From 23793296603e37f81dbb4e7b5a7c4cc51f53c830 Mon Sep 17 00:00:00 2001 From: snowykami Date: Wed, 28 Aug 2024 04:03:02 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20docs=20from=20@=20snowykami/mb?= =?UTF-8?q?cp@f26d189ecd4f72168d9713b58b7362b265de7431=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .nojekyll | 0 404.html | 21 ++ api-ex.html | 57 ++++ api/index.html | 24 ++ api/mp_math/angle.html | 125 +++++++++ api/mp_math/const.html | 24 ++ api/mp_math/equation.html | 79 ++++++ api/mp_math/index.html | 24 ++ api/mp_math/line.html | 216 ++++++++++++++++ api/mp_math/mp_math_typing.html | 24 ++ api/mp_math/plane.html | 243 ++++++++++++++++++ api/mp_math/point.html | 53 ++++ api/mp_math/segment.html | 37 +++ api/mp_math/utils.html | 97 +++++++ api/mp_math/vector.html | 139 ++++++++++ api/particle/index.html | 24 ++ api/presets/index.html | 24 ++ api/presets/model/index.html | 66 +++++ assets/api-ex.md.DOsKaL8H.js | 16 ++ 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create mode 100644 assets/inter-italic-greek-ext.1u6EdAuj.woff2 create mode 100644 assets/inter-italic-greek.DJ8dCoTZ.woff2 create mode 100644 assets/inter-italic-latin-ext.CN1xVJS-.woff2 create mode 100644 assets/inter-italic-latin.C2AdPX0b.woff2 create mode 100644 assets/inter-italic-vietnamese.BSbpV94h.woff2 create mode 100644 assets/inter-roman-cyrillic-ext.BBPuwvHQ.woff2 create mode 100644 assets/inter-roman-cyrillic.C5lxZ8CY.woff2 create mode 100644 assets/inter-roman-greek-ext.CqjqNYQ-.woff2 create mode 100644 assets/inter-roman-greek.BBVDIX6e.woff2 create mode 100644 assets/inter-roman-latin-ext.4ZJIpNVo.woff2 create mode 100644 assets/inter-roman-latin.Di8DUHzh.woff2 create mode 100644 assets/inter-roman-vietnamese.BjW4sHH5.woff2 create mode 100644 assets/md-ex.md.BX0WqOqv.js create mode 100644 assets/md-ex.md.BX0WqOqv.lean.js create mode 100644 assets/style.Bb0QBJmh.css create mode 100644 hashmap.json create mode 100644 index.html create mode 100644 md-ex.html diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 0000000..e69de29 diff --git a/404.html b/404.html new file mode 100644 index 0000000..3c5c336 --- /dev/null +++ b/404.html @@ -0,0 +1,21 @@ + + + + + + 404 | MBCP docs + + + + + + + + + + +
+ + + + \ No newline at end of file diff --git a/api-ex.html b/api-ex.html new file mode 100644 index 0000000..931de17 --- /dev/null +++ b/api-ex.html @@ -0,0 +1,57 @@ + + + + + + Runtime API Examples | MBCP docs + + + + + + + + + + + + + +
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Runtime API Examples ​

This page demonstrates usage of some of the runtime APIs provided by VitePress.

The main useData() API can be used to access site, theme, and page data for the current page. It works in both .md and .vue files:

md
<script setup>
+import { useData } from 'vitepress'
+
+const { theme, page, frontmatter } = useData()
+</script>
+
+## Results
+
+### Theme Data
+<pre>{{ theme }}</pre>
+
+### Page Data
+<pre>{{ page }}</pre>
+
+### Page Frontmatter
+<pre>{{ frontmatter }}</pre>

Results ​

Theme Data ​

{
+  "socialLinks": [
+    {
+      "icon": "github",
+      "link": "https://github.com/snowykami/mbcp"
+    }
+  ]
+}

Page Data ​

{
+  "title": "Runtime API Examples",
+  "description": "",
+  "frontmatter": {
+    "outline": "deep"
+  },
+  "headers": [],
+  "relativePath": "api-ex.md",
+  "filePath": "api-ex.md"
+}

Page Frontmatter ​

{
+  "outline": "deep"
+}

More ​

Check out the documentation for the full list of runtime APIs.

+ + + + \ No newline at end of file diff --git a/api/index.html b/api/index.html new file mode 100644 index 0000000..a6a05f2 --- /dev/null +++ b/api/index.html @@ -0,0 +1,24 @@ + + + + + + mbcp.\n\ninit\n\n | MBCP docs + + + + + + + + + + + + + +
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+ + + + \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html new file mode 100644 index 0000000..d696950 --- /dev/null +++ b/api/mp_math/angle.html @@ -0,0 +1,125 @@ + + + + + + mbcp.mp\nmath.angle | MBCP docs + + + + + + + + + + + + + +
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class AnyAngle ​

  def __init__(self, value: float, is_radian: bool) -> None ​

 任意角度。

Args:

value: 角度或弧度值
+
+is_radian: 是否为弧度，默认为否
+
源代码
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

  @property ​

  def complementary(self: Any) -> 'AnyAngle' ​

 余角：两角的和为90°。

Returns:

余角
+
源代码
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)

  @property ​

  def supplementary(self: Any) -> 'AnyAngle' ​

 补角：两角的和为180°。

Returns:

补角
+
源代码
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)

  @property ​

  def degree(self: Any) -> float ​

 角度。

Returns:

弧度
+
源代码
python
@property
+def degree(self) -> float:
+    """
+        角度。
+        Returns:
+            弧度
+        """
+    return self.radian * 180 / PI

  @property ​

  def minimum_positive(self: Any) -> 'AnyAngle' ​

 最小正角。

Returns:

最小正角度
+
源代码
python
@property
+def minimum_positive(self) -> 'AnyAngle':
+    """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+    return AnyAngle(self.radian % (2 * PI))

  @property ​

  def maximum_negative(self: Any) -> 'AnyAngle' ​

 最大负角。

Returns:

最大负角度
+
源代码
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)

  @property ​

  def sin(self: Any) -> float ​

 正弦值。

Returns:

正弦值
+
源代码
python
@property
+def sin(self) -> float:
+    """
+        正弦值。
+        Returns:
+            正弦值
+        """
+    return math.sin(self.radian)

  @property ​

  def cos(self: Any) -> float ​

 余弦值。

Returns:

余弦值
+
源代码
python
@property
+def cos(self) -> float:
+    """
+        余弦值。
+        Returns:
+            余弦值
+        """
+    return math.cos(self.radian)

  @property ​

  def tan(self: Any) -> float ​

 正切值。

Returns:

正切值
+
源代码
python
@property
+def tan(self) -> float:
+    """
+        正切值。
+        Returns:
+            正切值
+        """
+    return math.tan(self.radian)

