条直线是否近似相等。
+
+**引数**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**戻り値**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    """
+        判断两条直线是否近似相等。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似相等
+        """
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3) -> AnyAngle`
+
+
+计算直线和直线之间的夹角。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 夹角弧度
+
+**例外**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    """
+        计算直线和直线之间的夹角。
+        Args:
+            other: 另一条直线
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    return self.direction.cal_angle(other.direction)
+```
+</details>
+
+### *method* `cal_distance(self, other: Line3 | Point3) -> float`
+
+
+计算直线和直线或点之间的距离。
+
+**引数**:
+
+- other: 平行直线或点  
+
+**戻り値**:
+
+- 距离
+
+**例外**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_distance(self, other: 'Line3 | Point3') -> float:
+    """
+        计算直线和直线或点之间的距离。
+        Args:
+            other: 平行直线或点
+
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    elif isinstance(other, Point3):
+        return (other - self.point).cross(self.direction).length / self.direction.length
+    else:
+        raise TypeError('Unsupported type.')
+```
+</details>
+
+### *method* `cal_intersection(self, other: Line3) -> Point3`
+
+
+计算两条直线的交点。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 交点
+
+**例外**:
+
+- ValueError  直线平行
+
+- ValueError  直线不共面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_intersection(self, other: 'Line3') -> 'Point3':
+    """
+        计算两条直线的交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 直线平行
+            ValueError: 直线不共面
+        """
+    if self.is_parallel(other):
+        raise ValueError('Lines are parallel and do not intersect.')
+    if not self.is_coplanar(other):
+        raise ValueError('Lines are not coplanar and do not intersect.')
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
+```
+</details>
+
+### *method* `cal_perpendicular(self, point: Point3) -> Line3`
+
+
+计算直线经过指定点p的垂线。
+
+**引数**:
+
+- point: 指定点  
+
+**戻り値**:
+
+- 垂线
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    """
+        计算直线经过指定点p的垂线。
+        Args:
+            point: 指定点
+        Returns:
+            垂线
+        """
+    return Line3(point, self.direction.cross(point - self.point))
+```
+</details>
+
+### *method* `get_point(self, t: RealNumber) -> Point3`
+
+
+获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+
+**引数**:
+
+- t: 参数t  
+
+**戻り値**:
+
+- 点
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def get_point(self, t: RealNumber) -> 'Point3':
+    """
+        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+        Args:
+            t: 参数t
+        Returns:
+            点
+        """
+    return self.point + t * self.direction
+```
+</details>
+
+### *method* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
+
+
+获取直线的参数方程。
+
+**戻り値**:
+
+- x(t), y(t), z(t)
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    """
+        获取直线的参数方程。
+        Returns:
+            x(t), y(t), z(t)
+        """
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool`
+
+
+判断两条直线是否近似平行。
+
+**引数**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**戻り値**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    """
+        判断两条直线是否近似平行。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似平行
+        """
+    return self.direction.is_approx_parallel(other.direction, epsilon)
+```
+</details>
+
+### *method* `is_parallel(self, other: Line3) -> bool`
+
+
+判断两条直线是否平行。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_parallel(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否平行。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否平行
+        """
+    return self.direction.is_parallel(other.direction)
+```
+</details>
+
+### *method* `is_collinear(self, other: Line3) -> bool`
+
+
+判断两条直线是否共线。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 是否共线
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_collinear(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共线。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共线
+        """
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_point_on(self, point: Point3) -> bool`
+
+
+判断点是否在直线上。
+
+**引数**:
+
+- point: 点  
+
+**戻り値**:
+
+- 是否在直线上
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_point_on(self, point: 'Point3') -> bool:
+    """
+        判断点是否在直线上。
+        Args:
+            point: 点
+        Returns:
+            是否在直线上
+        """
+    return (point - self.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_coplanar(self, other: Line3) -> bool`
+
+
+判断两条直线是否共面。
+充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 是否共面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_coplanar(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共面。
+        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共面
+        """
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
+```
+</details>
+
+### *method* `simplify(self)`
+
+
+简化直线方程，等价相等。
+自体简化，不返回值。
+
+按照可行性一次对x y z 化 0 处理，并对向量单位化
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def simplify(self):
+    """
+        简化直线方程，等价相等。
+        自体简化，不返回值。
+
+        按照可行性一次对x y z 化 0 处理，并对向量单位化
+        """
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    if self.direction.y == 0:
+        self.point.y = 0
+    if self.direction.z == 0:
+        self.point.z = 0
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_points(cls, p1: Point3, p2: Point3) -> Line3`
+
+
+工厂函数 由两点构造直线。
+
+**引数**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+**戻り値**:
+
+- 直线
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    """
+        工厂函数 由两点构造直线。
+        Args:
+            p1: 点1
+            p2: 点2
+        Returns:
+            直线
+        """
+    direction = p2 - p1
+    return cls(p1, direction)
+```
+</details>
+
+### *method* `__and__(self, other: Line3) -> Line3 | Point3 | None`
+
+
+计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+
+**引数**:
+
+- other: 另一条直线  
+
+**戻り値**:
+
+- 交点
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    """
+        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        """
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+判断两条直线是否等价。
+
+v1 // v2 ∧ (p1 - p2) // v1
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    """
+        判断两条直线是否等价。
+
+        v1 // v2 ∧ (p1 - p2) // v1
+        Args:
+            other:
+
+        Returns:
+
+        """
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+

docs/ja/api/mp_math/mp_math_typing.md

@@ -0,0 +1,63 @@
+---
+title: mbcp.mp_math.mp_math_typing
+---
+### ***var*** `RealNumber = int | float`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `Number = RealNumber | complex`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `Var = SingleVar | ArrayVar`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `OneSingleVarFunc = Callable[[SingleVar], SingleVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `OneArrayFunc = Callable[[ArrayVar], ArrayVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `OneVarFunc = OneSingleVarFunc | OneArrayFunc`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `MultiSingleVarsFunc = Callable[..., SingleVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `MultiArraysFunc = Callable[..., ArrayVar]`
+
+- **タイプ**: `TypeAlias`
+
+### ***var*** `MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc`
+
+- **タイプ**: `TypeAlias`
+

docs/ja/api/mp_math/plane.md

@@ -0,0 +1,592 @@
+---
+title: mbcp.mp_math.plane
+---
+### **class** `Plane3`
+### *method* `__init__(self, a: float, b: float, c: float, d: float)`
+
+
+平面方程：ax + by + cz + d = 0
+
+**引数**:
+
+- a: x系数  
+
+- b: y系数  
+
+- c: z系数  
+
+- d: 常数项  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a: x系数
+            b: y系数
+            c: z系数
+            d: 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d
+```
+</details>
+
+### *method* `approx(self, other: Plane3) -> bool`
+
+
+判断两个平面是否近似相等。
+
+**引数**:
+
+- other: 另一个平面  
+
+**戻り値**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def approx(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3 | Plane3) -> AnyAngle`
+
+
+计算平面与平面之间的夹角。
+
+**引数**:
+
+- other: 另一个平面  
+
+**戻り値**:
+
+- 夹角弧度
+
+**例外**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        Args:
+            other: 另一个平面
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_distance(self, other: Plane3 | Point3) -> float`
+
+
+计算平面与平面或点之间的距离。
+
+**引数**:
+
+- other: 另一个平面或点  
+
+**戻り値**:
+
+- 距离
+
+**例外**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other: 另一个平面或点
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_intersection_line3(self, other: Plane3) -> Line3`
+
+
+计算两平面的交线。
+
+**引数**:
+
+- other: 另一个平面  
+
+**戻り値**:
+
+- 两平面的交线
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        Args:
+            other: 另一个平面
+        Returns:
+            两平面的交线
+        Raises:
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)
+```
+</details>
+
+### *method* `cal_intersection_point3(self, other: Line3) -> Point3`
+
+
+计算平面与直线的交点。
+
+**引数**:
+
+- other: 不与平面平行或在平面上的直线  
+
+**戻り値**:
+
+- 交点
+
+**例外**:
+
+- ValueError  平面与直线平行或重合
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other: 不与平面平行或在平面上的直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))
+```
+</details>
+
+### *method* `cal_parallel_plane3(self, point: Point3) -> Plane3`
+
+
+计算平行于该平面且过指定点的平面。
+
+**引数**:
+
+- point: 指定点  
+
+**戻り値**:
+
+- 所求平面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point: 指定点
+        Returns:
+            所求平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)
+```
+</details>
+
+### *method* `is_parallel(self, other: Plane3) -> bool`
+
+
+判断两个平面是否平行。
+
+**引数**:
+
+- other: 另一个平面  
+
+**戻り値**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否平行
+        """
+    return self.normal.is_parallel(other.normal)
+```
+</details>
+
+### `@property`
+### *method* `normal(self) -> Vector3`
+
+
+平面的法向量。
+
+**戻り値**:
+
+- 法向量
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+    return Vector3(self.a, self.b, self.c)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3`
+
+
+工厂函数 由点和法向量构造平面(点法式构造)。
+
+**引数**:
+
+- point: 平面上的一点  
+
+- normal: 法向量  
+
+**戻り値**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point: 平面上的一点
+            normal: 法向量
+        Returns:
+            平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3`
+
+
+工厂函数 由三点构造平面。
+
+**引数**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+- p3: 点3  
+
+**戻り値**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1: 点1
+            p2: 点2
+            p3: 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3`
+
+
+工厂函数 由两直线构造平面。
+
+**引数**:
+
+- l1: 直线1  
+
+- l2: 直线2  
+
+**戻り値**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1: 直线1
+            l2: 直线2
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_line(cls, point: Point3, line: Line3) -> Plane3`
+
+
+工厂函数 由点和直线构造平面。
+
+**引数**:
+
+- point: 面上一点  
+
+- line: 面上直线，不包含点  
+
+**戻り値**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point: 面上一点
+            line: 面上直线，不包含点
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Line3) -> Point3 | None`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Line3') -> 'Point3 | None':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Plane3) -> Line3 | None`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Plane3') -> 'Line3 | None':
+    ...
+```
+</details>
+
+### *method* `__and__(self, other)`
+
+
+取两平面的交集（人话：交线）
+
+**引数**:
+
+- other:   
+
+**戻り値**:
+
+- 不平行平面的交线，平面平行返回None
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other:
+        Returns:
+            不平行平面的交线，平面平行返回None
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    return self.approx(other)
+```
+</details>
+
+### *method* `__rand__(self, other: Line3) -> Point3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
+```
+</details>
+

