mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

Description: 三维空间中的直线。由一个点和一个方向向量确定。

Arguments:

• point (Point3): 直线上的一点
• direction (Vector3): 方向向量

Source code or View on GitHub

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 ([`Point3`](./point#class-point3)): 直线上的一点
            direction ([`Vector3`](./vector#class-vector3)): 方向向量
        """
    self.point = point
    self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool

Description: 判断两条直线是否近似相等。

Arguments:

• other (Line3): 另一条直线
• epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub

def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
    """
        判断两条直线是否近似相等。
        Args:
            other ([`Line3`](./line#class-line3)): 另一条直线
            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
        Returns:
            [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
        """
    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

Description: 计算直线和直线之间的夹角。

Arguments:

• other (Line3): 另一条直线

Return: AnyAngle: 夹角

Source code or View on GitHub

def cal_angle(self, other: 'Line3') -> 'AnyAngle':
    """
        计算直线和直线之间的夹角。
        Args:
            other ([`Line3`](./line#class-line3)): 另一条直线
        Returns:
            [`AnyAngle`](./angle#class-anyangle): 夹角
        """
    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

Description: 计算直线和直线或点之间的距离。

Arguments:

• other (Line3 | Point3): 另一条直线或点

Return: float: 距离

Raises:

• TypeError 不支持的类型

Source code or View on GitHub

def cal_distance(self, other: 'Line3 | Point3') -> float:
    """
        计算直线和直线或点之间的距离。
        Args:
            other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
        Returns:
            [`float`](https%3A//docs.python.org/3/library/functions.html#float): 距离
        Raises:
            [`TypeError`](https%3A//docs.python.org/3/library/exceptions.html#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.')

method cal_intersection(self, other: Line3) -> Point3

Description: 计算两条直线的交点。

Arguments:

• other (Line3): 另一条直线

Return: Point3: 交点

Raises:

• ValueError 直线平行
• ValueError 直线不共面

Source code or View on GitHub

def cal_intersection(self, other: 'Line3') -> 'Point3':
    """
        计算两条直线的交点。
        Args:
            other ([`Line3`](./line#class-line3)): 另一条直线
        Returns:
            [`Point3`](./point#class-point3): 交点
        Raises:
            [`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 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

method cal_perpendicular(self, point: Point3) -> Line3

Description: 计算直线经过指定点p的垂线。

Arguments:

• point (Point3): 指定点

Return: Line3: 垂线

Source code or View on GitHub

def cal_perpendicular(self, point: 'Point3') -> 'Line3':
    """
        计算直线经过指定点p的垂线。
        Args:
            point ([`Point3`](./point#class-point3)): 指定点
        Returns:
            [`Line3`](./line#class-line3): 垂线
        """
    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。

Arguments:

• t (RealNumber): 参数t

Return: Point3: 点

Source code or View on GitHub

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 ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
        Returns:
            [`Point3`](./point#class-point3): 点
        """
    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub

def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
    """
        获取直线的参数方程。
        Returns:
            [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
        """
    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)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

Description: 判断两条直线是否近似平行。

Arguments:

• other (Line3): 另一条直线
• epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub

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 ([`Line3`](./line#class-line3)): 另一条直线
            epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
        """
    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

Description: 判断两条直线是否平行。

Arguments:

• other (Line3): 另一

Return: bool: 是否平行

Source code or View on GitHub

def is_parallel(self, other: 'Line3') -> bool:
    """
        判断两条直线是否平行。
        Args:
            other ([`Line3`](./line#class-line3)): 另一
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
        """
    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

Description: 判断两条直线是否共线。

Arguments:

• other (Line3): 另一

Return: bool: 是否共线

Source code or View on GitHub

def is_collinear(self, other: 'Line3') -> bool:
    """
        判断两条直线是否共线。
        Args:
            other ([`Line3`](./line#class-line3)): 另一
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
        """
    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

Description: 判断点是否在直线上。

Arguments:

• point (Point3): 点

Return: bool: 是否在直线上

Source code or View on GitHub

def is_point_on(self, point: 'Point3') -> bool:
    """
        判断点是否在直线上。
        Args:
            point ([`Point3`](./point#class-point3)): 点
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
        """
    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

• other (Line3): 另一

Return: bool: 是否共面

Source code or View on GitHub

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 ([`Line3`](./line#class-line3)): 另一
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
        """
    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

Description: 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

Source code or View on GitHub

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

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

Description: 工厂函数 由两点构造直线。

Arguments:

• p1 (Point3): 点1
• p2 (Point3): 点2

Return: Line3: 直线

Source code or View on GitHub

@classmethod
def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
    """
        工厂函数 由两点构造直线。
        Args:
            p1 ([`Point3`](./point#class-point3)): 点1
            p2 ([`Point3`](./point#class-point3)): 点2
        Returns:
            [`Line3`](./line#class-line3): 直线
        """
    direction = p2 - p1
    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None

Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

Arguments:

• other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub

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 ([`Line3`](./line#class-line3)): 另一条直线
        Returns:
            [`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
        """
    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)

method __eq__(self, other) -> bool

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

• other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub

def __eq__(self, other) -> bool:
    """
        判断两条直线是否等价。

        v1 // v2 ∧ (p1 - p2) // v1
        Args:
            other ([`Line3`](./line#class-line3)): 另一条直线
        Returns:
            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
        """
    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)