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docs/.vitepress/cache docs/.vitepress/cache
litedoc/ litedoc/
docs/api/
docs/zht/api/
docs/en/api/
docs/ja/api/

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---
title: mbcp
---

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

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

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

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title: mbcp.mp_math
---

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---
title: mbcp.mp_math.line
---
### ***class*** `Line3`
### *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。
參數:
- point: 直线上的一点
- direction: 直线的方向向量
<details>
<summary>源碼</summary>
```python
def __init__(self, point: 'Point3', direction: 'Vector3'):
"""
三维空间中的直线。由一个点和一个方向向量确定。
Args:
point: 直线上的一点
direction: 直线的方向向量
"""
self.point = point
self.direction = direction
```
</details>
### *def* `approx(self, other: 'Line3', epsilon: float = APPROX) -> bool`
判断两条直线是否近似相等。
參數:
- other: 另一条直线
- epsilon: 误差
返回:
- 是否近似相等
<details>
<summary>源碼</summary>
```python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
"""
判断两条直线是否近似相等。
Args:
other: 另一条直线
epsilon: 误差
Returns:
是否近似相等
"""
return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
```
</details>
### *def* `cal_angle(self, other: 'Line3') -> 'AnyAngle'`
计算直线和直线之间的夹角。
參數:
- other: 另一条直线
返回:
- 夹角弧度
引發:
- TypeError 不支持的类型
<details>
<summary>源碼</summary>
```python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
"""
计算直线和直线之间的夹角。
Args:
other: 另一条直线
Returns:
夹角弧度
Raises:
TypeError: 不支持的类型
"""
return self.direction.cal_angle(other.direction)
```
</details>
### *def* `cal_distance(self, other: 'Line3 | Point3') -> float`
计算直线和直线或点之间的距离。
參數:
- other: 平行直线或点
返回:
- 距离
引發:
- TypeError 不支持的类型
<details>
<summary>源碼</summary>
```python
def cal_distance(self, other: 'Line3 | Point3') -> float:
"""
计算直线和直线或点之间的距离。
Args:
other: 平行直线或点
Returns:
距离
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Line3):
if self == other:
return 0
elif self.is_parallel(other):
return (other.point - self.point).cross(self.direction).length / self.direction.length
elif not self.is_coplanar(other):
return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
else:
return 0
elif isinstance(other, Point3):
return (other - self.point).cross(self.direction).length / self.direction.length
else:
raise TypeError('Unsupported type.')
```
</details>
### *def* `cal_intersection(self, other: 'Line3') -> 'Point3'`
计算两条直线的交点。
參數:
- other: 另一条直线
返回:
- 交点
引發:
- ValueError 直线平行
- ValueError 直线不共面
<details>
<summary>源碼</summary>
```python
def cal_intersection(self, other: 'Line3') -> 'Point3':
"""
计算两条直线的交点。
Args:
other: 另一条直线
Returns:
交点
Raises:
ValueError: 直线平行
ValueError: 直线不共面
"""
if self.is_parallel(other):
raise ValueError('Lines are parallel and do not intersect.')
if not self.is_coplanar(other):
raise ValueError('Lines are not coplanar and do not intersect.')
return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
```
</details>
### *def* `cal_perpendicular(self, point: 'Point3') -> 'Line3'`
计算直线经过指定点p的垂线。
參數:
- point: 指定点
返回:
- 垂线
<details>
<summary>源碼</summary>
```python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
"""
计算直线经过指定点p的垂线。
Args:
point: 指定点
Returns:
垂线
"""
return Line3(point, self.direction.cross(point - self.point))
```
</details>
### *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。
參數:
- t: 参数t
返回:
- 点
<details>
<summary>源碼</summary>
```python
def get_point(self, t: RealNumber) -> 'Point3':
"""
获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Args:
t: 参数t
Returns:
点
"""
return self.point + t * self.direction
```
</details>
### *def* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
获取直线的参数方程。
返回:
- x(t), y(t), z(t)
<details>
<summary>源碼</summary>
```python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
"""
获取直线的参数方程。
Returns:
x(t), y(t), z(t)
"""