docs/ja/api/mp_math/point.md

@@ -0,0 +1,186 @@
+---
+title: mbcp.mp_math.point
+---
+### **class** `Point3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+笛卡尔坐标系中的点。
+
+**引数**:
+
+- x: x 坐标  
+
+- y: y 坐标  
+
+- z: z 坐标  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        笛卡尔坐标系中的点。
+        Args:
+            x: x 坐标
+            y: y 坐标
+            z: z 坐标
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Point3, epsilon: float = APPROX) -> bool`
+
+
+判断两个点是否近似相等。
+
+**引数**:
+
+- other:   
+
+- epsilon:   
+
+**戻り値**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个点是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Point3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Point3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+P + V -> P
+P + P -> P
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        P + V -> P
+        P + P -> P
+        Args:
+            other:
+        Returns:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个点是否相等。
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个点是否相等。
+        Args:
+            other:
+        Returns:
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self - other: Point3 => Vector3`
+
+
+P - P -> V
+
+P - V -> P  已在 :class:`Vector3` 中实现
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __sub__(self, other: 'Point3') -> 'Vector3':
+    """
+        P - P -> V
+
+        P - V -> P  已在 :class:`Vector3` 中实现
+        Args:
+            other:
+        Returns:
+
+        """
+    from .vector import Vector3
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+```
+</details>
+

docs/ja/api/mp_math/segment.md

@@ -0,0 +1,34 @@
+---
+title: mbcp.mp_math.segment
+---
+### **class** `Segment3`
+### *method* `__init__(self, p1: Point3, p2: Point3)`
+
+
+三维空间中的线段。
+:param p1:
+:param p2:
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, p1: 'Point3', p2: 'Point3'):
+    """
+        三维空间中的线段。
+        :param p1:
+        :param p2:
+        """
+    self.p1 = p1
+    self.p2 = p2
+    '方向向量'
+    self.direction = self.p2 - self.p1
+    '长度'
+    self.length = self.direction.length
+    '中心点'
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
+```
+</details>
+

docs/ja/api/mp_math/utils.md

@@ -0,0 +1,218 @@
+---
+title: mbcp.mp_math.utils
+---
+### *func* `clamp() -> float`
+
+
+区间限定函数
+
+**引数**:
+
+- x: 待限定的值  
+
+- min_: 最小值  
+
+- max_: 最大值  
+
+**戻り値**:
+
+- 限制后的值
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def clamp(x: float, min_: float, max_: float) -> float:
+    """
+    区间限定函数
+    Args:
+        x: 待限定的值
+        min_: 最小值
+        max_: 最大值
+
+    Returns:
+        限制后的值
+    """
+    return max(min(x, max_), min_)
+```
+</details>
+
+### *func* `approx(x: float = 0.0, y: float = APPROX) -> bool`
+
+
+判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+
+**引数**:
+
+- x: 数1  
+
+- y: 数2  
+
+- epsilon: 误差  
+
+**戻り値**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    """
+    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+    Args:
+        x: 数1
+        y: 数2
+        epsilon: 误差
+    Returns:
+        是否近似相等
+    """
+    return abs(x - y) < epsilon
+```
+</details>
+
+### *func* `sign(x: float = False) -> str`
+
+
+获取数的符号。
+
+**引数**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**戻り値**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def sign(x: float, only_neg: bool=False) -> str:
+    """获取数的符号。
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return '+' if not only_neg else ''
+    elif x < 0:
+        return '-'
+    else:
+        return ''
+```
+</details>
+
+### *func* `sign_format(x: float = False) -> str`
+
+
+格式化符号数
+-1 -> -1
+1 -> +1
+0 -> ""
+
+**引数**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**戻り値**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def sign_format(x: float, only_neg: bool=False) -> str:
+    """格式化符号数
+    -1 -> -1
+    1 -> +1
+    0 -> ""
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return f'+{x}' if not only_neg else f'{x}'
+    elif x < 0:
+        return f'-{abs(x)}'
+    else:
+        return ''
+```
+</details>
+
+### **class** `Approx`
+### *method* `__init__(self, value: RealNumber)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, value: RealNumber):
+    self.value = value
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other):
+    if isinstance(self.value, (float, int)):
+        if isinstance(other, (float, int)):
+            return abs(self.value - other) < APPROX
+        else:
+            self.raise_type_error(other)
+    elif isinstance(self.value, Vector3):
+        if isinstance(other, (Vector3, Point3, Plane3, Line3)):
+            return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
+        else:
+            self.raise_type_error(other)
+```
+</details>
+
+### *method* `raise_type_error(self, other)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
+```
+</details>
+
+### *method* `__ne__(self, other)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __ne__(self, other):
+    return not self.__eq__(other)
+```
+</details>
+

docs/ja/api/mp_math/vector.md

@@ -0,0 +1,690 @@
+---
+title: mbcp.mp_math.vector
+---
+### **class** `Vector3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+3维向量
+
+**引数**:
+
+- x: x轴分量  
+
+- y: y轴分量  
+
+- z: z轴分量  
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        3维向量
+        Args:
+            x: x轴分量
+            y: y轴分量
+            z: z轴分量
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似相等。
+
+**引数**:
+
+- other:   
+
+- epsilon:   
+
+**戻り値**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### *method* `cal_angle(self, other: Vector3) -> AnyAngle`
+
+
+计算两个向量之间的夹角。
+
+**引数**:
+
+- other: 另一个向量  
+
+**戻り値**:
+
+- 夹角
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    """
+        计算两个向量之间的夹角。
+        Args:
+            other: 另一个向量
+        Returns:
+            夹角
+        """
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
+```
+</details>
+
+### *method* `cross(self, other: Vector3) -> Vector3`
+
+
+向量积 叉乘：v1 cross v2 -> v3
+
+叉乘为0，则两向量平行。
+其余结果的模为平行四边形的面积。
+
+
+**引数**:
+
+- other:   
+
+**戻り値**:
+
+- 行列式的结果
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def cross(self, other: 'Vector3') -> 'Vector3':
+    """
+        向量积 叉乘：v1 cross v2 -> v3
+
+        叉乘为0，则两向量平行。
+        其余结果的模为平行四边形的面积。
+
+        返回如下行列式的结果：
+
+        ``i  j  k``
+
+        ``x1 y1 z1``
+
+        ``x2 y2 z2``
+
+        Args:
+            other:
+        Returns:
+            行列式的结果
+        """
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似平行。
+
+**引数**:
+
+- other: 另一个向量  
+
+- epsilon: 允许的误差  
+
+**戻り値**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other: 另一个向量
+            epsilon: 允许的误差
+        Returns:
+            是否近似平行
+        """
+    return self.cross(other).length < epsilon
+```
+</details>
+
+### *method* `is_parallel(self, other: Vector3) -> bool`
+
+
+判断两个向量是否平行。
+
+**引数**:
+
+- other: 另一个向量  
+
+**戻り値**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def is_parallel(self, other: 'Vector3') -> bool:
+    """
+        判断两个向量是否平行。
+        Args:
+            other: 另一个向量
+        Returns:
+            是否平行
+        """
+    return self.cross(other).approx(zero_vector3)
+```
+</details>
+
+### *method* `normalize(self)`
+
+
+将向量归一化。
+
+自体归一化，不返回值。
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def normalize(self):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length
+```
+</details>
+
+### `@property`
+### *method* `np_array(self) -> np.ndarray`
+
+
+
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def np_array(self) -> 'np.ndarray':
+    """
+        返回numpy数组
+        Returns:
+        """
+    return np.array([self.x, self.y, self.z])
+```
+</details>
+
+### `@property`
+### *method* `length(self) -> float`
+
+
+向量的模。
+
+**戻り値**:
+
+- 模
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            模
+        """
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
+```
+</details>
+
+### `@property`
+### *method* `unit(self) -> Vector3`
+
+
+获取该向量的单位向量。
+
+**戻り値**:
+
+- 单位向量
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@property
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            单位向量
+        """
+    return self / self.length
+```
+</details>
+
+### *method* `__abs__(self)`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __abs__(self):
+    return self.length
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+V + P -> P
+
+V + V -> V
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个向量是否相等。
+
+**引数**:
+
+- other:   
+
+**戻り値**:
+
+- 是否相等
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个向量是否相等。
+        Args:
+            other:
+        Returns:
+            是否相等
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self + other: Point3 => Point3`
+
+
+P + V -> P
+
+别去点那边实现了。
+:param other:
+:return:
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __radd__(self, other: 'Point3') -> 'Point3':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        :param other:
+        :return:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Point3 => Point3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self - other`
+
+
+V - P -> P
+
+V - V -> V
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __sub__(self, other):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other:
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
+```
+</details>
+
+### *method* `self - other: Point3`
+
+
+P - V -> P
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __rsub__(self, other: 'Point3'):
+    """
+        P - V -> P
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
+```
+</details>
+
+### `@overload`
+### *method* `self * other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: RealNumber) -> 'Vector3':
+    ...
+```
+</details>
+
+### *method* `self * other: int | float | Vector3 => Vector3`
+
+
+数组运算 非点乘。点乘使用@，叉乘使用cross。
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other:
+
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
+```
+</details>
+
+### *method* `self @ other: Vector3 => RealNumber`
+
+
+点乘。
+
+**引数**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+    """
+        点乘。
+        Args:
+            other:
+        Returns:
+        """
+    return self.x * other.x + self.y * other.y + self.z * other.z
+```
+</details>
+
+### *method* `self / other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
+```
+</details>
+
+### *method* `- self`
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
+```
+</details>
+
+### ***var*** `zero_vector3 = Vector3(0, 0, 0)`
+
+- **タイプ**: `Vector3`
+
+- **説明**: 零向量
+
+### ***var*** `x_axis = Vector3(1, 0, 0)`
+
+- **タイプ**: `Vector3`
+
+- **説明**: x轴单位向量
+
+### ***var*** `y_axis = Vector3(0, 1, 0)`
+
+- **タイプ**: `Vector3`
+
+- **説明**: y轴单位向量
+
+### ***var*** `z_axis = Vector3(0, 0, 1)`
+
+- **タイプ**: `Vector3`
+
+- **説明**: z轴单位向量
+

