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]) ​

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