return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
```
</details>
### *def* `is_approx_parallel(self, other: 'Line3', epsilon: float = 1e-06) -> bool`
判断两条直线是否近似平行。
參數:
- other: 另一条直线
- epsilon: 误差
返回:
- 是否近似平行
<details>
<summary>源碼</summary>
```python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
"""
判断两条直线是否近似平行。
Args:
other: 另一条直线
epsilon: 误差
Returns:
是否近似平行
"""
return self.direction.is_approx_parallel(other.direction, epsilon)
```
</details>
### *def* `is_parallel(self, other: 'Line3') -> bool`
判断两条直线是否平行。
參數:
- other: 另一条直线
返回:
- 是否平行
<details>
<summary>源碼</summary>
```python
def is_parallel(self, other: 'Line3') -> bool:
"""
判断两条直线是否平行。
Args:
other: 另一条直线
Returns:
是否平行
"""
return self.direction.is_parallel(other.direction)
```
</details>
### *def* `is_collinear(self, other: 'Line3') -> bool`
判断两条直线是否共线。
參數:
- other: 另一条直线
返回:
- 是否共线
<details>
<summary>源碼</summary>
```python
def is_collinear(self, other: 'Line3') -> bool:
"""
判断两条直线是否共线。
Args:
other: 另一条直线
Returns:
是否共线
"""
return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
```
</details>
### *def* `is_point_on(self, point: 'Point3') -> bool`
判断点是否在直线上。
參數:
- point: 点
返回:
- 是否在直线上
<details>
<summary>源碼</summary>
```python
def is_point_on(self, point: 'Point3') -> bool:
"""
判断点是否在直线上。
Args:
point: 点
Returns:
是否在直线上
"""
return (point - self.point).is_parallel(self.direction)
```
</details>
### *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。
參數:
- other: 另一条直线
返回:
- 是否共面
<details>
<summary>源碼</summary>
```python
def is_coplanar(self, other: 'Line3') -> bool:
"""
判断两条直线是否共面。
充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Args:
other: 另一条直线
Returns:
是否共面
"""
return self.direction.cross(other.direction) @ (self.point - other.point) == 0
```
</details>
### *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
<details>
<summary>源碼</summary>
```python
def simplify(self):
"""
简化直线方程，等价相等。
自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
"""
self.direction.normalize()
if self.direction.x == 0:
self.point.x = 0
if self.direction.y == 0:
self.point.y = 0
if self.direction.z == 0:
self.point.z = 0
```
</details>
### `@classmethod`
### *def* `from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3'`
工厂函数 由两点构造直线。
參數:
- p1: 点1
- p2: 点2
返回:
- 直线
<details>
<summary>源碼</summary>
```python
@classmethod
def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
"""
工厂函数 由两点构造直线。
Args:
p1: 点1
p2: 点2
Returns:
直线
"""
direction = p2 - p1
return cls(p1, direction)
```
</details>
### *def* `__and__(self, other: 'Line3') -> 'Line3 | Point3 | None'`
计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
參數:
- other: 另一条直线
返回:
- 交点
<details>
<summary>源碼</summary>
```python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
"""
计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Args:
other: 另一条直线
Returns:
交点
"""
if self.is_collinear(other):
return self
elif self.is_parallel(other) or not self.is_coplanar(other):
return None
else:
return self.cal_intersection(other)
```
</details>
### *def* `__eq__(self, other) -> bool`
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
參數:
- other:
<details>
<summary>源碼</summary>
```python
def __eq__(self, other) -> bool:
"""
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Args:
other:
Returns:
"""
return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
```
</details>
### *def* `__str__(self)`
<details>
<summary>源碼</summary>
```python
def __str__(self):
"""
返回点向式（x-x0）
Returns:
"""
s = 'Line3: '
if self.direction.x != 0:
s += f'(x{sign_format(-self.point.x)})/{self.direction.x}'
if self.direction.y != 0:
s += f' = (y{sign_format(-self.point.y)})/{self.direction.y}'
if self.direction.z != 0:
s += f' = (z{sign_format(-self.point.z)})/{self.direction.z}'
return s
```
</details>
### *def* `__repr__(self)`
<details>
<summary>源碼</summary>
```python
def __repr__(self):
return f'Line3({self.point}, {self.direction})'
```
</details>