docs/ja/api/particle/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.particle
+---

docs/ja/api/presets/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.presets
+---

docs/ja/api/presets/model/index.md

@@ -0,0 +1,47 @@
+---
+title: mbcp.presets.model
+---
+### **class** `GeometricModels`
+### `@staticmethod`
+### *method* `sphere(radius: float, density: float)`
+
+
+生成球体上的点集。
+
+**引数**:
+
+- radius:   
+
+- density:   
+
+**戻り値**:
+
+- List[Point3]: 球体上的点集。
+
+
+
+<details>
+<summary> <i>ソースコード</i> </summary>
+
+```python
+@staticmethod
+def sphere(radius: float, density: float):
+    """
+        生成球体上的点集。
+        Args:
+            radius:
+            density:
+        Returns:
+            List[Point3]: 球体上的点集。
+        """
+    area = 4 * np.pi * radius ** 2
+    num = int(area * density)
+    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
+    theta_list = np.sqrt(num * np.pi) * phi_list
+    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
+    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
+    z_array = radius * np.cos(phi_list)
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
+```
+</details>
+

docs/zht/api/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp
+---

docs/zht/api/mp_math/angle.md

@@ -0,0 +1,423 @@
+---
+title: mbcp.mp_math.angle
+---
+### **class** `Angle`
+### **class** `AnyAngle(Angle)`
+### *method* `__init__(self, value: float, is_radian: bool = False)`
+
+
+任意角度。
+
+**變數説明**:
+
+- value: 角度或弧度值  
+
+- is_radian: 是否为弧度，默认为否  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, value: float, is_radian: bool=False):
+    """
+        任意角度。
+        Args:
+            value: 角度或弧度值
+            is_radian: 是否为弧度，默认为否
+        """
+    if is_radian:
+        self.radian = value
+    else:
+        self.radian = value * PI / 180
+```
+</details>
+
+### `@property`
+### *method* `complementary(self) -> AnyAngle`
+
+
+余角：两角的和为90°。
+
+**返回**:
+
+- 余角
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def complementary(self) -> 'AnyAngle':
+    """
+        余角：两角的和为90°。
+        Returns:
+            余角
+        """
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `supplementary(self) -> AnyAngle`
+
+
+补角：两角的和为180°。
+
+**返回**:
+
+- 补角
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def supplementary(self) -> 'AnyAngle':
+    """
+        补角：两角的和为180°。
+        Returns:
+            补角
+        """
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `degree(self) -> float`
+
+
+角度。
+
+**返回**:
+
+- 弧度
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def degree(self) -> float:
+    """
+        角度。
+        Returns:
+            弧度
+        """
+    return self.radian * 180 / PI
+```
+</details>
+
+### `@property`
+### *method* `minimum_positive(self) -> AnyAngle`
+
+
+最小正角。
+
+**返回**:
+
+- 最小正角度
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def minimum_positive(self) -> 'AnyAngle':
+    """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+    return AnyAngle(self.radian % (2 * PI))
+```
+</details>
+
+### `@property`
+### *method* `maximum_negative(self) -> AnyAngle`
+
+
+最大负角。
+
+**返回**:
+
+- 最大负角度
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def maximum_negative(self) -> 'AnyAngle':
+    """
+        最大负角。
+        Returns:
+            最大负角度
+        """
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
+```
+</details>
+
+### `@property`
+### *method* `sin(self) -> float`
+
+
+正弦值。
+
+**返回**:
+
+- 正弦值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def sin(self) -> float:
+    """
+        正弦值。
+        Returns:
+            正弦值
+        """
+    return math.sin(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cos(self) -> float`
+
+
+余弦值。
+
+**返回**:
+
+- 余弦值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def cos(self) -> float:
+    """
+        余弦值。
+        Returns:
+            余弦值
+        """
+    return math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `tan(self) -> float`
+
+
+正切值。
+
+**返回**:
+
+- 正切值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def tan(self) -> float:
+    """
+        正切值。
+        Returns:
+            正切值
+        """
+    return math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `cot(self) -> float`
+
+
+余切值。
+
+**返回**:
+
+- 余切值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def cot(self) -> float:
+    """
+        余切值。
+        Returns:
+            余切值
+        """
+    return 1 / math.tan(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `sec(self) -> float`
+
+
+正割值。
+
+**返回**:
+
+- 正割值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def sec(self) -> float:
+    """
+        正割值。
+        Returns:
+            正割值
+        """
+    return 1 / math.cos(self.radian)
+```
+</details>
+
+### `@property`
+### *method* `csc(self) -> float`
+
+
+余割值。
+
+**返回**:
+
+- 余割值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def csc(self) -> float:
+    """
+        余割值。
+        Returns:
+            余割值
+        """
+    return 1 / math.sin(self.radian)
+```
+</details>
+
+### *method* `self + other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other):
+    return approx(self.radian, other.radian)
+```
+</details>
+
+### *method* `self - other: AnyAngle => AnyAngle`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
+```
+</details>
+
+### *method* `self * other: float => AnyAngle`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
+```
+</details>
+
+### `@overload`
+### *method* `self / other: float => AnyAngle`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: float) -> 'AnyAngle':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self / other: AnyAngle => float`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __truediv__(self, other: 'AnyAngle') -> float:
+    ...
+```
+</details>
+
+### *method* `self / other`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __truediv__(self, other):
+    if isinstance(other, AnyAngle):
+        return self.radian / other.radian
+    return AnyAngle(self.radian / other, is_radian=True)
+```
+</details>
+

docs/zht/api/mp_math/const.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math.const
+---

docs/zht/api/mp_math/equation.md

@@ -0,0 +1,162 @@
+---
+title: mbcp.mp_math.equation
+---
+### *func* `get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc`
+
+
+求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+
+**變數説明**:
+
+- func: 函数  
+
+- var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)  
+
+- epsilon: 偏移量  
+
+**返回**:
+
+- 偏导函数
+
+**抛出**:
+
+- ValueError  无效变量类型
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    """
+    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    Args:
+        func: 函数
+        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
+        epsilon: 偏移量
+    Returns:
+        偏导函数
+    Raises:
+        ValueError: 无效变量类型
+    """
+    if isinstance(var, int):
+
+        def partial_derivative_func(*args: Var) -> Var:
+            args_list_plus = list(args)
+            args_list_plus[var] += epsilon
+            args_list_minus = list(args)
+            args_list_minus[var] -= epsilon
+            return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+        return partial_derivative_func
+    elif isinstance(var, tuple):
+
+        def high_order_partial_derivative_func(*args: Var) -> Var:
+            result_func = func
+            for v in var:
+                result_func = get_partial_derivative_func(result_func, v, epsilon)
+            return result_func(*args)
+        return high_order_partial_derivative_func
+    else:
+        raise ValueError('Invalid var type')
+```
+</details>
+
+### *func* `partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def partial_derivative_func(*args: Var) -> Var:
+    args_list_plus = list(args)
+    args_list_plus[var] += epsilon
+    args_list_minus = list(args)
+    args_list_minus[var] -= epsilon
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
+```
+</details>
+
+### *func* `high_order_partial_derivative_func() -> Var`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def high_order_partial_derivative_func(*args: Var) -> Var:
+    result_func = func
+    for v in var:
+        result_func = get_partial_derivative_func(result_func, v, epsilon)
+    return result_func(*args)
+```
+</details>
+
+### **class** `CurveEquation`
+### *method* `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`
+
+
+曲线方程。
+
+**變數説明**:
+
+- x_func: x函数  
+
+- y_func: y函数  
+
+- z_func: z函数  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    """
+        曲线方程。
+        Args:
+            x_func: x函数
+            y_func: y函数
+            z_func: z函数
+        """
+    self.x_func = x_func
+    self.y_func = y_func
+    self.z_func = z_func
+```
+</details>
+
+### *method* `__call__(self) -> Point3 | tuple[Point3, ...]`
+
+
+计算曲线上的点。
+
+**變數説明**:
+
+- *t:   
+
+- 参数:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    """
+        计算曲线上的点。
+        Args:
+            *t:
+                参数
+        Returns:
+
+        """
+    if len(t) == 1:
+        return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
+    else:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
+```
+</details>
+

docs/zht/api/mp_math/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.mp_math
+---