  @property ​

  def cot(self: Any) -> float ​

 余切值。

Returns:

余切值
+
源代码
python
@property
+def cot(self) -> float:
+    """
+        余切值。
+        Returns:
+            余切值
+        """
+    return 1 / math.tan(self.radian)

  @property ​

  def sec(self: Any) -> float ​

 正割值。

Returns:

正割值
+
源代码
python
@property
+def sec(self) -> float:
+    """
+        正割值。
+        Returns:
+            正割值
+        """
+    return 1 / math.cos(self.radian)

  @property ​

  def csc(self: Any) -> float ​

 余割值。

Returns:

余割值
+
源代码
python
@property
+def csc(self) -> float:
+    """
+        余割值。
+        Returns:
+            余割值
+        """
+    return 1 / math.sin(self.radian)
+ + + + \ No newline at end of file diff --git a/api/mp_math/const.html b/api/mp_math/const.html new file mode 100644 index 0000000..527ccae --- /dev/null +++ b/api/mp_math/const.html @@ -0,0 +1,24 @@ + + + + + + mbcp.mp\nmath.const | MBCP docs + + + + + + + + + + + + + +
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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 ​

+ + + + \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html new file mode 100644 index 0000000..0ea964b --- /dev/null +++ b/api/mp_math/equation.html @@ -0,0 +1,79 @@ + + + + + + mbcp.mp\nmath.equation | MBCP docs + + + + + + + + + + + + + +
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def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number) -> 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
+
源代码
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')

def partial_derivative_func() -> Var ​

源代码
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)

def high_order_partial_derivative_func() -> Var ​

源代码
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)

class CurveEquation ​

  def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) -> None ​

 曲线方程。

:param x_func:

:param y_func:

:param z_func:

源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    """
+        曲线方程。
+        :param x_func:
+        :param y_func:
+        :param z_func:
+        """
+    self.x_func = x_func
+    self.y_func = y_func
+    self.z_func = z_func

var args_list_plus = list(args) ​

var args_list_minus = list(args) ​

var result_func = func ​

var result_func = get_partial_derivative_func(result_func, v, epsilon) ​

+ + + + \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html new file mode 100644 index 0000000..36a8ec5 --- /dev/null +++ b/api/mp_math/index.html @@ -0,0 +1,24 @@ + + + + + + mbcp.mp\nmath.\n\ninit\n\n | MBCP docs + + + + + + + + + + + + + +
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+ + + + \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html new file mode 100644 index 0000000..84932ef --- /dev/null +++ b/api/mp_math/line.html @@ -0,0 +1,216 @@ + + + + + + mbcp.mp\nmath.line | MBCP docs + + + + + + + + + + + + + +
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class Line3 ​

  def __init__(self, point: 'Point3', direction: 'Vector3') -> None ​

 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
+
源代码
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

  def approx(self, other: 'Line3', epsilon: float) -> 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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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.')

  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
+
源代码
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

  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
+
源代码
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))

  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
+
源代码
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

  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)
+
源代码
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)

  def is_approx_parallel(self, other: 'Line3', epsilon: float) -> 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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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

  def simplify(self) -> None ​

 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

源代码
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

  @classmethod ​

  def from_two_points(cls: Any, 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
+
源代码
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)

var direction = p2 - p1 ​

var s = 'Line3: ' ​

+ + + + \ No newline at end of file diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html new file mode 100644 index 0000000..f39333e --- /dev/null +++ b/api/mp_math/mp_math_typing.html @@ -0,0 +1,24 @@ + + + + + + mbcp.mp\nmath.mp\nmath\ntyping | MBCP docs + + + + + + + + + + + + + +
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var SingleVar = TypeVar('SingleVar', bound=Number) ​

var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​

+ + + + \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html new file mode 100644 index 0000000..2e7bd78 --- /dev/null +++ b/api/mp_math/plane.html @@ -0,0 +1,243 @@ + + + + + + mbcp.mp\nmath.plane | MBCP docs + + + + + + + + + + + + + +
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class Plane3 ​

  def __init__(self, a: float, b: float, c: float, d: float) -> None ​

 平面方程：ax + by + cz + d = 0

Args:

a:
+
+b:
+
+c:
+
+d:
+
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a:
+            b:
+            c:
+            d:
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

  def approx(self, other: 'Plane3', epsilon: float) -> bool ​

 判断两个平面是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
python
def approx(self, other: 'Plane3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        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

  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
+
源代码
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)}')

  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
+
源代码
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)}')

  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。

Args:

other: 另一个平面
+

Returns:

交线
+

Raises:

源代码
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。
+        Args:
+            other: 另一个平面
+        Returns:
+            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)

  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
+
源代码
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))

  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:

平面
+
源代码
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:
+            平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

  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
+
源代码
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)

  @property ​

  def normal(self: Any) -> 'Vector3' ​

 平面的法向量。

Returns:

法向量
+
源代码
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+    return Vector3(self.a, self.b, self.c)

  @classmethod ​

  def from_point_and_normal(cls: Any, 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
+
源代码
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)

  @classmethod ​

  def from_three_points(cls: Any, 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
+
源代码
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)

  @classmethod ​

  def from_two_lines(cls: Any, 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
+
源代码
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))

  @classmethod ​

  def from_point_and_line(cls: Any, 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
+
源代码
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)

var direction = self.normal.cross(other.normal) ​

var 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) ​

var d = -a * point.x - b * point.y - c * point.z ​

var v1 = p2 - p1 ​

var v2 = p3 - p1 ​

var normal = v1.cross(v2) ​

var v1 = l1.direction ​

var v2 = l2.point - l1.point ​

var s = 'Plane3: ' ​

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]) ​

+ + + + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html new file mode 100644 index 0000000..5d38d3d --- /dev/null +++ b/api/mp_math/point.html @@ -0,0 +1,53 @@ + + + + + + mbcp.mp\nmath.point | MBCP docs + + + + + + + + + + + + + +
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class Point3 ​

  def __init__(self, x: float, y: float, z: float) -> None ​

 笛卡尔坐标系中的点。

Args:

x: x 坐标
+
+y: y 坐标
+
+z: z 坐标
+
源代码
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

  def approx(self, other: 'Point3', epsilon: float) -> bool ​

 判断两个点是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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])
+ + + + \ No newline at end of file diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html new file mode 100644 index 0000000..378c75d --- /dev/null +++ b/api/mp_math/segment.html @@ -0,0 +1,37 @@ + + + + + + mbcp.mp\nmath.segment | MBCP docs + + + + + + + + + + + + + +
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class Segment3 ​

  def __init__(self, p1: 'Point3', p2: 'Point3') -> None ​

 三维空间中的线段。

:param p1:

:param p2:

源代码
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)
+ + + + \ No newline at end of file diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html new file mode 100644 index 0000000..e5322b1 --- /dev/null +++ b/api/mp_math/utils.html @@ -0,0 +1,97 @@ + + + + + + mbcp.mp\nmath.utils | MBCP docs + + + + + + + + + + + + + +
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def clamp(x: float, min_: float, max_: float) -> float ​

区间截断函数。

Args:

x:
+
+min_:
+
+max_:
+

Returns:

限制后的值
+
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+    """
+    区间截断函数。
+    Args:
+        x:
+        min_:
+        max_:
+
+    Returns:
+        限制后的值
+    """
+    return max(min(x, max_), min_)

def approx(x: float, y: float, epsilon: float) -> 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:
+
+y:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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:
+        y:
+        epsilon:
+
+    Returns:
+        是否近似相等
+    """
+    return abs(x - y) < epsilon

def sign(x: float, only_neg: bool) -> 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 + - ""
+
源代码
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 ''

def sign_format(x: float, only_neg: bool) -> 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 + - ""
+
源代码
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 ''

class Approx ​

用于近似比较对象

已实现对象 实数 Vector3 Point3 Plane3 Line3

  def __init__(self, value: RealNumber) -> None ​

 

源代码
python
def __init__(self, value: RealNumber):
+    self.value = value

  def raise_type_error(self, other: Any) -> None ​

 

源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
+ + + + \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html new file mode 100644 index 0000000..7445219 --- /dev/null +++ b/api/mp_math/vector.html @@ -0,0 +1,139 @@ + + + + + + mbcp.mp\nmath.vector | MBCP docs + + + + + + + + + + + + + +
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class Vector3 ​

  def __init__(self, x: float, y: float, z: float) -> None ​

 3维向量

Args:

x: x轴分量
+
+y: y轴分量
+
+z: z轴分量
+
源代码
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

  def approx(self, other: 'Vector3', epsilon: float) -> bool ​

 判断两个向量是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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])

  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
+
源代码
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)

  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
+
源代码
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)

  def is_approx_parallel(self, other: 'Vector3', epsilon: float) -> 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
+
源代码
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

  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
+
源代码
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)

  def normalize(self) -> None ​

 将向量归一化。

自体归一化，不返回值。

源代码
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

  @property ​

  def np_array(self: Any) -> 'np.ndarray' ​

 返回numpy数组

Returns:

源代码
python
@property
+def np_array(self) -> 'np.ndarray':
+    """
+        返回numpy数组
+        Returns:
+        """
+    return np.array([self.x, self.y, self.z])

  @property ​

  def length(self: Any) -> float ​

 向量的模。

Returns:

模
+
源代码
python
@property
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            模
+        """
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

  @property ​

  def unit(self: Any) -> 'Vector3' ​

 获取该向量的单位向量。

Returns:

单位向量
+
源代码
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

var zero_vector3 = Vector3(0, 0, 0) ​

var x_axis = Vector3(1, 0, 0) ​

var y_axis = Vector3(0, 1, 0) ​

var z_axis = Vector3(0, 0, 1) ​

var length = self.length ​

+ + + + \ No newline at end of file diff --git a/api/particle/index.html b/api/particle/index.html new file mode 100644 index 0000000..fb560ac --- /dev/null +++ b/api/particle/index.html @@ -0,0 +1,24 @@ + + + + + + mbcp.particle.\n\ninit\n\n | MBCP docs + + + + + + + + + + + + + +
MBCP docs

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+ + + + \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html new file mode 100644 index 0000000..17c9720 --- /dev/null +++ b/api/presets/index.html @@ -0,0 +1,24 @@ + + + + + + mbcp.presets.\n\ninit\n\n | MBCP docs + + + + + + + + + + + + + +
MBCP docs

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+ + + + \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html new file mode 100644 index 0000000..19dfbff --- /dev/null +++ b/api/presets/model/index.html @@ -0,0 +1,66 @@ + + + + + + mbcp.presets.model.\n\ninit\n\n | MBCP docs + + + + + + + + + + + + + +
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def sphere(radius: float, density: float) -> None ​

生成球体上的点集。

Args:

radius:
+
+density:
+

Returns:

List[Point3]: 球体上的点集。
+
源代码
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)]

class GeometricModels ​

  @staticmethod ​

  def sphere(radius: float, density: float) -> None ​

 生成球体上的点集。

Args:

radius:
+
+density:
+

Returns:

List[Point3]: 球体上的点集。
+
源代码
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)]

var area = 4 * np.pi * radius ** 2 ​

var num = int(area * density) ​

var phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)]) ​

var theta_list = np.sqrt(num * np.pi) * phi_list ​

var x_array = radius * np.sin(phi_list) * np.cos(theta_list) ​

var y_array = radius * np.sin(phi_list) * np.sin(theta_list) ​

var z_array = radius * np.cos(phi_list) ​

+ + + + \ No newline at end of file diff --git a/assets/api-ex.md.DOsKaL8H.js b/assets/api-ex.md.DOsKaL8H.js new file mode 100644 index 0000000..8273956 --- /dev/null +++ b/assets/api-ex.md.DOsKaL8H.js @@ -0,0 +1,16 @@ +import{u as h,c as p,j as s,t as i,k as e,a2 as r,a,o as k}from"./chunks/framework.BV61Qrc0.js";const d=r(`

Runtime API Examples ​

This page demonstrates usage of some of the runtime APIs provided by VitePress.

The main useData() API can be used to access site, theme, and page data for the current page. It works in both .md and .vue files:

md
<script setup>
+import { useData } from 'vitepress'
+
+const { theme, page, frontmatter } = useData()
+</script>
+
+## Results
+
+### Theme Data
+<pre>{{ theme }}</pre>
+
+### Page Data
+<pre>{{ page }}</pre>
+
+### Page Frontmatter
+<pre>{{ frontmatter }}</pre>