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

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---
title: mbcp.mp_math.plane
---
### ***class*** `Plane3`
### *def* `__init__(self, a: float, b: float, c: float, d: float)`
平面方程：ax + by + cz + d = 0
參數:
- a:
- b:
- c:
- d:
<details>
<summary>源碼</summary>
```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
```
</details>
### *def* `approx(self, other: 'Plane3') -> bool`
判断两个平面是否近似相等。
參數:
- other:
返回:
- 是否近似相等
<details>
<summary>源碼</summary>
```python
def approx(self, other: 'Plane3') -> bool:
"""
判断两个平面是否近似相等。
Args:
other:
Returns:
是否近似相等
"""
a = 3
if self.a != 0:
k = other.a / self.a
return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
elif self.b != 0:
k = other.b / self.b
return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
elif self.c != 0:
k = other.c / self.c
return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
else:
return False
```
</details>
### *def* `cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle'`
计算平面与平面之间的夹角。
參數:
- other: 另一个平面
返回:
- 夹角弧度
引發:
- TypeError 不支持的类型
<details>
<summary>源碼</summary>
```python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
"""
计算平面与平面之间的夹角。
Args:
other: 另一个平面
Returns:
夹角弧度
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Line3):
return self.normal.cal_angle(other.direction).complementary
elif isinstance(other, Plane3):
return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
else:
raise TypeError(f'Unsupported type: {type(other)}')
```
</details>
### *def* `cal_distance(self, other: 'Plane3 | Point3') -> float`
计算平面与平面或点之间的距离。
參數:
- other: 另一个平面或点
返回:
- 距离
引發:
- TypeError 不支持的类型
<details>
<summary>源碼</summary>
```python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
"""
计算平面与平面或点之间的距离。
Args:
other: 另一个平面或点
Returns:
距离
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Plane3):
return 0
elif isinstance(other, Point3):
return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
else:
raise TypeError(f'Unsupported type: {type(other)}')
```
</details>
### *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。
參數:
- other: 另一个平面
返回:
- 交线
<details>
<summary>源碼</summary>
```python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
"""
计算两平面的交线。该方法有问题，待修复。
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)
```
</details>
### *def* `cal_intersection_point3(self, other: 'Line3') -> 'Point3'`
计算平面与直线的交点。
參數:
- other: 不与平面平行或在平面上的直线
返回:
- 交点
引發:
- ValueError 平面与直线平行或重合
<details>
<summary>源碼</summary>
```python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
"""
计算平面与直线的交点。
Args:
other: 不与平面平行或在平面上的直线
Returns:
交点
Raises:
ValueError: 平面与直线平行或重合
"""
if self.normal @ other.direction == 0:
raise ValueError('The plane and the line are parallel or coincident.')
x, y, z = other.get_parametric_equations()
t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
return Point3(x(t), y(t), z(t))
```
</details>
### *def* `cal_parallel_plane3(self, point: 'Point3') -> 'Plane3'`
计算平行于该平面且过指定点的平面。
參數:
- point: 指定点
返回:
- 平面
<details>
<summary>源碼</summary>
```python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
"""
计算平行于该平面且过指定点的平面。
Args:
point: 指定点
Returns:
平面
"""
return Plane3.from_point_and_normal(point, self.normal)
```
</details>
### *def* `is_parallel(self, other: 'Plane3') -> bool`
判断两个平面是否平行。
參數:
- other: 另一个平面
返回:
- 是否平行
<details>
<summary>源碼</summary>
```python
def is_parallel(self, other: 'Plane3') -> bool:
"""
判断两个平面是否平行。
Args:
other: 另一个平面
Returns:
是否平行
"""
return self.normal.is_parallel(other.normal)
```
</details>
### `@property`
### *def* `normal(self) -> 'Vector3'`
平面的法向量。
返回:
- 法向量
<details>
<summary>源碼</summary>
```python
@property
def normal(self) -> 'Vector3':
"""
平面的法向量。
Returns:
法向量
"""
return Vector3(self.a, self.b, self.c)
```
</details>
### `@classmethod`
### *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)。
參數:
- point: 平面上的一点
- normal: 法向量
返回:
- 平面
<details>
<summary>源碼</summary>
```python