docs/zht/api/mp_math/line.md

@@ -0,0 +1,581 @@
+---
+title: mbcp.mp_math.line
+---
+### **class** `Line3`
+### *method* `__init__(self, point: Point3, direction: Vector3)`
+
+
+三维空间中的直线。由一个点和一个方向向量确定。
+
+**變數説明**:
+
+- point: 直线上的一点  
+
+- direction: 直线的方向向量  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, point: 'Point3', direction: 'Vector3'):
+    """
+        三维空间中的直线。由一个点和一个方向向量确定。
+        Args:
+            point: 直线上的一点
+            direction: 直线的方向向量
+        """
+    self.point = point
+    self.direction = direction
+```
+</details>
+
+### *method* `approx(self, other: Line3, epsilon: float = APPROX) -> bool`
+
+
+判断两条直线是否近似相等。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**返回**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    """
+        判断两条直线是否近似相等。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似相等
+        """
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3) -> AnyAngle`
+
+
+计算直线和直线之间的夹角。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 夹角弧度
+
+**抛出**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    """
+        计算直线和直线之间的夹角。
+        Args:
+            other: 另一条直线
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    return self.direction.cal_angle(other.direction)
+```
+</details>
+
+### *method* `cal_distance(self, other: Line3 | Point3) -> float`
+
+
+计算直线和直线或点之间的距离。
+
+**變數説明**:
+
+- other: 平行直线或点  
+
+**返回**:
+
+- 距离
+
+**抛出**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_distance(self, other: 'Line3 | Point3') -> float:
+    """
+        计算直线和直线或点之间的距离。
+        Args:
+            other: 平行直线或点
+
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    elif isinstance(other, Point3):
+        return (other - self.point).cross(self.direction).length / self.direction.length
+    else:
+        raise TypeError('Unsupported type.')
+```
+</details>
+
+### *method* `cal_intersection(self, other: Line3) -> Point3`
+
+
+计算两条直线的交点。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 交点
+
+**抛出**:
+
+- ValueError  直线平行
+
+- ValueError  直线不共面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_intersection(self, other: 'Line3') -> 'Point3':
+    """
+        计算两条直线的交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 直线平行
+            ValueError: 直线不共面
+        """
+    if self.is_parallel(other):
+        raise ValueError('Lines are parallel and do not intersect.')
+    if not self.is_coplanar(other):
+        raise ValueError('Lines are not coplanar and do not intersect.')
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
+```
+</details>
+
+### *method* `cal_perpendicular(self, point: Point3) -> Line3`
+
+
+计算直线经过指定点p的垂线。
+
+**變數説明**:
+
+- point: 指定点  
+
+**返回**:
+
+- 垂线
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    """
+        计算直线经过指定点p的垂线。
+        Args:
+            point: 指定点
+        Returns:
+            垂线
+        """
+    return Line3(point, self.direction.cross(point - self.point))
+```
+</details>
+
+### *method* `get_point(self, t: RealNumber) -> Point3`
+
+
+获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+
+**變數説明**:
+
+- t: 参数t  
+
+**返回**:
+
+- 点
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def get_point(self, t: RealNumber) -> 'Point3':
+    """
+        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
+        Args:
+            t: 参数t
+        Returns:
+            点
+        """
+    return self.point + t * self.direction
+```
+</details>
+
+### *method* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
+
+
+获取直线的参数方程。
+
+**返回**:
+
+- x(t), y(t), z(t)
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    """
+        获取直线的参数方程。
+        Returns:
+            x(t), y(t), z(t)
+        """
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool`
+
+
+判断两条直线是否近似平行。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+- epsilon: 误差  
+
+**返回**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    """
+        判断两条直线是否近似平行。
+        Args:
+            other: 另一条直线
+            epsilon: 误差
+        Returns:
+            是否近似平行
+        """
+    return self.direction.is_approx_parallel(other.direction, epsilon)
+```
+</details>
+
+### *method* `is_parallel(self, other: Line3) -> bool`
+
+
+判断两条直线是否平行。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_parallel(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否平行。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否平行
+        """
+    return self.direction.is_parallel(other.direction)
+```
+</details>
+
+### *method* `is_collinear(self, other: Line3) -> bool`
+
+
+判断两条直线是否共线。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 是否共线
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_collinear(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共线。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共线
+        """
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_point_on(self, point: Point3) -> bool`
+
+
+判断点是否在直线上。
+
+**變數説明**:
+
+- point: 点  
+
+**返回**:
+
+- 是否在直线上
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_point_on(self, point: 'Point3') -> bool:
+    """
+        判断点是否在直线上。
+        Args:
+            point: 点
+        Returns:
+            是否在直线上
+        """
+    return (point - self.point).is_parallel(self.direction)
+```
+</details>
+
+### *method* `is_coplanar(self, other: Line3) -> bool`
+
+
+判断两条直线是否共面。
+充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 是否共面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_coplanar(self, other: 'Line3') -> bool:
+    """
+        判断两条直线是否共面。
+        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
+        Args:
+            other: 另一条直线
+        Returns:
+            是否共面
+        """
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
+```
+</details>
+
+### *method* `simplify(self)`
+
+
+简化直线方程，等价相等。
+自体简化，不返回值。
+
+按照可行性一次对x y z 化 0 处理，并对向量单位化
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def simplify(self):
+    """
+        简化直线方程，等价相等。
+        自体简化，不返回值。
+
+        按照可行性一次对x y z 化 0 处理，并对向量单位化
+        """
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    if self.direction.y == 0:
+        self.point.y = 0
+    if self.direction.z == 0:
+        self.point.z = 0
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_points(cls, p1: Point3, p2: Point3) -> Line3`
+
+
+工厂函数 由两点构造直线。
+
+**變數説明**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+**返回**:
+
+- 直线
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    """
+        工厂函数 由两点构造直线。
+        Args:
+            p1: 点1
+            p2: 点2
+        Returns:
+            直线
+        """
+    direction = p2 - p1
+    return cls(p1, direction)
+```
+</details>
+
+### *method* `__and__(self, other: Line3) -> Line3 | Point3 | None`
+
+
+计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+
+**變數説明**:
+
+- other: 另一条直线  
+
+**返回**:
+
+- 交点
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    """
+        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
+        Args:
+            other: 另一条直线
+        Returns:
+            交点
+        """
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+判断两条直线是否等价。
+
+v1 // v2 ∧ (p1 - p2) // v1
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    """
+        判断两条直线是否等价。
+
+        v1 // v2 ∧ (p1 - p2) // v1
+        Args:
+            other:
+
+        Returns:
+
+        """
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
+```
+</details>
+

docs/zht/api/mp_math/mp_math_typing.md

@@ -0,0 +1,63 @@
+---
+title: mbcp.mp_math.mp_math_typing
+---
+### ***var*** `RealNumber = int | float`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `Number = RealNumber | complex`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `Var = SingleVar | ArrayVar`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `OneSingleVarFunc = Callable[[SingleVar], SingleVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `OneArrayFunc = Callable[[ArrayVar], ArrayVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `OneVarFunc = OneSingleVarFunc | OneArrayFunc`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `MultiSingleVarsFunc = Callable[..., SingleVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `MultiArraysFunc = Callable[..., ArrayVar]`
+
+- **類型**: `TypeAlias`
+
+### ***var*** `MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc`
+
+- **類型**: `TypeAlias`
+

docs/zht/api/mp_math/plane.md

@@ -0,0 +1,592 @@
+---
+title: mbcp.mp_math.plane
+---
+### **class** `Plane3`
+### *method* `__init__(self, a: float, b: float, c: float, d: float)`
+
+
+平面方程：ax + by + cz + d = 0
+
+**變數説明**:
+
+- a: x系数  
+
+- b: y系数  
+
+- c: z系数  
+
+- d: 常数项  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a: x系数
+            b: y系数
+            c: z系数
+            d: 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d
+```
+</details>
+
+### *method* `approx(self, other: Plane3) -> bool`
+
+
+判断两个平面是否近似相等。
+
+**變數説明**:
+
+- other: 另一个平面  
+
+**返回**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def approx(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False
+```
+</details>
+
+### *method* `cal_angle(self, other: Line3 | Plane3) -> AnyAngle`
+
+
+计算平面与平面之间的夹角。
+
+**變數説明**:
+
+- other: 另一个平面  
+
+**返回**:
+
+- 夹角弧度
+
+**抛出**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        Args:
+            other: 另一个平面
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_distance(self, other: Plane3 | Point3) -> float`
+
+
+计算平面与平面或点之间的距离。
+
+**變數説明**:
+
+- other: 另一个平面或点  
+
+**返回**:
+
+- 距离
+
+**抛出**:
+
+- TypeError  不支持的类型
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other: 另一个平面或点
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')
+```
+</details>
+
+### *method* `cal_intersection_line3(self, other: Plane3) -> Line3`
+
+
+计算两平面的交线。
+
+**變數説明**:
+
+- other: 另一个平面  
+
+**返回**:
+
+- 两平面的交线
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        Args:
+            other: 另一个平面
+        Returns:
+            两平面的交线
+        Raises:
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)
+```
+</details>
+
+### *method* `cal_intersection_point3(self, other: Line3) -> Point3`
+
+
+计算平面与直线的交点。
+
+**變數説明**:
+
+- other: 不与平面平行或在平面上的直线  
+
+**返回**:
+
+- 交点
+
+**抛出**:
+
+- ValueError  平面与直线平行或重合
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other: 不与平面平行或在平面上的直线
+        Returns:
+            交点
+        Raises:
+            ValueError: 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))
+```
+</details>
+
+### *method* `cal_parallel_plane3(self, point: Point3) -> Plane3`
+
+
+计算平行于该平面且过指定点的平面。
+
+**變數説明**:
+
+- point: 指定点  
+
+**返回**:
+
+- 所求平面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point: 指定点
+        Returns:
+            所求平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)
+```
+</details>
+
+### *method* `is_parallel(self, other: Plane3) -> bool`
+
+
+判断两个平面是否平行。
+
+**變數説明**:
+
+- other: 另一个平面  
+
+**返回**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other: 另一个平面
+        Returns:
+            是否平行
+        """
+    return self.normal.is_parallel(other.normal)
+```
+</details>
+
+### `@property`
+### *method* `normal(self) -> Vector3`
+
+
+平面的法向量。
+
+**返回**:
+
+- 法向量
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+    return Vector3(self.a, self.b, self.c)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3`
+
+
+工厂函数 由点和法向量构造平面(点法式构造)。
+
+**變數説明**:
+
+- point: 平面上的一点  
+
+- normal: 法向量  
+
+**返回**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point: 平面上的一点
+            normal: 法向量
+        Returns:
+            平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3`
+
+
+工厂函数 由三点构造平面。
+
+**變數説明**:
+
+- p1: 点1  
+
+- p2: 点2  
+
+- p3: 点3  
+
+**返回**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1: 点1
+            p2: 点2
+            p3: 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)
+```
+</details>
+
+### `@classmethod`
+### *method* `from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3`
+
+
+工厂函数 由两直线构造平面。
+
+**變數説明**:
+
+- l1: 直线1  
+
+- l2: 直线2  
+
+**返回**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1: 直线1
+            l2: 直线2
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
+```
+</details>
+
+### `@classmethod`
+### *method* `from_point_and_line(cls, point: Point3, line: Line3) -> Plane3`
+
+
+工厂函数 由点和直线构造平面。
+
+**變數説明**:
+
+- point: 面上一点  
+
+- line: 面上直线，不包含点  
+
+**返回**:
+
+- 平面
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point: 面上一点
+            line: 面上直线，不包含点
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Line3) -> Point3 | None`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Line3') -> 'Point3 | None':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `__and__(self, other: Plane3) -> Line3 | None`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __and__(self, other: 'Plane3') -> 'Line3 | None':
+    ...
+```
+</details>
+
+### *method* `__and__(self, other)`
+
+
+取两平面的交集（人话：交线）
+
+**變數説明**:
+
+- other:   
+
+**返回**:
+
+- 不平行平面的交线，平面平行返回None
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other:
+        Returns:
+            不平行平面的交线，平面平行返回None
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other) -> bool`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other) -> bool:
+    return self.approx(other)
+```
+</details>
+
+### *method* `__rand__(self, other: Line3) -> Point3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
+```
+</details>
+

