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# Module `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
python

    def __init__(self, point: 'Point3', direction: 'Vector3'):
        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
python

    def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
        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
python

    def cal_angle(self, other: 'Line3') -> 'AnyAngle':
        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
python

    def cal_distance(self, other: 'Line3 | Point3') -> float:
        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
python

    def cal_intersection(self, other: 'Line3') -> 'Point3':
        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
python

    def cal_perpendicular(self, point: 'Point3') -> 'Line3':
        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
python

    def get_point(self, t: RealNumber) -> 'Point3':
        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
python

    def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
        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
python

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

    def is_parallel(self, other: 'Line3') -> bool:
        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
python

    def is_collinear(self, other: 'Line3') -> bool:
        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
python

    def is_point_on(self, point: 'Point3') -> bool:
        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
python

    def is_coplanar(self, other: 'Line3') -> bool:
        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
python

    def simplify(self):
        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
python

    @classmethod
    def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
        direction = p2 - p1
        return cls(p1, direction)

#### method `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
python

    def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
        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 `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
python

    def __eq__(self, other) -> bool:
        return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)