From 7018a25beb36211abf8ab0d9d7cb3d96b4a9c606 Mon Sep 17 00:00:00 2001
From: snowykami <snowykami@outlook.com>
Date: Fri, 6 Sep 2024 15:42:16 +0800
Subject: [PATCH] :memo: docs: add some tips

---
 docs/.vitepress/config/common.ts              |  2 +-
 docs/.vitepress/theme/index.ts                | 27 ++++++++++++++++++-
 docs/zh/refer/7-differential-euqtion/index.md |  5 ++++
 mbcp/mp_math/plane.py                         | 25 +++++++++++++++--
 mbcp/mp_math/vector.py                        | 27 +++++++++----------
 pyproject.toml                                |  2 +-
 6 files changed, 69 insertions(+), 19 deletions(-)
 create mode 100644 docs/zh/refer/7-differential-euqtion/index.md

diff --git a/docs/.vitepress/config/common.ts b/docs/.vitepress/config/common.ts
index 50925d5..32cb237 100644
--- a/docs/.vitepress/config/common.ts
+++ b/docs/.vitepress/config/common.ts
@@ -1,7 +1,7 @@
 // 共有配置项，导入index用
-
 import {defineConfig} from 'vitepress'
 import {generateSidebar} from 'vitepress-sidebar';
+import {useData} from "vitepress";
 import {zh} from "./zh";
 import {en} from "./en";
 import {ja} from "./ja";
diff --git a/docs/.vitepress/theme/index.ts b/docs/.vitepress/theme/index.ts
index 254c539..631772e 100644
--- a/docs/.vitepress/theme/index.ts
+++ b/docs/.vitepress/theme/index.ts
@@ -1,4 +1,29 @@
 import DefaultTheme from 'vitepress/theme-without-fonts'
+import Theme from 'vitepress/theme'
+import {createI18n} from 'vue-i18n'
 import './fonts.css'
 
-export default DefaultTheme
\ No newline at end of file
+const i18n = createI18n({
+    // something vue-i18n options here ..
+    messages: {
+        en: {
+            tip: "TIP",
+        },
+        ja: {
+            tip: "ヒント",
+        },
+        zh: {
+            tip: "提示",
+        },
+        zht: {
+            tip: "提示",
+        }
+    }
+})
+
+export default {
+    extends: Theme,
+    enhanceApp({app}) {
+        app.use(i18n)
+    }
+}
\ No newline at end of file
diff --git a/docs/zh/refer/7-differential-euqtion/index.md b/docs/zh/refer/7-differential-euqtion/index.md
new file mode 100644
index 0000000..270c37e
--- /dev/null
+++ b/docs/zh/refer/7-differential-euqtion/index.md
@@ -0,0 +1,5 @@
+---
+title: 微分方程
+---
+
+# 微分方程
diff --git a/mbcp/mp_math/plane.py b/mbcp/mp_math/plane.py
index d874287..32b2426 100644
--- a/mbcp/mp_math/plane.py
+++ b/mbcp/mp_math/plane.py
@@ -52,8 +52,18 @@ class Plane3:
             return False
 
     def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-        """
+        r"""
         计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\theta = \arccos(\frac{n1 \cdot n2}{|n1| \cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\theta = \arccos(\frac{n \cdot d}{|n| \cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
         Args:
             other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
         Returns:
@@ -86,8 +96,19 @@ class Plane3:
             raise TypeError(f"Unsupported type: {type(other)}")
 
     def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-        """
+        r"""
         计算两平面的交线。
+        :::tip {{ $t('tip') }}
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \begin{cases} x = x_0 + dt \\ y = y_0 + dt \\ z = z_0 + dt \end{cases} $$
+        或
+        $$ \frac{x - x_0}{m} = \frac{y - y_0}{n} = \frac{z - z_0}{p} $$
+        :::
+
         Args:
             other ([`Plane3`](./plane#class-plane3)): 另一个平面
         Returns:
diff --git a/mbcp/mp_math/vector.py b/mbcp/mp_math/vector.py
index a6102b6..d2d020d 100644
--- a/mbcp/mp_math/vector.py
+++ b/mbcp/mp_math/vector.py
@@ -40,8 +40,12 @@ class Vector3:
         return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
 
     def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
-        """
+        r"""
         计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\theta = \arccos(\frac{v1 \cdot v2}{|v1| \cdot |v2|})$$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
@@ -50,20 +54,15 @@ class Vector3:
         return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
 
     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``
+        r"""
+        向量积 叉乘：v1 x v2 -> v3
 
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \times v2 = (v1_y \cdot v2_z - v1_z \cdot v2_y, v1_z \cdot v2_x - v1_x \cdot v2_z, v1_x \cdot v2_y - v1_y \cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \times v2 = \begin{vmatrix} i & j & k \\ v1_x & v1_y & v1_z \\ v2_x & v2_y & v2_z \end{vmatrix} $$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
diff --git a/pyproject.toml b/pyproject.toml
index a130ecf..fd29375 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -6,7 +6,7 @@ authors = [
     {name = "snowykami", email = "snowykami@outlook.com"},
 ]
 dependencies = [
-    "numpy~=2.0.1",
+    "numpy>=2.1.1",
     "liteyukibot>=6.3.9",
 ]
 requires-python = ">=3.10"