docs/zht/api/mp_math/point.md

@@ -0,0 +1,186 @@
+---
+title: mbcp.mp_math.point
+---
+### **class** `Point3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+笛卡尔坐标系中的点。
+
+**變數説明**:
+
+- x: x 坐标  
+
+- y: y 坐标  
+
+- z: z 坐标  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        笛卡尔坐标系中的点。
+        Args:
+            x: x 坐标
+            y: y 坐标
+            z: z 坐标
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Point3, epsilon: float = APPROX) -> bool`
+
+
+判断两个点是否近似相等。
+
+**變數説明**:
+
+- other:   
+
+- epsilon:   
+
+**返回**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个点是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Point3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Point3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+P + V -> P
+P + P -> P
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        P + V -> P
+        P + P -> P
+        Args:
+            other:
+        Returns:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个点是否相等。
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个点是否相等。
+        Args:
+            other:
+        Returns:
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self - other: Point3 => Vector3`
+
+
+P - P -> V
+
+P - V -> P  已在 :class:`Vector3` 中实现
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __sub__(self, other: 'Point3') -> 'Vector3':
+    """
+        P - P -> V
+
+        P - V -> P  已在 :class:`Vector3` 中实现
+        Args:
+            other:
+        Returns:
+
+        """
+    from .vector import Vector3
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+```
+</details>
+

docs/zht/api/mp_math/segment.md

@@ -0,0 +1,34 @@
+---
+title: mbcp.mp_math.segment
+---
+### **class** `Segment3`
+### *method* `__init__(self, p1: Point3, p2: Point3)`
+
+
+三维空间中的线段。
+:param p1:
+:param p2:
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, p1: 'Point3', p2: 'Point3'):
+    """
+        三维空间中的线段。
+        :param p1:
+        :param p2:
+        """
+    self.p1 = p1
+    self.p2 = p2
+    '方向向量'
+    self.direction = self.p2 - self.p1
+    '长度'
+    self.length = self.direction.length
+    '中心点'
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
+```
+</details>
+

docs/zht/api/mp_math/utils.md

@@ -0,0 +1,218 @@
+---
+title: mbcp.mp_math.utils
+---
+### *func* `clamp() -> float`
+
+
+区间限定函数
+
+**變數説明**:
+
+- x: 待限定的值  
+
+- min_: 最小值  
+
+- max_: 最大值  
+
+**返回**:
+
+- 限制后的值
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def clamp(x: float, min_: float, max_: float) -> float:
+    """
+    区间限定函数
+    Args:
+        x: 待限定的值
+        min_: 最小值
+        max_: 最大值
+
+    Returns:
+        限制后的值
+    """
+    return max(min(x, max_), min_)
+```
+</details>
+
+### *func* `approx(x: float = 0.0, y: float = APPROX) -> bool`
+
+
+判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+
+**變數説明**:
+
+- x: 数1  
+
+- y: 数2  
+
+- epsilon: 误差  
+
+**返回**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    """
+    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
+    Args:
+        x: 数1
+        y: 数2
+        epsilon: 误差
+    Returns:
+        是否近似相等
+    """
+    return abs(x - y) < epsilon
+```
+</details>
+
+### *func* `sign(x: float = False) -> str`
+
+
+获取数的符号。
+
+**變數説明**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**返回**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def sign(x: float, only_neg: bool=False) -> str:
+    """获取数的符号。
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return '+' if not only_neg else ''
+    elif x < 0:
+        return '-'
+    else:
+        return ''
+```
+</details>
+
+### *func* `sign_format(x: float = False) -> str`
+
+
+格式化符号数
+-1 -> -1
+1 -> +1
+0 -> ""
+
+**變數説明**:
+
+- x: 数  
+
+- only_neg: 是否只返回负数的符号  
+
+**返回**:
+
+- 符号 + - ""
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def sign_format(x: float, only_neg: bool=False) -> str:
+    """格式化符号数
+    -1 -> -1
+    1 -> +1
+    0 -> ""
+    Args:
+        x: 数
+        only_neg: 是否只返回负数的符号
+    Returns:
+        符号 + - ""
+    """
+    if x > 0:
+        return f'+{x}' if not only_neg else f'{x}'
+    elif x < 0:
+        return f'-{abs(x)}'
+    else:
+        return ''
+```
+</details>
+
+### **class** `Approx`
+### *method* `__init__(self, value: RealNumber)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, value: RealNumber):
+    self.value = value
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other):
+    if isinstance(self.value, (float, int)):
+        if isinstance(other, (float, int)):
+            return abs(self.value - other) < APPROX
+        else:
+            self.raise_type_error(other)
+    elif isinstance(self.value, Vector3):
+        if isinstance(other, (Vector3, Point3, Plane3, Line3)):
+            return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
+        else:
+            self.raise_type_error(other)
+```
+</details>
+
+### *method* `raise_type_error(self, other)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
+```
+</details>
+
+### *method* `__ne__(self, other)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __ne__(self, other):
+    return not self.__eq__(other)
+```
+</details>
+

docs/zht/api/mp_math/vector.md

@@ -0,0 +1,690 @@
+---
+title: mbcp.mp_math.vector
+---
+### **class** `Vector3`
+### *method* `__init__(self, x: float, y: float, z: float)`
+
+
+3维向量
+
+**變數説明**:
+
+- x: x轴分量  
+
+- y: y轴分量  
+
+- z: z轴分量  
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __init__(self, x: float, y: float, z: float):
+    """
+        3维向量
+        Args:
+            x: x轴分量
+            y: y轴分量
+            z: z轴分量
+        """
+    self.x = x
+    self.y = y
+    self.z = z
+```
+</details>
+
+### *method* `approx(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似相等。
+
+**變數説明**:
+
+- other:   
+
+- epsilon:   
+
+**返回**:
+
+- 是否近似相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        Returns:
+            是否近似相等
+        """
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
+```
+</details>
+
+### *method* `cal_angle(self, other: Vector3) -> AnyAngle`
+
+
+计算两个向量之间的夹角。
+
+**變數説明**:
+
+- other: 另一个向量  
+
+**返回**:
+
+- 夹角
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    """
+        计算两个向量之间的夹角。
+        Args:
+            other: 另一个向量
+        Returns:
+            夹角
+        """
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
+```
+</details>
+
+### *method* `cross(self, other: Vector3) -> Vector3`
+
+
+向量积 叉乘：v1 cross v2 -> v3
+
+叉乘为0，则两向量平行。
+其余结果的模为平行四边形的面积。
+
+
+**變數説明**:
+
+- other:   
+
+**返回**:
+
+- 行列式的结果
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def cross(self, other: 'Vector3') -> 'Vector3':
+    """
+        向量积 叉乘：v1 cross v2 -> v3
+
+        叉乘为0，则两向量平行。
+        其余结果的模为平行四边形的面积。
+
+        返回如下行列式的结果：
+
+        ``i  j  k``
+
+        ``x1 y1 z1``
+
+        ``x2 y2 z2``
+
+        Args:
+            other:
+        Returns:
+            行列式的结果
+        """
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
+```
+</details>
+
+### *method* `is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool`
+
+
+判断两个向量是否近似平行。
+
+**變數説明**:
+
+- other: 另一个向量  
+
+- epsilon: 允许的误差  
+
+**返回**:
+
+- 是否近似平行
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other: 另一个向量
+            epsilon: 允许的误差
+        Returns:
+            是否近似平行
+        """
+    return self.cross(other).length < epsilon
+```
+</details>
+
+### *method* `is_parallel(self, other: Vector3) -> bool`
+
+
+判断两个向量是否平行。
+
+**變數説明**:
+
+- other: 另一个向量  
+
+**返回**:
+
+- 是否平行
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def is_parallel(self, other: 'Vector3') -> bool:
+    """
+        判断两个向量是否平行。
+        Args:
+            other: 另一个向量
+        Returns:
+            是否平行
+        """
+    return self.cross(other).approx(zero_vector3)
+```
+</details>
+
+### *method* `normalize(self)`
+
+
+将向量归一化。
+
+自体归一化，不返回值。
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def normalize(self):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length
+```
+</details>
+
+### `@property`
+### *method* `np_array(self) -> np.ndarray`
+
+
+
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def np_array(self) -> 'np.ndarray':
+    """
+        返回numpy数组
+        Returns:
+        """
+    return np.array([self.x, self.y, self.z])
+```
+</details>
+
+### `@property`
+### *method* `length(self) -> float`
+
+
+向量的模。
+
+**返回**:
+
+- 模
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            模
+        """
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
+```
+</details>
+
+### `@property`
+### *method* `unit(self) -> Vector3`
+
+
+获取该向量的单位向量。
+
+**返回**:
+
+- 单位向量
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@property
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            单位向量
+        """
+    return self / self.length
+```
+</details>
+
+### *method* `__abs__(self)`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __abs__(self):
+    return self.length
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self + other: Point3 => Point3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __add__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self + other`
+
+
+V + P -> P
+
+V + V -> V
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __add__(self, other):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `__eq__(self, other)`
+
+
+判断两个向量是否相等。
+
+**變數説明**:
+
+- other:   
+
+**返回**:
+
+- 是否相等
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __eq__(self, other):
+    """
+        判断两个向量是否相等。
+        Args:
+            other:
+        Returns:
+            是否相等
+        """
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
+```
+</details>
+
+### *method* `self + other: Point3 => Point3`
+
+
+P + V -> P
+
+别去点那边实现了。
+:param other:
+:return:
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __radd__(self, other: 'Point3') -> 'Point3':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        :param other:
+        :return:
+        """
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self - other: Point3 => Point3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __sub__(self, other: 'Point3') -> 'Point3':
+    ...
+```
+</details>
+
+### *method* `self - other`
+
+
+V - P -> P
+
+V - V -> V
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __sub__(self, other):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other:
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
+```
+</details>
+
+### *method* `self - other: Point3`
+
+
+P - V -> P
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __rsub__(self, other: 'Point3'):
+    """
+        P - V -> P
+        Args:
+            other:
+        Returns:
+
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
+```
+</details>
+
+### `@overload`
+### *method* `self * other: Vector3 => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...
+```
+</details>
+
+### `@overload`
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@overload
+def __mul__(self, other: RealNumber) -> 'Vector3':
+    ...
+```
+</details>
+
+### *method* `self * other: int | float | Vector3 => Vector3`
+
+
+数组运算 非点乘。点乘使用@，叉乘使用cross。
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other:
+
+        Returns:
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
+```
+</details>
+
+### *method* `self * other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
+```
+</details>
+
+### *method* `self @ other: Vector3 => RealNumber`
+
+
+点乘。
+
+**變數説明**:
+
+- other:   
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+    """
+        点乘。
+        Args:
+            other:
+        Returns:
+        """
+    return self.x * other.x + self.y * other.y + self.z * other.z
+```
+</details>
+
+### *method* `self / other: RealNumber => Vector3`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
+```
+</details>
+
+### *method* `- self`
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
+```
+</details>
+
+### ***var*** `zero_vector3 = Vector3(0, 0, 0)`
+
+- **類型**: `Vector3`
+
+- **説明**: 零向量
+
+### ***var*** `x_axis = Vector3(1, 0, 0)`
+
+- **類型**: `Vector3`
+
+- **説明**: x轴单位向量
+
+### ***var*** `y_axis = Vector3(0, 1, 0)`
+
+- **類型**: `Vector3`
+
+- **説明**: y轴单位向量
+
+### ***var*** `z_axis = Vector3(0, 0, 1)`
+
+- **類型**: `Vector3`
+
+- **説明**: z轴单位向量
+