Results ​

Theme Data ​

`,6),o=s("h3",{id:"page-data",tabindex:"-1"},[a("Page Data "),s("a",{class:"header-anchor",href:"#page-data","aria-label":'Permalink to "Page Data"'},"​")],-1),E=s("h3",{id:"page-frontmatter",tabindex:"-1"},[a("Page Frontmatter "),s("a",{class:"header-anchor",href:"#page-frontmatter","aria-label":'Permalink to "Page Frontmatter"'},"​")],-1),g=s("h2",{id:"more",tabindex:"-1"},[a("More "),s("a",{class:"header-anchor",href:"#more","aria-label":'Permalink to "More"'},"​")],-1),c=s("p",null,[a("Check out the documentation for the "),s("a",{href:"https://vitepress.dev/reference/runtime-api#usedata",target:"_blank",rel:"noreferrer"},"full list of runtime APIs"),a(".")],-1),D=JSON.parse('{"title":"Runtime API Examples","description":"","frontmatter":{"outline":"deep"},"headers":[],"relativePath":"api-ex.md","filePath":"api-ex.md"}'),m={name:"api-ex.md"},F=Object.assign(m,{setup(u){const{site:y,theme:t,page:n,frontmatter:l}=h();return(_,f)=>(k(),p("div",null,[d,s("pre",null,i(e(t)),1),o,s("pre",null,i(e(n)),1),E,s("pre",null,i(e(l)),1),g,c]))}});export{D as __pageData,F as default}; diff --git a/assets/api-ex.md.DOsKaL8H.lean.js b/assets/api-ex.md.DOsKaL8H.lean.js new file mode 100644 index 0000000..686b36e --- /dev/null +++ b/assets/api-ex.md.DOsKaL8H.lean.js @@ -0,0 +1 @@ +import{u as h,c as p,j as s,t as i,k as e,a2 as r,a,o as k}from"./chunks/framework.BV61Qrc0.js";const d=r("",6),o=s("h3",{id:"page-data",tabindex:"-1"},[a("Page Data "),s("a",{class:"header-anchor",href:"#page-data","aria-label":'Permalink to "Page Data"'},"​")],-1),E=s("h3",{id:"page-frontmatter",tabindex:"-1"},[a("Page Frontmatter "),s("a",{class:"header-anchor",href:"#page-frontmatter","aria-label":'Permalink to "Page Frontmatter"'},"​")],-1),g=s("h2",{id:"more",tabindex:"-1"},[a("More "),s("a",{class:"header-anchor",href:"#more","aria-label":'Permalink to "More"'},"​")],-1),c=s("p",null,[a("Check out the documentation for the "),s("a",{href:"https://vitepress.dev/reference/runtime-api#usedata",target:"_blank",rel:"noreferrer"},"full list of runtime APIs"),a(".")],-1),D=JSON.parse('{"title":"Runtime API Examples","description":"","frontmatter":{"outline":"deep"},"headers":[],"relativePath":"api-ex.md","filePath":"api-ex.md"}'),m={name:"api-ex.md"},F=Object.assign(m,{setup(u){const{site:y,theme:t,page:n,frontmatter:l}=h();return(_,f)=>(k(),p("div",null,[d,s("pre",null,i(e(t)),1),o,s("pre",null,i(e(n)),1),E,s("pre",null,i(e(l)),1),g,c]))}});export{D as __pageData,F as default}; diff --git a/assets/api_index.md.CsKClHFh.js b/assets/api_index.md.CsKClHFh.js new file mode 100644 index 0000000..5e98a95 --- /dev/null +++ b/assets/api_index.md.CsKClHFh.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/index.md","filePath":"api/index.md"}'),a={name:"api/index.md"};function i(o,r,c,p,d,s){return n(),t("div")}const l=e(a,[["render",i]]);export{_ as __pageData,l as default}; diff --git a/assets/api_index.md.CsKClHFh.lean.js b/assets/api_index.md.CsKClHFh.lean.js new file mode 100644 index 0000000..5e98a95 --- /dev/null +++ b/assets/api_index.md.CsKClHFh.lean.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/index.md","filePath":"api/index.md"}'),a={name:"api/index.md"};function i(o,r,c,p,d,s){return n(),t("div")}const l=e(a,[["render",i]]);export{_ as __pageData,l as default}; diff --git a/assets/api_mp_math_angle.md.9eUTSIe4.js b/assets/api_mp_math_angle.md.9eUTSIe4.js new file mode 100644 index 0000000..94733bd --- /dev/null +++ b/assets/api_mp_math_angle.md.9eUTSIe4.js @@ -0,0 +1,102 @@ +import{_ as s,c as a,o as i,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp\\\\nmath.angle","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.angle","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),e={name:"api/mp_math/angle.md"},t=n(`

class AnyAngle ​

  def __init__(self, value: float, is_radian: bool) -> None ​

 任意角度。

Args:

value: 角度或弧度值
+
+is_radian: 是否为弧度，默认为否
+
源代码
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

  @property ​

  def complementary(self: Any) -> 'AnyAngle' ​

 余角：两角的和为90°。

Returns:

余角
+
源代码
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)

  @property ​

  def supplementary(self: Any) -> 'AnyAngle' ​

 补角：两角的和为180°。

Returns:

补角
+
源代码
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)

  @property ​

  def degree(self: Any) -> float ​

 角度。

Returns:

弧度
+
源代码
python
@property
+def degree(self) -> float:
+    """
+        角度。
+        Returns:
+            弧度
+        """
+    return self.radian * 180 / PI

  @property ​

  def minimum_positive(self: Any) -> 'AnyAngle' ​

 最小正角。

Returns:

最小正角度
+
源代码
python
@property
+def minimum_positive(self) -> 'AnyAngle':
+    """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+    return AnyAngle(self.radian % (2 * PI))

  @property ​

  def maximum_negative(self: Any) -> 'AnyAngle' ​

 最大负角。

Returns:

最大负角度
+
源代码
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)

  @property ​

  def sin(self: Any) -> float ​

 正弦值。

Returns:

正弦值
+
源代码
python
@property
+def sin(self) -> float:
+    """
+        正弦值。
+        Returns:
+            正弦值
+        """
+    return math.sin(self.radian)

  @property ​

  def cos(self: Any) -> float ​

 余弦值。

Returns:

余弦值
+
源代码
python
@property
+def cos(self) -> float:
+    """
+        余弦值。
+        Returns:
+            余弦值
+        """
+    return math.cos(self.radian)

  @property ​

  def tan(self: Any) -> float ​

 正切值。

Returns:

正切值
+
源代码
python
@property
+def tan(self) -> float:
+    """
+        正切值。
+        Returns:
+            正切值
+        """
+    return math.tan(self.radian)

  @property ​

  def cot(self: Any) -> float ​

 余切值。

Returns:

余切值
+
源代码
python
@property
+def cot(self) -> float:
+    """
+        余切值。
+        Returns:
+            余切值
+        """
+    return 1 / math.tan(self.radian)

  @property ​

  def sec(self: Any) -> float ​

 正割值。

Returns:

正割值
+
源代码
python
@property
+def sec(self) -> float:
+    """
+        正割值。
+        Returns:
+            正割值
+        """
+    return 1 / math.cos(self.radian)

  @property ​

  def csc(self: Any) -> float ​

 余割值。

Returns:

余割值
+
源代码
python
@property
+def csc(self) -> float:
+    """
+        余割值。
+        Returns:
+            余割值
+        """
+    return 1 / math.sin(self.radian)
`,72),p=[t];function l(h,k,r,d,o,y){return i(),a("div",null,p)}const c=s(e,[["render",l]]);export{F as __pageData,c as default}; diff --git a/assets/api_mp_math_angle.md.9eUTSIe4.lean.js b/assets/api_mp_math_angle.md.9eUTSIe4.lean.js new file mode 100644 index 0000000..a668d4f --- /dev/null +++ b/assets/api_mp_math_angle.md.9eUTSIe4.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp\\\\nmath.angle","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.angle","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),e={name:"api/mp_math/angle.md"},t=n("",72),p=[t];function l(h,k,r,d,o,y){return i(),a("div",null,p)}const c=s(e,[["render",l]]);export{F as __pageData,c as default}; diff --git a/assets/api_mp_math_const.md.Bhz27OPg.js b/assets/api_mp_math_const.md.Bhz27OPg.js new file mode 100644 index 0000000..3a2275d --- /dev/null +++ b/assets/api_mp_math_const.md.Bhz27OPg.js @@ -0,0 +1 @@ +import{_ as a,c as e,o as t,a2 as r}from"./chunks/framework.BV61Qrc0.js";const v=JSON.parse('{"title":"mbcp.mp\\\\nmath.const","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.const","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"api/mp_math/const.md"}'),o={name:"api/mp_math/const.md"},n=r('

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 ​

',6),s=[n];function m(c,h,i,d,l,p){return t(),e("div",null,s)}const P=a(o,[["render",m]]);export{v as __pageData,P as default}; diff --git a/assets/api_mp_math_const.md.Bhz27OPg.lean.js b/assets/api_mp_math_const.md.Bhz27OPg.lean.js new file mode 100644 index 0000000..11fcd53 --- /dev/null +++ b/assets/api_mp_math_const.md.Bhz27OPg.lean.js @@ -0,0 +1 @@ +import{_ as a,c as e,o as t,a2 as r}from"./chunks/framework.BV61Qrc0.js";const v=JSON.parse('{"title":"mbcp.mp\\\\nmath.const","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.const","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"api/mp_math/const.md"}'),o={name:"api/mp_math/const.md"},n=r("",6),s=[n];function m(c,h,i,d,l,p){return t(),e("div",null,s)}const P=a(o,[["render",m]]);export{v as __pageData,P as default}; diff --git a/assets/api_mp_math_equation.md.xiyFVY1c.js b/assets/api_mp_math_equation.md.xiyFVY1c.js new file mode 100644 index 0000000..ed33888 --- /dev/null +++ b/assets/api_mp_math_equation.md.xiyFVY1c.js @@ -0,0 +1,56 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp\\\\nmath.equation","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.equation","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n(`

def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number) -> 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
+
源代码
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')

def partial_derivative_func() -> Var ​

源代码
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)

def high_order_partial_derivative_func() -> Var ​

源代码
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)

class CurveEquation ​

  def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) -> None ​

 曲线方程。

:param x_func:

:param y_func:

:param z_func:

源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    """
+        曲线方程。
+        :param x_func:
+        :param y_func:
+        :param z_func:
+        """
+    self.x_func = x_func
+    self.y_func = y_func
+    self.z_func = z_func

var args_list_plus = list(args) ​

var args_list_minus = list(args) ​

var result_func = func ​

var result_func = get_partial_derivative_func(result_func, v, epsilon) ​

`,24),e=[l];function h(p,k,r,d,E,g){return a(),i("div",null,e)}const o=s(t,[["render",h]]);export{u as __pageData,o as default}; diff --git a/assets/api_mp_math_equation.md.xiyFVY1c.lean.js b/assets/api_mp_math_equation.md.xiyFVY1c.lean.js new file mode 100644 index 0000000..3b86eb7 --- /dev/null +++ b/assets/api_mp_math_equation.md.xiyFVY1c.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp\\\\nmath.equation","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.equation","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",24),e=[l];function h(p,k,r,d,E,g){return a(),i("div",null,e)}const o=s(t,[["render",h]]);export{u as __pageData,o as default}; diff --git a/assets/api_mp_math_index.md.DTIfeUA1.js b/assets/api_mp_math_index.md.DTIfeUA1.js new file mode 100644 index 0000000..2362a78 --- /dev/null +++ b/assets/api_mp_math_index.md.DTIfeUA1.js @@ -0,0 +1 @@ +import{_ as t,c as e,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.mp\\\\nmath.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/index.md","filePath":"api/mp_math/index.md"}'),a={name:"api/mp_math/index.md"};function i(p,o,m,r,c,d){return n(),e("div")}const h=t(a,[["render",i]]);export{_ as __pageData,h as default}; diff --git a/assets/api_mp_math_index.md.DTIfeUA1.lean.js b/assets/api_mp_math_index.md.DTIfeUA1.lean.js new file mode 100644 index 0000000..2362a78 --- /dev/null +++ b/assets/api_mp_math_index.md.DTIfeUA1.lean.js @@ -0,0 +1 @@ +import{_ as t,c as e,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.mp\\\\nmath.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/index.md","filePath":"api/mp_math/index.md"}'),a={name:"api/mp_math/index.md"};function i(p,o,m,r,c,d){return n(),e("div")}const h=t(a,[["render",i]]);export{_ as __pageData,h as default}; diff --git a/assets/api_mp_math_line.md.BybnyRUL.js b/assets/api_mp_math_line.md.BybnyRUL.js new file mode 100644 index 0000000..c0b376e --- /dev/null +++ b/assets/api_mp_math_line.md.BybnyRUL.js @@ -0,0 +1,193 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp\\\\nmath.line","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.line","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),e={name:"api/mp_math/line.md"},l=n(`

class Line3 ​

  def __init__(self, point: 'Point3', direction: 'Vector3') -> None ​

 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
+
源代码
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

  def approx(self, other: 'Line3', epsilon: float) -> 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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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.')

  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
+
源代码
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

  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
+
源代码
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))

  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
+
源代码
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

  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)
+
源代码
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)

  def is_approx_parallel(self, other: 'Line3', epsilon: float) -> 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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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)