@classmethod
def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
"""
工厂函数 由点和法向量构造平面(点法式构造)。
Args:
point: 平面上的一点
normal: 法向量
Returns:
平面
"""
a, b, c = (normal.x, normal.y, normal.z)
d = -a * point.x - b * point.y - c * point.z
return cls(a, b, c, d)
```
</details>
### `@classmethod`
### *def* `from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3'`
工厂函数 由三点构造平面。
參數:
- p1: 点1
- p2: 点2
- p3: 点3
返回:
- 平面
<details>
<summary>源碼</summary>
```python
@classmethod
def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
"""
工厂函数 由三点构造平面。
Args:
p1: 点1
p2: 点2
p3: 点3
Returns:
平面
"""
v1 = p2 - p1
v2 = p3 - p1
normal = v1.cross(v2)
return cls.from_point_and_normal(p1, normal)
```
</details>
### `@classmethod`
### *def* `from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3'`
工厂函数 由两直线构造平面。
參數:
- l1: 直线1
- l2: 直线2
返回:
- 平面
<details>
<summary>源碼</summary>
```python
@classmethod
def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
"""
工厂函数 由两直线构造平面。
Args:
l1: 直线1
l2: 直线2
Returns:
平面
"""
v1 = l1.direction
v2 = l2.point - l1.point
if v2 == zero_vector3:
v2 = l2.get_point(1) - l1.point
return cls.from_point_and_normal(l1.point, v1.cross(v2))
```
</details>
### `@classmethod`
### *def* `from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3'`
工厂函数 由点和直线构造平面。
參數:
- point: 面上一点
- line: 面上直线，不包含点
返回:
- 平面
<details>
<summary>源碼</summary>
```python
@classmethod
def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
"""
工厂函数 由点和直线构造平面。
Args:
point: 面上一点
line: 面上直线，不包含点
Returns:
平面
"""
return cls.from_point_and_normal(point, line.direction)
```
</details>
### *def* `__repr__(self)`
<details>
<summary>源碼</summary>
```python
def __repr__(self):
return f'Plane3({self.a}, {self.b}, {self.c}, {self.d})'
```
</details>
### *def* `__str__(self)`
<details>
<summary>源碼</summary>
```python
def __str__(self):
s = 'Plane3: '
if self.a != 0:
s += f'{sign(self.a, only_neg=True)}{abs(self.a)}x'
if self.b != 0:
s += f' {sign(self.b)} {abs(self.b)}y'
if self.c != 0:
s += f' {sign(self.c)} {abs(self.c)}z'
if self.d != 0:
s += f' {sign(self.d)} {abs(self.d)}'
return s + ' = 0'
```
</details>
### `@overload`
### *def* `__and__(self, other: 'Line3') -> 'Point3 | None'`
<details>
<summary>源碼</summary>
```python
@overload
def __and__(self, other: 'Line3') -> 'Point3 | None':
...
```
</details>
### `@overload`
### *def* `__and__(self, other: 'Plane3') -> 'Line3 | None'`
<details>
<summary>源碼</summary>
```python
@overload
def __and__(self, other: 'Plane3') -> 'Line3 | None':
...
```
</details>
### *def* `__and__(self, other)`
取两平面的交集（人话：交线）
參數:
- other:
返回:
- 不平行平面的交线，平面平行返回None
<details>
<summary>源碼</summary>
```python
def __and__(self, other):
"""
取两平面的交集（人话：交线）
Args:
other:
Returns:
不平行平面的交线，平面平行返回None
"""
if isinstance(other, Plane3):
if self.normal.is_parallel(other.normal):
return None
return self.cal_intersection_line3(other)
elif isinstance(other, Line3):
if self.normal @ other.direction == 0:
return None
return self.cal_intersection_point3(other)
else:
raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
```
</details>
### *def* `__eq__(self, other) -> bool`
<details>
<summary>源碼</summary>
```python
def __eq__(self, other) -> bool:
return self.approx(other)
```
</details>
### *def* `__rand__(self, other: 'Line3') -> 'Point3'`
<details>
<summary>源碼</summary>
```python
def __rand__(self, other: 'Line3') -> 'Point3':
return self.cal_intersection_point3(other)
```
</details>
### ***var*** `k = other.a / self.a`
### ***var*** `A = np.array([[self.b, self.c], [other.b, other.c]])`
### ***var*** `B = np.array([-self.d, -other.d])`
### ***var*** `v2 = l2.get_point(1) - l1.point`
### ***var*** `k = other.b / self.b`
### ***var*** `A = np.array([[self.a, self.c], [other.a, other.c]])`
### ***var*** `B = np.array([-self.d, -other.d])`
### ***var*** `k = other.c / self.c`
### ***var*** `A = np.array([[self.a, self.b], [other.a, other.b]])`
### ***var*** `B = np.array([-self.d, -other.d])`