docs/zht/api/particle/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.particle
+---

docs/zht/api/presets/index.md

@@ -0,0 +1,3 @@
+---
+title: mbcp.presets
+---

docs/zht/api/presets/model/index.md

@@ -0,0 +1,47 @@
+---
+title: mbcp.presets.model
+---
+### **class** `GeometricModels`
+### `@staticmethod`
+### *method* `sphere(radius: float, density: float)`
+
+
+生成球体上的点集。
+
+**變數説明**:
+
+- radius:   
+
+- density:   
+
+**返回**:
+
+- List[Point3]: 球体上的点集。
+
+
+
+<details>
+<summary> <i>源碼</i> </summary>
+
+```python
+@staticmethod
+def sphere(radius: float, density: float):
+    """
+        生成球体上的点集。
+        Args:
+            radius:
+            density:
+        Returns:
+            List[Point3]: 球体上的点集。
+        """
+    area = 4 * np.pi * radius ** 2
+    num = int(area * density)
+    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
+    theta_list = np.sqrt(num * np.pi) * phi_list
+    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
+    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
+    z_array = radius * np.cos(phi_list)
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
+```
+</details>
+

litedoc/__main__.py

@@ -18,7 +18,7 @@ import argparse
 import os
 import sys
 
-from liteyuki_autodoc.output import generate_from_module
+from litedoc.output import generate_from_module
 
 
 def main():

litedoc/docstring/docstring.py

@@ -12,7 +12,7 @@ from typing import Optional
 
 from pydantic import BaseModel, Field
 
-from liteyuki_autodoc.i18n import get_text
+from litedoc.i18n import get_text
 
 
 class Attr(BaseModel):
@@ -126,24 +126,24 @@ class Docstring(BaseModel):
         # print(self.reduction())
         # print(self.desc, self.return_)
         if self.args:
-            ret += PREFIX + f"{get_text(lang, 'docstring.args')}:\n\n"
+            ret += PREFIX + f"**{get_text(lang, 'docstring.args')}**:\n\n"
             for arg in self.args:
                 ret += PREFIX + f"- {arg.name}: {arg.type}  {arg.desc}\n\n"
         if self.attrs:
-            ret += PREFIX + f"{get_text(lang, 'docstring.attrs')}:\n\n"
+            ret += PREFIX + f"**{get_text(lang, 'docstring.attrs')}**:\n\n"
             for attr in self.attrs:
                 ret += PREFIX + f"- {attr.name}: {attr.type}  {attr.desc}\n\n"
         if self.return_ is not None:
-            ret += PREFIX + f"{get_text(lang, 'docstring.return')}:\n\n"
+            ret += PREFIX + f"**{get_text(lang, 'docstring.return')}**:\n\n"
             ret += PREFIX + f"- {self.return_.desc}\n\n"
         if self.raise_:
-            ret += PREFIX + f"{get_text(lang, 'docstring.raises')}:\n\n"
+            ret += PREFIX + f"**{get_text(lang, 'docstring.raises')}**:\n\n"
             for exception in self.raise_:
                 ret += PREFIX + f"- {exception.name}  {exception.desc}\n\n"
         if self.example:
-            ret += PREFIX + f"{get_text(lang, 'docstring.example')}:\n\n"
+            ret += PREFIX + f"**{get_text(lang, 'docstring.example')}**:\n\n"
             for example in self.example:
-                ret += PREFIX + f"- {example.desc}\n        Input: {example.input}\n        Output: {example.output}\n\n"
+                ret += PREFIX + f"- {example.desc}\n        **{get_text(lang, 'docs.input')}**: {example.input}\n        **{get_text(lang, 'docs.output')}**: {example.output}\n\n"
         return ret
 
     def __str__(self):

litedoc/docstring/parser.py

@@ -3,7 +3,7 @@ Google docstring parser for Python.
 """
 from typing import Optional
 
-from liteyuki_autodoc.docstring.docstring import Docstring
+from litedoc.docstring.docstring import Docstring
 
 
 class Parser:
@@ -52,10 +52,30 @@ class GoogleDocstringParser(Parser):
 
         self.docstring = Docstring()
 
+    def read_line(self, move: bool = True) -> str:
+        """
+        每次读取一行
+        Args:
+            move: 是否移动指针
+        Returns:
+        """
+        if self.lineno >= len(self.lines):
+            return ""
+        line = self.lines[self.lineno]
+        if move:
+            self.lineno += 1
+        return line
+
     def match_token(self) -> Optional[str]:
+        """
+        解析下一行的token
+        Returns:
+
+        """
         for token in self._tokens:
-            if self.lines[self.lineno][self.char:].startswith(token):
+            line = self.read_line(move=False)
-                self.char += len(token)
+            if line.strip().startswith(token):
+                self.lineno += 1
                 return self._tokens[token]
         return None
 
@@ -115,17 +135,12 @@ class GoogleDocstringParser(Parser):
         在一个子解析器中，解析下一行，直到缩进小于等于当前行的缩进
         Returns:
         """
-        while (self.lineno + 1) < len(self.lines):
+        line = self.read_line(move=False)
-            line = self.lines[self.lineno + 1]
+        if line.startswith(" " * self.indent):
-            if line.startswith(" " * self.indent):
+            self.lineno += 1
-                line = line[self.indent:]
+            return line[self.indent:]
-                self.lineno += 1
+        else:
-                return line
+            return None
-            else:
-                self.lineno += 1
-                return None
-        self.lineno += 1
-        return None
 
     def parse(self) -> Docstring:
         """

litedoc/i18n.py

@@ -9,7 +9,7 @@ NestedDict: TypeAlias = dict[str, 'str | NestedDict']
 i18n_dict: dict[str, NestedDict] = {
         "en"     : {
                 "docstring": {
-                        "args"     : "Args",
+                        "args"     : "Arguments",
                         "return"   : "Return",
                         "attribute": "Attribute",
                         "raises"   : "Raises",
@@ -17,6 +17,8 @@ i18n_dict: dict[str, NestedDict] = {
                         "yields"   : "Yields",
                 },
                 "src": "Source code",
+                "desc": "Description",
+                "type": "Type",
         },
         "zh-Hans": {
                 "docstring": {
@@ -27,18 +29,22 @@ i18n_dict: dict[str, NestedDict] = {
                         "example"  : "示例",
                         "yields"   : "产出",
                 },
-                "src": "源码",
+                "src": "源代码",
+                "desc": "说明",
+                "type": "类型",
         },
         "zh-Hant": {
                 "docstring": {
-                        "args"     : "參數",
+                        "args"     : "變數説明",
                         "return"   : "返回",
                         "attribute": "屬性",
-                        "raises"   : "引發",
+                        "raises"   : "抛出",
-                        "example"  : "示例",
+                        "example"  : "範例",
                         "yields"   : "產出",
                 },
                 "src": "源碼",
+                "desc": "説明",
+                "type": "類型",
         },
         "ja"     : {
                 "docstring": {
@@ -50,6 +56,8 @@ i18n_dict: dict[str, NestedDict] = {
                         "yields"   : "生成",
                 },
                 "src": "ソースコード",
+                "desc": "説明",
+                "type": "タイプ",
         },
 }
 

litedoc/output.py

@@ -10,8 +10,8 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
 """
 import os.path
 
-from liteyuki_autodoc.style.markdown import generate
+from litedoc.style.markdown import generate
-from liteyuki_autodoc.syntax.astparser import AstParser
+from litedoc.syntax.astparser import AstParser
 
 
 def write_to_file(content: str, output: str) -> None:

litedoc/style/markdown.py

@@ -10,9 +10,9 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
 """
 from typing import Optional
 
-from liteyuki_autodoc.syntax.astparser import AstParser
+from litedoc.syntax.astparser import AstParser
-from liteyuki_autodoc.syntax.node import *
+from litedoc.syntax.node import *
-from liteyuki_autodoc.i18n import get_text
+from litedoc.i18n import get_text
 
 
 def generate(parser: AstParser, lang: str, frontmatter: Optional[dict] = None) -> str:
@@ -36,24 +36,24 @@ def generate(parser: AstParser, lang: str, frontmatter: Optional[dict] = None) -
 
     # var > func > class
 
+    """遍历函数"""
     for func in parser.functions:
+        if func.name.startswith("_"):
+            continue
         md += func.markdown(lang)
 