  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
+
源代码
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

  def simplify(self) -> None ​

 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

源代码
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

  @classmethod ​

  def from_two_points(cls: Any, 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
+
源代码
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)

var direction = p2 - p1 ​

var s = 'Line3: ' ​

`,110),p=[l];function t(h,k,r,d,o,g){return a(),i("div",null,p)}const c=s(e,[["render",t]]);export{E as __pageData,c as default}; diff --git a/assets/api_mp_math_line.md.BybnyRUL.lean.js b/assets/api_mp_math_line.md.BybnyRUL.lean.js new file mode 100644 index 0000000..a5a9e33 --- /dev/null +++ b/assets/api_mp_math_line.md.BybnyRUL.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp\\\\nmath.line","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.line","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),e={name:"api/mp_math/line.md"},l=n("",110),p=[l];function t(h,k,r,d,o,g){return a(),i("div",null,p)}const c=s(e,[["render",t]]);export{E as __pageData,c as default}; diff --git a/assets/api_mp_math_mp_math_typing.md.DXaadYgy.js b/assets/api_mp_math_mp_math_typing.md.DXaadYgy.js new file mode 100644 index 0000000..3796359 --- /dev/null +++ b/assets/api_mp_math_mp_math_typing.md.DXaadYgy.js @@ -0,0 +1 @@ +import{_ as a,c as r,o as e,a2 as t}from"./chunks/framework.BV61Qrc0.js";const b=JSON.parse('{"title":"mbcp.mp\\\\nmath.mp\\\\nmath\\\\ntyping","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.mp\\\\nmath\\\\ntyping","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/mp_math_typing.md","filePath":"api/mp_math/mp_math_typing.md"}'),n={name:"api/mp_math/mp_math_typing.md"},o=t('

var SingleVar = TypeVar('SingleVar', bound=Number) ​

var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​

',2),m=[o];function p(i,_,d,s,c,l){return e(),r("div",null,m)}const u=a(n,[["render",p]]);export{b as __pageData,u as default}; diff --git a/assets/api_mp_math_mp_math_typing.md.DXaadYgy.lean.js b/assets/api_mp_math_mp_math_typing.md.DXaadYgy.lean.js new file mode 100644 index 0000000..ff2adae --- /dev/null +++ b/assets/api_mp_math_mp_math_typing.md.DXaadYgy.lean.js @@ -0,0 +1 @@ +import{_ as a,c as r,o as e,a2 as t}from"./chunks/framework.BV61Qrc0.js";const b=JSON.parse('{"title":"mbcp.mp\\\\nmath.mp\\\\nmath\\\\ntyping","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.mp\\\\nmath\\\\ntyping","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/mp_math_typing.md","filePath":"api/mp_math/mp_math_typing.md"}'),n={name:"api/mp_math/mp_math_typing.md"},o=t("",2),m=[o];function p(i,_,d,s,c,l){return e(),r("div",null,m)}const u=a(n,[["render",p]]);export{b as __pageData,u as default}; diff --git a/assets/api_mp_math_plane.md.Cdj0PlKB.js b/assets/api_mp_math_plane.md.Cdj0PlKB.js new file mode 100644 index 0000000..cb489f6 --- /dev/null +++ b/assets/api_mp_math_plane.md.Cdj0PlKB.js @@ -0,0 +1,220 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.plane","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.plane","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`

class Plane3 ​

  def __init__(self, a: float, b: float, c: float, d: float) -> None ​

 平面方程：ax + by + cz + d = 0

Args:

a:
+
+b:
+
+c:
+
+d:
+
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a:
+            b:
+            c:
+            d:
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

  def approx(self, other: 'Plane3', epsilon: float) -> bool ​

 判断两个平面是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
python
def approx(self, other: 'Plane3', epsilon: float=APPROX) -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other:
+            epsilon:
+
+        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

  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
+
源代码
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)}')

  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
+
源代码
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)}')

  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。

Args:

other: 另一个平面
+

Returns:

交线
+

Raises:

源代码
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。
+        Args:
+            other: 另一个平面
+        Returns:
+            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)

  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
+
源代码
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))

  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:

平面
+
源代码
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:
+            平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

  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
+
源代码
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)

  @property ​

  def normal(self: Any) -> 'Vector3' ​

 平面的法向量。

Returns:

法向量
+
源代码
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+    return Vector3(self.a, self.b, self.c)

  @classmethod ​

  def from_point_and_normal(cls: Any, 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
+
源代码
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)

  @classmethod ​

  def from_three_points(cls: Any, 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
+
源代码
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)

  @classmethod ​

  def from_two_lines(cls: Any, 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
+
源代码
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))

  @classmethod ​

  def from_point_and_line(cls: Any, 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
+
源代码
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)

var direction = self.normal.cross(other.normal) ​

var 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) ​

var d = -a * point.x - b * point.y - c * point.z ​

var v1 = p2 - p1 ​

var v2 = p3 - p1 ​

var normal = v1.cross(v2) ​

var v1 = l1.direction ​

var v2 = l2.point - l1.point ​

var s = 'Plane3: ' ​

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]) ​

`,119),t=[h];function e(p,k,r,d,o,E){return a(),i("div",null,t)}const F=s(l,[["render",e]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_plane.md.Cdj0PlKB.lean.js b/assets/api_mp_math_plane.md.Cdj0PlKB.lean.js new file mode 100644 index 0000000..ba3f172 --- /dev/null +++ b/assets/api_mp_math_plane.md.Cdj0PlKB.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.plane","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.plane","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n("",119),t=[h];function e(p,k,r,d,o,E){return a(),i("div",null,t)}const F=s(l,[["render",e]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_point.md.D3f-vzVt.js b/assets/api_mp_math_point.md.D3f-vzVt.js new file mode 100644 index 0000000..5d4d56f --- /dev/null +++ b/assets/api_mp_math_point.md.D3f-vzVt.js @@ -0,0 +1,30 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.point","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.point","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),t={name:"api/mp_math/point.md"},l=n(`

class Point3 ​

  def __init__(self, x: float, y: float, z: float) -> None ​

 笛卡尔坐标系中的点。

Args:

x: x 坐标
+
+y: y 坐标
+
+z: z 坐标
+
源代码
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

  def approx(self, other: 'Point3', epsilon: float) -> bool ​

 判断两个点是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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])
`,13),p=[l];function h(e,k,o,r,d,E){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_point.md.D3f-vzVt.lean.js b/assets/api_mp_math_point.md.D3f-vzVt.lean.js new file mode 100644 index 0000000..af38377 --- /dev/null +++ b/assets/api_mp_math_point.md.D3f-vzVt.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.point","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.point","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),t={name:"api/mp_math/point.md"},l=n("",13),p=[l];function h(e,k,o,r,d,E){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_segment.md.DIViBThe.js b/assets/api_mp_math_segment.md.DIViBThe.js new file mode 100644 index 0000000..92632ee --- /dev/null +++ b/assets/api_mp_math_segment.md.DIViBThe.js @@ -0,0 +1,14 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp\\\\nmath.segment","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.segment","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n(`

class Segment3 ​

  def __init__(self, p1: 'Point3', p2: 'Point3') -> None ​

 三维空间中的线段。

:param p1:

:param p2:

源代码
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)
`,6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default}; diff --git a/assets/api_mp_math_segment.md.DIViBThe.lean.js b/assets/api_mp_math_segment.md.DIViBThe.lean.js new file mode 100644 index 0000000..79b1fab --- /dev/null +++ b/assets/api_mp_math_segment.md.DIViBThe.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp\\\\nmath.segment","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.segment","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n("",6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default}; diff --git a/assets/api_mp_math_utils.md.CDwq4icO.js b/assets/api_mp_math_utils.md.CDwq4icO.js new file mode 100644 index 0000000..8bd265a --- /dev/null +++ b/assets/api_mp_math_utils.md.CDwq4icO.js @@ -0,0 +1,74 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.utils","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.utils","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),t={name:"api/mp_math/utils.md"},l=n(`

def clamp(x: float, min_: float, max_: float) -> float ​

区间截断函数。

Args:

x:
+
+min_:
+
+max_:
+

Returns:

限制后的值
+
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+    """
+    区间截断函数。
+    Args:
+        x:
+        min_:
+        max_:
+
+    Returns:
+        限制后的值
+    """
+    return max(min(x, max_), min_)

def approx(x: float, y: float, epsilon: float) -> 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:
+
+y:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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:
+        y:
+        epsilon:
+
+    Returns:
+        是否近似相等
+    """
+    return abs(x - y) < epsilon

def sign(x: float, only_neg: bool) -> 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 + - ""
+
源代码
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 ''

def sign_format(x: float, only_neg: bool) -> 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 + - ""
+
源代码
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 ''

class Approx ​

用于近似比较对象

已实现对象 实数 Vector3 Point3 Plane3 Line3

  def __init__(self, value: RealNumber) -> None ​

 

源代码
python
def __init__(self, value: RealNumber):
+    self.value = value

  def raise_type_error(self, other: Any) -> None ​

 

源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
`,40),p=[l];function h(e,k,r,d,o,g){return a(),i("div",null,p)}const E=s(t,[["render",h]]);export{y as __pageData,E as default}; diff --git a/assets/api_mp_math_utils.md.CDwq4icO.lean.js b/assets/api_mp_math_utils.md.CDwq4icO.lean.js new file mode 100644 index 0000000..f89f56a --- /dev/null +++ b/assets/api_mp_math_utils.md.CDwq4icO.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.utils","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.utils","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),t={name:"api/mp_math/utils.md"},l=n("",40),p=[l];function h(e,k,r,d,o,g){return a(),i("div",null,p)}const E=s(t,[["render",h]]);export{y as __pageData,E as default}; diff --git a/assets/api_mp_math_vector.md.BgK1TmFY.js b/assets/api_mp_math_vector.md.BgK1TmFY.js new file mode 100644 index 0000000..a82fc7a --- /dev/null +++ b/assets/api_mp_math_vector.md.BgK1TmFY.js @@ -0,0 +1,116 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.vector","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.vector","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),e={name:"api/mp_math/vector.md"},t=n(`

class Vector3 ​

  def __init__(self, x: float, y: float, z: float) -> None ​

 3维向量

Args:

x: x轴分量
+
+y: y轴分量
+
+z: z轴分量
+
源代码
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

  def approx(self, other: 'Vector3', epsilon: float) -> bool ​

 判断两个向量是否近似相等。

Args:

other:
+
+epsilon:
+

Returns:

是否近似相等
+
源代码
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])

  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
+
源代码
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)

  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
+
源代码
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)

  def is_approx_parallel(self, other: 'Vector3', epsilon: float) -> 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
+
源代码
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

  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
+
源代码
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)

  def normalize(self) -> None ​

 将向量归一化。

自体归一化，不返回值。

源代码
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

  @property ​

  def np_array(self: Any) -> 'np.ndarray' ​

 返回numpy数组

Returns:

源代码
python
@property
+def np_array(self) -> 'np.ndarray':
+    """
+        返回numpy数组
+        Returns:
+        """
+    return np.array([self.x, self.y, self.z])

  @property ​

  def length(self: Any) -> float ​

 向量的模。

Returns:

模
+
源代码
python
@property
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            模
+        """
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

  @property ​

  def unit(self: Any) -> 'Vector3' ​

 获取该向量的单位向量。

Returns:

单位向量
+
源代码
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

var zero_vector3 = Vector3(0, 0, 0) ​

var x_axis = Vector3(1, 0, 0) ​

var y_axis = Vector3(0, 1, 0) ​

var z_axis = Vector3(0, 0, 1) ​

var length = self.length ​

`,73),l=[t];function p(h,k,r,o,d,g){return a(),i("div",null,l)}const F=s(e,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_vector.md.BgK1TmFY.lean.js b/assets/api_mp_math_vector.md.BgK1TmFY.lean.js new file mode 100644 index 0000000..c02c385 --- /dev/null +++ b/assets/api_mp_math_vector.md.BgK1TmFY.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp\\\\nmath.vector","description":"","frontmatter":{"title":"mbcp.mp\\\\nmath.vector","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),e={name:"api/mp_math/vector.md"},t=n("",73),l=[t];function p(h,k,r,o,d,g){return a(),i("div",null,l)}const F=s(e,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/api_particle_index.md.BqH-w2FR.js b/assets/api_particle_index.md.BqH-w2FR.js new file mode 100644 index 0000000..46b9b1e --- /dev/null +++ b/assets/api_particle_index.md.BqH-w2FR.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as a}from"./chunks/framework.BV61Qrc0.js";const m=JSON.parse('{"title":"mbcp.particle.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.particle.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/particle/index.md","filePath":"api/particle/index.md"}'),n={name:"api/particle/index.md"};function i(r,c,p,o,d,s){return a(),t("div")}const _=e(n,[["render",i]]);export{m as __pageData,_ as default}; diff --git a/assets/api_particle_index.md.BqH-w2FR.lean.js b/assets/api_particle_index.md.BqH-w2FR.lean.js new file mode 100644 index 0000000..46b9b1e --- /dev/null +++ b/assets/api_particle_index.md.BqH-w2FR.lean.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as a}from"./chunks/framework.BV61Qrc0.js";const m=JSON.parse('{"title":"mbcp.particle.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.particle.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/particle/index.md","filePath":"api/particle/index.md"}'),n={name:"api/particle/index.md"};function i(r,c,p,o,d,s){return a(),t("div")}const _=e(n,[["render",i]]);export{m as __pageData,_ as default}; diff --git a/assets/api_presets_index.md.CvgR5vOS.js b/assets/api_presets_index.md.CvgR5vOS.js new file mode 100644 index 0000000..4baa138 --- /dev/null +++ b/assets/api_presets_index.md.CvgR5vOS.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.presets.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.presets.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/presets/index.md","filePath":"api/presets/index.md"}'),r={name:"api/presets/index.md"};function s(a,i,p,o,c,d){return n(),t("div")}const l=e(r,[["render",s]]);export{_ as __pageData,l as default}; diff --git a/assets/api_presets_index.md.CvgR5vOS.lean.js b/assets/api_presets_index.md.CvgR5vOS.lean.js new file mode 100644 index 0000000..4baa138 --- /dev/null +++ b/assets/api_presets_index.md.CvgR5vOS.lean.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as n}from"./chunks/framework.BV61Qrc0.js";const _=JSON.parse('{"title":"mbcp.presets.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.presets.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/presets/index.md","filePath":"api/presets/index.md"}'),r={name:"api/presets/index.md"};function s(a,i,p,o,c,d){return n(),t("div")}const l=e(r,[["render",s]]);export{_ as __pageData,l as default}; diff --git a/assets/api_presets_model_index.md.D1iZ1qEr.js b/assets/api_presets_model_index.md.D1iZ1qEr.js new file mode 100644 index 0000000..b06171a --- /dev/null +++ b/assets/api_presets_model_index.md.D1iZ1qEr.js @@ -0,0 +1,43 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model.\\\\n\\\\ninit\\\\n\\\\n","description":"","frontmatter":{"title":"mbcp.presets.model.\\\\n\\\\ninit\\\\n\\\\n","order":1,"icon":"laptop-code","category":"API"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`

def sphere(radius: float, density: float) -> None ​

生成球体上的点集。

Args:

radius:
+
+density:
+

Returns:

List[Point3]: 球体上的点集。
+
源代码
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)]

class GeometricModels ​

  @staticmethod ​

  def sphere(radius: float, density: float) -> None ​

 生成球体上的点集。

Args:

radius:
+
+density:
+

Returns:

List[Point3]: 球体上的点集。
+
源代码
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)]

var area = 4 * np.pi * radius ** 2 ​

var num = int(area * density) ​

var phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)]) ​

var theta_list = np.sqrt(num * np.pi) * phi_list ​

var x_array = radius * np.sin(phi_list) * np.cos(theta_list) ​

var y_array = radius * np.sin(phi_list) * np.sin(theta_list) ​

var z_array = radius * np.cos(phi_list) ​

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zizzp}Vpq>(cbwuS_@9HIZtsc|D5OR4;l-OjO419|G9^OaSh#HmuQn3__U4^%zn z3zgSqZxa>eaxJTKUNVOv6Uo z`X5fo9Yr~HBKacaY3`IbR;|aks-P`>O1VkOG_I>{NTDuSv`m+}h$cZj>CC@RMLedAtNKe_txQ}ii6@>>mJd?Ca++0|y0RHN9eQpvSJW5EsC|Cvl}f(r qg8F^wNJLW9HXag++f*3l>qLgABq|+GP_C@lsDY~<*Z+^97XScAUqWF3 literal 0 HcmV?d00001 diff --git a/assets/md-ex.md.BX0WqOqv.js b/assets/md-ex.md.BX0WqOqv.js new file mode 100644 index 0000000..31360cd --- /dev/null +++ b/assets/md-ex.md.BX0WqOqv.js @@ -0,0 +1,33 @@ +import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const g=JSON.parse('{"title":"Markdown Extension Examples","description":"","frontmatter":{},"headers":[],"relativePath":"md-ex.md","filePath":"md-ex.md"}'),t={name:"md-ex.md"},e=n(`

This page demonstrates some of the built-in markdown extensions provided by VitePress.

Syntax Highlighting ​

VitePress provides Syntax Highlighting powered by Shiki, with additional features like line-highlighting:

Input

md
\`\`\`js{4}
+export default {
+  data () {
+    return {
+      msg: 'Highlighted!'
+    }
+  }
+}
+\`\`\`

Output

js
export default {
+  data () {
+    return {
+      msg: 'Highlighted!'
+    }
+  }
+}

Custom Containers ​

Input

md
::: info
+This is an info box.
+:::
+
+::: tip
+This is a tip.
+:::
+
+::: warning
+This is a warning.
+:::
+
+::: danger
+This is a dangerous warning.
+:::
+
+::: details
+This is a details block.
+:::

Output

INFO

This is an info box.

TIP

This is a tip.

WARNING

This is a warning.

DANGER

This is a dangerous warning.

Details

This is a details block.

More ​

Check out the documentation for the full list of markdown extensions.

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b/hashmap.json new file mode 100644 index 0000000..0e11d89 --- /dev/null +++ b/hashmap.json @@ -0,0 +1 @@ +{"api-ex.md":"DOsKaL8H","api_index.md":"CsKClHFh","api_mp_math_angle.md":"9eUTSIe4","api_mp_math_const.md":"Bhz27OPg","api_mp_math_equation.md":"xiyFVY1c","api_mp_math_index.md":"DTIfeUA1","api_mp_math_line.md":"BybnyRUL","api_mp_math_mp_math_typing.md":"DXaadYgy","api_mp_math_plane.md":"Cdj0PlKB","api_mp_math_point.md":"D3f-vzVt","api_mp_math_segment.md":"DIViBThe","api_mp_math_utils.md":"CDwq4icO","api_mp_math_vector.md":"BgK1TmFY","api_particle_index.md":"BqH-w2FR","api_presets_index.md":"CvgR5vOS","api_presets_model_index.md":"D1iZ1qEr","index.md":"CJvRmMfL","md-ex.md":"BX0WqOqv"} diff --git a/index.html b/index.html new file mode 100644 index 0000000..233f2df --- /dev/null +++ b/index.html @@ -0,0 +1,24 @@ + + + + + + MBCP docs + + + + + + + + + + + + + +
MBCP docs

简体中文

English

简体中文

English

Appearance

MBCP docs

More basic change particle

用于几何运算和粒子制作的库

快速开始
API文档

高可用性

通过简单的接口，实现了大部分几何运算和粒子制作的需求

高集成度

对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单

内置预设

提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作

+ + + + \ No newline at end of file diff --git a/md-ex.html b/md-ex.html new file mode 100644 index 0000000..e8653c1 --- /dev/null +++ b/md-ex.html @@ -0,0 +1,56 @@ + + + + + + Markdown Extension Examples | MBCP docs + + + + + + + + + + + + + +
MBCP docs

简体中文

English

简体中文

English

Appearance

Markdown Extension Examples ​

This page demonstrates some of the built-in markdown extensions provided by VitePress.

Syntax Highlighting ​

VitePress provides Syntax Highlighting powered by Shiki, with additional features like line-highlighting:

Input

md
```js{4}
+export default {
+  data () {
+    return {
+      msg: 'Highlighted!'
+    }
+  }
+}
+```

Output

js
export default {
+  data () {
+    return {
+      msg: 'Highlighted!'
+    }
+  }
+}

Custom Containers ​

Input

md
::: info
+This is an info box.
+:::
+
+::: tip
+This is a tip.
+:::
+
+::: warning
+This is a warning.
+:::
+
+::: danger
+This is a dangerous warning.
+:::
+
+::: details
+This is a details block.
+:::

Output

INFO

This is an info box.

TIP

This is a tip.

WARNING

This is a warning.

DANGER

This is a dangerous warning.

Details

This is a details block.

More ​

Check out the documentation for the full list of markdown extensions.

+ + + + \ No newline at end of file

Markdown Extension Examples ​