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

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

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@ -1,220 +0,0 @@
---
title: mbcp.mp_math.utils
---
### *def* `clamp() -> float`
区间截断函数。
參數:
- x:
- min_:
- max_:
返回:
- 限制后的值
<details>
<summary>源碼</summary>
```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_)
```
</details>
### *def* `approx(x: float = 0.0, y: float = APPROX) -> bool`
判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
參數:
- x:
- y:
- epsilon:
返回:
- 是否近似相等
<details>
<summary>源碼</summary>
```python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
"""
判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Args:
x:
y:
epsilon:
Returns:
是否近似相等
"""
return abs(x - y) < epsilon
```
</details>
### *def* `sign(x: float = False) -> str`
获取数的符号。
參數:
- x: 数
- only_neg: 是否只返回负数的符号
返回:
- 符号 + - ""
<details>
<summary>源碼</summary>
```python
def sign(x: float, only_neg: bool=False) -> str:
"""获取数的符号。
Args:
x: 数
only_neg: 是否只返回负数的符号
Returns:
符号 + - ""
"""
if x > 0:
return '+' if not only_neg else ''
elif x < 0:
return '-'
else:
return ''
```
</details>
### *def* `sign_format(x: float = False) -> str`
格式化符号数
-1 -> -1
1 -> +1
0 -> ""
參數:
- x: 数
- only_neg: 是否只返回负数的符号
返回:
- 符号 + - ""
<details>
<summary>源碼</summary>
```python
def sign_format(x: float, only_neg: bool=False) -> str:
"""格式化符号数
-1 -> -1
1 -> +1
0 -> ""
Args:
x: 数
only_neg: 是否只返回负数的符号
Returns:
符号 + - ""
"""
if x > 0:
return f'+{x}' if not only_neg else f'{x}'
elif x < 0:
return f'-{abs(x)}'
else:
return ''
```
</details>
### ***class*** `Approx`
### *def* `__init__(self, value: RealNumber)`
<details>
<summary>源碼</summary>
```python
def __init__(self, value: RealNumber):
self.value = value
```
</details>
### *def* `__eq__(self, other)`
<details>
<summary>源碼</summary>
```python
def __eq__(self, other):
if isinstance(self.value, (float, int)):
if isinstance(other, (float, int)):
return abs(self.value - other) < APPROX
else:
self.raise_type_error(other)
elif isinstance(self.value, Vector3):
if isinstance(other, (Vector3, Point3, Plane3, Line3)):
return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
else:
self.raise_type_error(other)
```
</details>
### *def* `raise_type_error(self, other)`
<details>
<summary>源碼</summary>
```python
def raise_type_error(self, other):
raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
```
</details>
### *def* `__ne__(self, other)`
<details>
<summary>源碼</summary>
```python
def __ne__(self, other):
return not self.__eq__(other)
```
</details>

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

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---
title: mbcp.particle
---

3
docs/zh-Hant/api/presets/index.md
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---
title: mbcp.presets
---

48
docs/zh-Hant/api/presets/model/index.md
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@ -1,48 +0,0 @@
---
title: mbcp.presets.model
---
### ***class*** `GeometricModels`
### `@staticmethod`
### *def* `sphere(radius: float, density: float)`
生成球体上的点集。
參數:
- radius:
- density:
返回:
- List[Point3]: 球体上的点集。
<details>
<summary>源碼</summary>
```python
@staticmethod
def sphere(radius: float, density: float):
"""
生成球体上的点集。
Args:
radius:
density:
Returns:
List[Point3]: 球体上的点集。
"""
area = 4 * np.pi * radius ** 2
num = int(area * density)
phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
theta_list = np.sqrt(num * np.pi) * phi_list
x_array = radius * np.sin(phi_list) * np.cos(theta_list)
y_array = radius * np.sin(phi_list) * np.sin(theta_list)
z_array = radius * np.cos(phi_list)
return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
```
</details>

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