+    """遍历类"""
+
     for cls in parser.classes:
-        md += f"### ***class*** `{cls.name}`\n\n"
+        md += cls.markdown(lang)
-        for mtd in cls.methods:
-            md += mtd.markdown(lang, 2, True)
-
-        for attr in cls.attrs:
-            if attr.type == TypeHint.NO_TYPEHINT:
-                md += f"#### ***attr*** `{attr.name} = {attr.value}`\n\n"
-            else:
-                md += f"#### ***attr*** `{attr.name}: {attr.type} = {attr.value}`\n\n"
 
+    """遍历变量"""
     for var in parser.variables:
-        if var.type == TypeHint.NO_TYPEHINT:
+        md += f"### ***var*** `{var.name} = {var.value}`\n\n"
-            md += f"### ***var*** `{var.name} = {var.value}`\n\n"
+        if var.type != TypeHint.NO_TYPEHINT:
-        else:
+            md += f"- **{get_text(lang, 'type')}**: `{var.type}`\n\n"
-            md += f"### ***var*** `{var.name}: {var.type} = {var.value}`\n\n"
+
+        if var.docs is not None:
+            md += f"- **{get_text(lang, 'desc')}**: {var.docs}\n\n"
 
     return md

litedoc/syntax/astparser.py

@@ -9,11 +9,11 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
 @Software: PyCharm
 """
 import ast
+import inspect
 
 from .node import *
 from ..docstring.parser import parse
 
-
 class AstParser:
     def __init__(self, code: str):
         self.code = code
@@ -25,6 +25,51 @@ class AstParser:
 
         self.parse()
 
+    @staticmethod
+    def clear_quotes(s: str) -> str:
+        """
+        去除类型注解中的引号
+        Args:
+            s:
+        Returns:
+        """
+        return s.replace("'", "").replace('"', "")
+
+    def get_line_content(self, lineno: int, ignore_index_out: bool = True) -> str:
+        """获取代码行内容
+        Args:
+            lineno: 行号
+            ignore_index_out: 是否忽略索引越界
+        Returns:
+            代码行内容
+        """
+        if ignore_index_out:
+            if lineno < 1 or lineno > len(self.code.split("\n")):
+                return ""
+        return self.code.split("\n")[lineno - 1]
+
+    @staticmethod
+    def match_line_docs(linecontent: str) -> str:
+        """匹配行内注释
+        Args:
+            linecontent: 行内容
+        Returns:
+            文档字符串
+        """
+        in_string = False
+        string_char = ''
+        for i, char in enumerate(linecontent):
+            if char in ('"', "'"):
+                if in_string:
+                    if char == string_char:
+                        in_string = False
+                else:
+                    in_string = True
+                    string_char = char
+            elif char == '#' and not in_string:
+                return linecontent[i + 1:].strip()
+        return ""
+
     def parse(self):
         for node in ast.walk(self.tree):
             if isinstance(node, ast.ClassDef):
@@ -47,21 +92,21 @@ class AstParser:
                             posonlyargs=[
                                     ArgNode(
                                         name=arg.arg,
-                                        type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                        type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                                     )
                                     for arg in sub_node.args.posonlyargs
                             ],
                             args=[
                                     ArgNode(
                                         name=arg.arg,
-                                        type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                        type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                                     )
                                     for arg in sub_node.args.args
                             ],
                             kwonlyargs=[
                                     ArgNode(
                                         name=arg.arg,
-                                        type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                        type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                                     )
                                     for arg in sub_node.args.kwonlyargs
                             ],
@@ -77,26 +122,27 @@ class AstParser:
                                     )
                                     for default in sub_node.args.defaults
                             ],
-                            return_=ast.unparse(sub_node.returns).strip() if sub_node.returns else TypeHint.NO_RETURN,
+                            return_=self.clear_quotes(ast.unparse(sub_node.returns).strip()) if sub_node.returns else TypeHint.NO_RETURN,
                             decorators=[ast.unparse(decorator).strip() for decorator in sub_node.decorator_list],
                             is_async=isinstance(sub_node, ast.AsyncFunctionDef),
-                            src=ast.unparse(sub_node).strip()
+                            src=ast.unparse(sub_node).strip(),
+                            is_classmethod=True
                         ))
-                    elif isinstance(sub_node, (ast.Assign, ast.AnnAssign)):
+                    # elif isinstance(sub_node, (ast.Assign, ast.AnnAssign)):
-                        if isinstance(sub_node, ast.Assign):
+                    #     if isinstance(sub_node, ast.Assign):
-                            class_node.attrs.append(AttrNode(
+                    #         class_node.attrs.append(AttrNode(
-                                name=sub_node.targets[0].id,  # type: ignore
+                    #             name=sub_node.targets[0].id,  # type: ignore
-                                type=TypeHint.NO_TYPEHINT,
+                    #             type=TypeHint.NO_TYPEHINT,
-                                value=ast.unparse(sub_node.value).strip()
+                    #             value=ast.unparse(sub_node.value).strip()
-                            ))
+                    #         ))
-                        elif isinstance(sub_node, ast.AnnAssign):
+                    #     elif isinstance(sub_node, ast.AnnAssign):
-                            class_node.attrs.append(AttrNode(
+                    #         class_node.attrs.append(AttrNode(
-                                name=sub_node.target.id,
+                    #             name=sub_node.target.id,
-                                type=ast.unparse(sub_node.annotation).strip(),
+                    #             type=ast.unparse(sub_node.annotation).strip(),
-                                value=ast.unparse(sub_node.value).strip() if sub_node.value else TypeHint.NO_DEFAULT
+                    #             value=ast.unparse(sub_node.value).strip() if sub_node.value else TypeHint.NO_DEFAULT
-                            ))
+                    #         ))
-                        else:
+                    #     else:
-                            raise ValueError(f"Unsupported node type: {type(sub_node)}")
+                    #         raise ValueError(f"Unsupported node type: {type(sub_node)}")
 
             elif isinstance(node, (ast.FunctionDef, ast.AsyncFunctionDef)):
                 # 仅打印模块级别的函数
@@ -109,21 +155,21 @@ class AstParser:
                     posonlyargs=[
                             ArgNode(
                                 name=arg.arg,
-                                type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                             )
                             for arg in node.args.posonlyargs
                     ],
                     args=[
                             ArgNode(
                                 name=arg.arg,
-                                type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                             )
                             for arg, default in zip(node.args.args, node.args.defaults)
                     ],
                     kwonlyargs=[
                             ArgNode(
                                 name=arg.arg,
-                                type=ast.unparse(arg.annotation).strip() if arg.annotation else TypeHint.NO_TYPEHINT,
+                                type=self.clear_quotes(ast.unparse(arg.annotation).strip()) if arg.annotation else TypeHint.NO_TYPEHINT,
                             )
                             for arg in node.args.kwonlyargs
                     ],
@@ -139,7 +185,7 @@ class AstParser:
                             )
                             for default in node.args.defaults
                     ],
-                    return_=ast.unparse(node.returns).strip() if node.returns else TypeHint.NO_RETURN,
+                    return_=self.clear_quotes(ast.unparse(node.returns).strip()) if node.returns else TypeHint.NO_RETURN,
                     decorators=[ast.unparse(decorator).strip() for decorator in node.decorator_list],
                     is_async=isinstance(node, ast.AsyncFunctionDef),
                     src=ast.unparse(node).strip()
@@ -147,23 +193,40 @@ class AstParser:
 
             elif isinstance(node, (ast.Assign, ast.AnnAssign)):
                 if not self._is_module_level_variable2(node):
-                    # print("变量不在模块级别", ast.unparse(node))
                     continue
                 else:
                     pass
-                if isinstance(node, ast.Assign):
+                lineno = node.lineno
-                    for target in node.targets:
+                prev_line = self.get_line_content(lineno - 1).strip()
-                        if isinstance(target, ast.Name):
+                curr_line = self.get_line_content(lineno).strip()
-                            self.variables.append(AssignNode(
+                next_line = self.get_line_content(lineno + 1).strip()
-                                name=target.id,
+
-                                value=ast.unparse(node.value).strip(),
+                # 获取文档字符串，优先检测下行"""
-                                type=ast.unparse(node.annotation).strip() if isinstance(node, ast.AnnAssign) else TypeHint.NO_TYPEHINT
+                if next_line.startswith('"""'):
-                            ))
+                    docs = next_line[3:-3]
-                elif isinstance(node, ast.AnnAssign):
+                elif prev_line.startswith('"""'):
+                    docs = prev_line[3:-3]
+                else:
+                    curr_docs = self.match_line_docs(curr_line)
+                    if curr_docs:
+                        docs = curr_docs
+                    else:
+                        docs = None
+
+                # if isinstance(node, ast.Assign):
+                #     for target in node.targets:
+                #         if isinstance(target, ast.Name):
+                #             self.variables.append(AssignNode(
+                #                 name=target.id,
+                #                 value=ast.unparse(node.value).strip(),
+                #                 type=ast.unparse(node.annotation).strip() if isinstance(node, ast.AnnAssign) else TypeHint.NO_TYPEHINT
+                #             ))
+                if isinstance(node, ast.AnnAssign):
                     self.variables.append(AssignNode(
                         name=node.target.id,
                         value=ast.unparse(node.value).strip() if node.value else TypeHint.NO_DEFAULT,
-                        type=ast.unparse(node.annotation).strip()
+                        type=ast.unparse(node.annotation).strip(),
+                        docs=docs
                     ))
 
     def _is_module_level_function(self, node: ast.FunctionDef | ast.AsyncFunctionDef):

litedoc/syntax/node.py

@@ -13,8 +13,8 @@ from enum import Enum
 
 from pydantic import BaseModel, Field
 
-from liteyuki_autodoc.docstring.docstring import Docstring
+from litedoc.docstring.docstring import Docstring
-from liteyuki_autodoc.i18n import get_text
+from litedoc.i18n import get_text
 
 
 class TypeHint:
@@ -37,6 +37,7 @@ class AssignNode(BaseModel):
     name: str
     type: str = ""
     value: str
+    docs: Optional[str] = ""
 
 
 class ArgNode(BaseModel):
@@ -123,6 +124,22 @@ class FunctionNode(BaseModel):
     decorators: list[str] = []
     src: str
     is_async: bool = False
+    is_classmethod: bool = False
+
+    magic_methods: dict[str, str] = {
+            "__add__"    : "+",
+            "__radd__"   : "+",
+            "__sub__"    : "-",
+            "__rsub__"   : "-",
+            "__mul__"    : "*",
+            "__rmul__"   : "*",
+            "__matmul__" : "@",
+            "__rmatmul__": "@",
+            "__mod__"    : "%",
+            "__truediv__": "/",
+            "__rtruediv__": "/",
+            "__neg__"    : "-",
+    }  # 魔术方法, 例如运算符
 
     def is_private(self):
         """
@@ -140,12 +157,11 @@ class FunctionNode(BaseModel):
         """
         return self.name.startswith("__") and self.name.endswith("__")
 
