import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n(`

mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class `Plane3`

method `init(self, a: float, b: float, c: float, d: float)`

说明: 平面方程：ax + by + cz + d = 0

参数:

a (float): x系数
b (float): y系数
c (float): z系数
d (float): 常数项

源代码 或在GitHub上查看

python

def __init__(self, a: float, b: float, c: float, d: float):
    """
        平面方程：ax + by + cz + d = 0
        Args:
            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
            b (\`float\`): y系数
            c (\`float\`): z系数
            d (\`float\`): 常数项
        """
    self.a = a
    self.b = b
    self.c = c
    self.d = d

method `approx(self, other: Plane3) -> bool`

说明: 判断两个平面是否近似相等。

参数:

other (Plane3): 另一个平面

返回: bool: 是否近似相等

源代码 或在GitHub上查看

python

def approx(self, other: 'Plane3') -> bool:
    """
        判断两个平面是否近似相等。
        Args:
            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
        Returns:
            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 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

method `cal_angle(self, other: Line3 | Plane3) -> AnyAngle`

说明: 计算平面与平面之间的夹角。

参数:

other (Line3 | Plane3): 另一个平面或直线

返回: AnyAngle: 夹角

引发:

TypeError 不支持的类型

源代码 或在GitHub上查看

python

def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
    """
        计算平面与平面之间的夹角。
        Args:
            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
        Returns:
            [\`AnyAngle\`](./angle#class-anyangle): 夹角
        Raises:
            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#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)}')

method `cal_distance(self, other: Plane3 | Point3) -> float`

说明: 计算平面与平面或点之间的距离。

参数:

other (Plane3 | Point3): 另一个平面或点

返回: float: 距离

引发:

TypeError 不支持的类型

源代码 或在GitHub上查看

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 ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
        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, 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)}')

method `cal_intersection_line3(self, other: Plane3) -> Line3`

说明: 计算两平面的交线。

参数:

other (Plane3): 另一个平面

返回: Line3: 交线

引发:

ValueError 平面平行且无交线

源代码 或在GitHub上查看

python

def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
    """
        计算两平面的交线。
        Args:
            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
        Returns:
            [\`Line3\`](./line#class-line3): 交线
        Raises:
            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
        """
    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)

method `cal_intersection_point3(self, other: Line3) -> Point3`

说明: 计算平面与直线的交点。

参数:

other (Line3): 直线

返回: Point3: 交点

引发:

ValueError 平面与直线平行或重合

源代码 或在GitHub上查看

python

def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
    """
        计算平面与直线的交点。
        Args:
            other ([\`Line3\`](./line#class-line3)): 直线
        Returns:
            [\`Point3\`](./point#class-point3): 交点
        Raises:
            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#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))

method `cal_parallel_plane3(self, point: Point3) -> Plane3`

说明: 计算平行于该平面且过指定点的平面。

参数:

point (Point3): 指定点

返回: Plane3: 平面

源代码 或在GitHub上查看

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 ([\`Point3\`](./point#class-point3)): 指定点
        Returns:
            [\`Plane3\`](./plane#class-plane3): 平面
        """
    return Plane3.from_point_and_normal(point, self.normal)

method `is_parallel(self, other: Plane3) -> bool`

说明: 判断两个平面是否平行。

参数:

other (Plane3): 另一个平面

返回: bool: 是否平行

源代码 或在GitHub上查看

python

def is_parallel(self, other: 'Plane3') -> bool:
    """
        判断两个平面是否平行。
        Args:
            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
        """
    return self.normal.is_parallel(other.normal)

@property

method `normal(self) -> Vector3`

说明: 平面的法向量。

返回: Vector3: 法向量

源代码 或在GitHub上查看

python

@property
def normal(self) -> 'Vector3':
    """
        平面的法向量。
        Returns:
            [\`Vector3\`](./vector#class-vector3): 法向量
        """
    return Vector3(self.a, self.b, self.c)

@classmethod

method `from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3`

说明: 工厂函数由点和法向量构造平面(点法式构造)。

参数:

point (Point3): 平面上一点
normal (Vector3): 法向量

返回: Plane3: 平面

源代码 或在GitHub上查看

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 ([\`Point3\`](./point#class-point3)): 平面上一点
            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
        Returns:
            [\`Plane3\`](./plane#class-plane3): 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

method `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3`

说明: 工厂函数由三点构造平面。

参数:

p1 (Point3): 点1
p2 (Point3): 点2
p3 (Point3): 点3

返回: 平面

源代码 或在GitHub上查看

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 ([\`Point3\`](./point#class-point3)): 点1
            p2 (\`Point3\`): 点2
            p3 (\`Point3\`): 点3
        Returns:
            平面
        """
    v1 = p2 - p1
    v2 = p3 - p1
    normal = v1.cross(v2)
    return cls.from_point_and_normal(p1, normal)

@classmethod

method `from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3`

说明: 工厂函数由两直线构造平面。

参数:

l1 (Line3): 直线
l2 (Line3): 直线

返回: 平面

源代码 或在GitHub上查看

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 ([\`Line3\`](./line#class-line3)): 直线
            l2 (\`Line3\`): 直线
        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

method `from_point_and_line(cls, point: Point3, line: Line3) -> Plane3`

说明: 工厂函数由点和直线构造平面。

参数:

point (Point3): 平面上一点
line (Line3): 直线

返回: 平面

源代码 或在GitHub上查看

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 ([\`Point3\`](./point#class-point3)): 平面上一点
            line ([\`Line3\`](./line#class-line3)): 直线
        Returns:
            平面
        """
    return cls.from_point_and_normal(point, line.direction)

@overload

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

源代码 或在GitHub上查看

python

@overload
def __and__(self, other: 'Line3') -> 'Point3 | None':
    ...

@overload

method `and(self, other: Plane3) -> Line3 | None`

源代码 或在GitHub上查看

python

@overload
def __and__(self, other: 'Plane3') -> 'Line3 | None':
    ...

method `and(self, other)`

说明: 取两平面的交集（人话：交线）

参数:

other (Line3 | Plane3): 另一个平面或直线

返回: Line3 | Point3 | None: 交集

引发:

TypeError 不支持的类型

源代码 或在GitHub上查看

python

def __and__(self, other):
    """
        取两平面的交集（人话：交线）
        Args:
            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
        Returns:
            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
        Raises:
            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
        """
    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)}'")

method `eq(self, other) -> bool`

说明: 判断两个平面是否等价。

参数:

other (Plane3): 另一个平面

返回: bool: 是否等价

源代码 或在GitHub上查看

python

def __eq__(self, other) -> bool:
    """
        判断两个平面是否等价。
        Args:
            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
        """
    return self.approx(other)

method `rand(self, other: Line3) -> Point3`

源代码 或在GitHub上查看

python

def __rand__(self, other: 'Line3') -> 'Point3':
    return self.cal_intersection_point3(other)

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