-    def markdown(self, lang: str, indent: int = 0, is_classmethod: bool = False) -> str:
+    def markdown(self, lang: str, indent: int = 0) -> str:
         """
         Args:
             indent: int
                 The number of spaces to indent the markdown.
-            is_classmethod: bool
             lang: str
                 The language of the
         Returns:
@@ -155,21 +171,20 @@ class FunctionNode(BaseModel):
         PREFIX = "" * indent
         # if is_classmethod:
         #     PREFIX = "- #"
+        func_type = "func" if not self.is_classmethod else "method"
 
         md = ""
-
         # 装饰器部分
         if len(self.decorators) > 0:
             for decorator in self.decorators:
                 md += PREFIX + f"### `@{decorator}`\n"
 
         if self.is_async:
-            md += PREFIX + "### *async def* "
+            md += PREFIX + f"### *async {func_type}* "
         else:
-            md += PREFIX + "### *def* "
+            md += PREFIX + f"### *{func_type}* "
-
-        md += f"`{self.name}("  # code start
 
+        # code start
         # 配对位置参数和位置参数默认值，无默认值用TypeHint.NO_DEFAULT
         args: list[str] = []  # 可直接", ".join(args)得到位置参数部分
         arg_i = 0
@@ -204,25 +219,33 @@ class FunctionNode(BaseModel):
                 arg_text = f"{arg.name}"
                 if arg.type != TypeHint.NO_TYPEHINT:
                     arg_text += f": {arg.type}"
-
                 if kw_default.value != TypeHint.NO_DEFAULT:
                     arg_text += f" = {kw_default.value}"
                 args.append(arg_text)
 
-        md += ", ".join(args) + ")"
+        """魔法方法"""
-
+        if self.name in self.magic_methods:
-        if self.return_ != TypeHint.NO_RETURN:
+            if len(args) == 2:
-            md += f" -> {self.return_}"
+                md += f"`{args[0]} {self.magic_methods[self.name]} {args[1]}"
+            elif len(args) == 1:
+                md += f"`{self.magic_methods[self.name]} {args[0]}"
+            if self.return_ != TypeHint.NO_RETURN:
+                md += f" => {self.return_}"
+        else:
+            md += f"`{self.name}("  # code start
+            md += ", ".join(args) + ")"
+            if self.return_ != TypeHint.NO_RETURN:
+                md += f" -> {self.return_}"
 
         md += "`\n\n"  # code end
 
         """此处预留docstring"""
         if self.docs is not None:
-            md += f"\n{self.docs.markdown(lang, indent, is_classmethod)}\n"
+            md += f"\n{self.docs.markdown(lang, indent)}\n"
         else:
             pass
         # 源码展示
-        md += PREFIX + f"\n<details>\n<summary>{get_text(lang, 'src')}</summary>\n\n```python\n{self.src}\n```\n</details>\n\n"
+        md += PREFIX + f"\n<details>\n<summary> <i>{get_text(lang, 'src')}</i> </summary>\n\n```python\n{self.src}\n```\n</details>\n\n"
 
         return md
 
@@ -251,11 +274,41 @@ class ClassNode(BaseModel):
             The attributes of the class.
         methods: list[MethodNode] = []
             The methods of the class.
-        inherit: list["ClassNode"] = []
+        inherits: list["ClassNode"] = []
             The classes that the class inherits from
     """
     name: str
     docs: Optional[Docstring] = None
     attrs: list[AttrNode] = []
     methods: list[FunctionNode] = []
-    inherit: list["ClassNode"] = []
+    inherits: list[str] = []
+
+    def markdown(self, lang: str) -> str:
+        """
+        返回类的markdown文档
+        Args:
+            lang: str
+                The language of the
+        Returns:
+            markdown style document
+        """
+        hidden_methods = [
+                "__str__",
+                "__repr__",
+        ]
+        md = ""
+        md += f"### **class** `{self.name}"
+        if len(self.inherits) > 0:
+            md += f"({', '.join([cls for cls in self.inherits])})"
+        md += "`\n"
+        for method in self.methods:
+            if method.name in hidden_methods:
+                continue
+            md += method.markdown(lang, 2)
+        for attr in self.attrs:
+            if attr.type == TypeHint.NO_TYPEHINT:
+                md += f"#### ***attr*** `{attr.name} = {attr.value}`\n\n"
+            else:
+                md += f"#### ***attr*** `{attr.name}: {attr.type} = {attr.value}`\n\n"
+
+        return md

litedoc/translator.py

@@ -0,0 +1,47 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/29 下午12:02
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : translator.py
+@Software: PyCharm
+"""
+from typing import Optional
+
+from translate import Translator  # type: ignore
+
+# 特殊映射语言
+i18n_lang2googletrans_lang = {
+        "zh-Hans": "zh-cn",
+        "zh-Hant": "zh-tw",
+        "en"     : "en",
+}
+
+
+def get_google_lang(lang: str) -> str:
+    """
+    Get google translate language
+    Args:
+        lang: language
+    Returns:
+        google translate language
+    """
+    return i18n_lang2googletrans_lang.get(lang, lang)
+
+
+def translate(text: str, lang: str, source_lang: str) -> str:
+    """
+    Translate text to target language
+    Args:
+        source_lang:
+        text: text
+        lang: target language
+    Returns:
+        translated text
+    """
+    if lang == source_lang:
+        return text
+    google_lang = get_google_lang(lang)
+    return Translator(to_lang=google_lang, from_lang=source_lang).translate(text)

mbcp/mp_math/plane.py

@@ -22,10 +22,10 @@ class Plane3:
         """
         平面方程：ax + by + cz + d = 0
         Args:
-            a:
+            a: x系数
-            b:
+            b: y系数
-            c:
+            c: z系数
-            d:
+            d: 常数项
         """
         self.a = a
         self.b = b
@@ -36,13 +36,10 @@ class Plane3:
         """
         判断两个平面是否近似相等。
         Args:
-            other:
+            other: 另一个平面
-
         Returns:
             是否近似相等
         """
-
-        a = 3   # 测试变量
         if self.a != 0:
             k = other.a / self.a
             return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
@@ -91,11 +88,11 @@ class Plane3:
 
     def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
         """
-        计算两平面的交线。该方法有问题，待修复。
+        计算两平面的交线。
         Args:
             other: 另一个平面
         Returns:
-            交线
+            两平面的交线
         Raises:
         """
         if self.normal.is_parallel(other.normal):
@@ -105,6 +102,7 @@ class Plane3:
         x, y, z = 0, 0, 0
         # 依次判断条件假设x=0, y=0, z=0，找到合适的点
         # 先假设其中一个系数不为0，则令此坐标为0，构建增广矩阵，解出另外两个坐标
+
         if self.a != 0 and other.a != 0:
             A = np.array([[self.b, self.c], [other.b, other.c]])
             B = np.array([-self.d, -other.d])
@@ -146,7 +144,7 @@ class Plane3:
         Args:
             point: 指定点
         Returns:
-            平面
+            所求平面
         """
         return Plane3.from_point_and_normal(point, self.normal)
 

mbcp/mp_math/utils.py

@@ -22,11 +22,11 @@ if TYPE_CHECKING:
 
 def clamp(x: float, min_: float, max_: float) -> float:
     """
-    区间截断函数。
+    区间限定函数
     Args:
-        x:
+        x: 待限定的值
-        min_:
+        min_: 最小值
-        max_:
+        max_: 最大值
 
     Returns:
         限制后的值
@@ -40,7 +40,6 @@ class Approx:
 
     已实现对象 实数 Vector3 Point3 Plane3 Line3
     """
-
     def __init__(self, value: RealNumber):
         self.value = value
 
@@ -67,10 +66,9 @@ def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
-        x:
+        x: 数1
-        y:
+        y: 数2
-        epsilon:
+        epsilon: 误差
-
     Returns:
         是否近似相等
     """

mbcp/mp_math/vector.py

@@ -263,11 +263,11 @@ class Vector3:
         return f"Vector3({self.x}, {self.y}, {self.z})"
 
 
-zero_vector3 = Vector3(0, 0, 0)
+zero_vector3: Vector3 = Vector3(0, 0, 0)
 """零向量"""
-x_axis = Vector3(1, 0, 0)
+x_axis: Vector3 = Vector3(1, 0, 0)
 """x轴单位向量"""
-y_axis = Vector3(0, 1, 0)
+y_axis: Vector3 = Vector3(0, 1, 0)
 """y轴单位向量"""
-z_axis = Vector3(0, 0, 1)
+z_axis: Vector3 = Vector3(0, 0, 1)
 """z轴单位向量"""

mkdoc.bat

@@ -0,0 +1,4 @@
+python -m litedoc mbcp -o docs/api -l zh-Hans
+python -m litedoc mbcp -o docs/en/api -l en
+python -m litedoc mbcp -o docs/ja/api -l ja
+python -m litedoc mbcp -o docs/zht/api -l zh-Hant

pyproject.toml

@@ -21,3 +21,8 @@ build-backend = "pdm.backend"
 
 [tool.pdm]
 distribution = true
+
+[tool.pdm.dev-dependencies]
+dev = [
+    "translate>=3.6.1",
+]

tests/test_doc_translator.py

@@ -0,0 +1,16 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/29 下午12:06
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : test_doc_translator.py
+@Software: PyCharm
+"""
+
+from litedoc.translator import translate
+
+
+def test():
+    print(translate("Hello, world!", "Chinese", "English"))