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582 lines
11 KiB
Markdown
582 lines
11 KiB
Markdown
---
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title: mbcp.mp_math.line
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---
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### **class** `Line3`
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### *method* `__init__(self, point: Point3, direction: Vector3)`
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三维空间中的直线。由一个点和一个方向向量确定。
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**Arguments**:
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- point: 直线上的一点
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- direction: 直线的方向向量
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __init__(self, point: 'Point3', direction: 'Vector3'):
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"""
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三维空间中的直线。由一个点和一个方向向量确定。
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Args:
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point: 直线上的一点
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direction: 直线的方向向量
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"""
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self.point = point
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self.direction = direction
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```
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</details>
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### *method* `approx(self, other: Line3, epsilon: float = APPROX) -> bool`
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判断两条直线是否近似相等。
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**Arguments**:
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- other: 另一条直线
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- epsilon: 误差
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**Return**:
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- 是否近似相等
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
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"""
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判断两条直线是否近似相等。
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Args:
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other: 另一条直线
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epsilon: 误差
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Returns:
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是否近似相等
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"""
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return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
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```
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</details>
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### *method* `cal_angle(self, other: Line3) -> AnyAngle`
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计算直线和直线之间的夹角。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 夹角弧度
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**Raises**:
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- TypeError 不支持的类型
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cal_angle(self, other: 'Line3') -> 'AnyAngle':
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"""
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计算直线和直线之间的夹角。
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Args:
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other: 另一条直线
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Returns:
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夹角弧度
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Raises:
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TypeError: 不支持的类型
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"""
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return self.direction.cal_angle(other.direction)
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```
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</details>
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### *method* `cal_distance(self, other: Line3 | Point3) -> float`
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计算直线和直线或点之间的距离。
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**Arguments**:
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- other: 平行直线或点
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**Return**:
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- 距离
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**Raises**:
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- TypeError 不支持的类型
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cal_distance(self, other: 'Line3 | Point3') -> float:
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"""
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计算直线和直线或点之间的距离。
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Args:
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other: 平行直线或点
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Returns:
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距离
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Raises:
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TypeError: 不支持的类型
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"""
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if isinstance(other, Line3):
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if self == other:
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return 0
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elif self.is_parallel(other):
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return (other.point - self.point).cross(self.direction).length / self.direction.length
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elif not self.is_coplanar(other):
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return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
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else:
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return 0
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elif isinstance(other, Point3):
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return (other - self.point).cross(self.direction).length / self.direction.length
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else:
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raise TypeError('Unsupported type.')
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```
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</details>
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### *method* `cal_intersection(self, other: Line3) -> Point3`
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计算两条直线的交点。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 交点
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**Raises**:
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- ValueError 直线平行
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- ValueError 直线不共面
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cal_intersection(self, other: 'Line3') -> 'Point3':
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"""
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计算两条直线的交点。
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Args:
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other: 另一条直线
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Returns:
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交点
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Raises:
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ValueError: 直线平行
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ValueError: 直线不共面
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"""
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if self.is_parallel(other):
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raise ValueError('Lines are parallel and do not intersect.')
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if not self.is_coplanar(other):
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raise ValueError('Lines are not coplanar and do not intersect.')
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return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
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```
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</details>
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### *method* `cal_perpendicular(self, point: Point3) -> Line3`
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计算直线经过指定点p的垂线。
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**Arguments**:
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- point: 指定点
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**Return**:
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- 垂线
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cal_perpendicular(self, point: 'Point3') -> 'Line3':
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"""
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计算直线经过指定点p的垂线。
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Args:
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point: 指定点
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Returns:
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垂线
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"""
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return Line3(point, self.direction.cross(point - self.point))
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```
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</details>
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### *method* `get_point(self, t: RealNumber) -> Point3`
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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。
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**Arguments**:
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- t: 参数t
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**Return**:
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- 点
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def get_point(self, t: RealNumber) -> 'Point3':
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"""
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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。
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Args:
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t: 参数t
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Returns:
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点
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"""
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return self.point + t * self.direction
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```
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</details>
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### *method* `get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]`
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获取直线的参数方程。
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**Return**:
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- x(t), y(t), z(t)
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
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"""
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获取直线的参数方程。
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Returns:
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x(t), y(t), z(t)
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"""
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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)
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```
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</details>
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### *method* `is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool`
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判断两条直线是否近似平行。
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**Arguments**:
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- other: 另一条直线
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- epsilon: 误差
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**Return**:
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- 是否近似平行
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
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"""
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判断两条直线是否近似平行。
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Args:
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other: 另一条直线
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epsilon: 误差
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Returns:
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是否近似平行
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"""
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return self.direction.is_approx_parallel(other.direction, epsilon)
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```
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</details>
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### *method* `is_parallel(self, other: Line3) -> bool`
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判断两条直线是否平行。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 是否平行
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_parallel(self, other: 'Line3') -> bool:
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"""
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判断两条直线是否平行。
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Args:
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other: 另一条直线
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Returns:
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是否平行
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"""
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return self.direction.is_parallel(other.direction)
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```
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</details>
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### *method* `is_collinear(self, other: Line3) -> bool`
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判断两条直线是否共线。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 是否共线
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_collinear(self, other: 'Line3') -> bool:
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"""
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判断两条直线是否共线。
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Args:
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other: 另一条直线
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Returns:
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是否共线
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"""
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return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
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```
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</details>
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### *method* `is_point_on(self, point: Point3) -> bool`
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判断点是否在直线上。
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**Arguments**:
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- point: 点
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**Return**:
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- 是否在直线上
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_point_on(self, point: 'Point3') -> bool:
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"""
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判断点是否在直线上。
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Args:
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point: 点
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Returns:
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是否在直线上
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"""
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return (point - self.point).is_parallel(self.direction)
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```
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</details>
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### *method* `is_coplanar(self, other: Line3) -> bool`
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判断两条直线是否共面。
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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。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 是否共面
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_coplanar(self, other: 'Line3') -> bool:
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"""
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判断两条直线是否共面。
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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。
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Args:
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other: 另一条直线
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Returns:
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是否共面
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"""
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return self.direction.cross(other.direction) @ (self.point - other.point) == 0
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```
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</details>
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### *method* `simplify(self)`
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简化直线方程，等价相等。
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自体简化，不返回值。
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按照可行性一次对x y z 化 0 处理，并对向量单位化
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def simplify(self):
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"""
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简化直线方程，等价相等。
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自体简化，不返回值。
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按照可行性一次对x y z 化 0 处理，并对向量单位化
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"""
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self.direction.normalize()
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if self.direction.x == 0:
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self.point.x = 0
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if self.direction.y == 0:
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self.point.y = 0
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if self.direction.z == 0:
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self.point.z = 0
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```
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</details>
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### `@classmethod`
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### *method* `from_two_points(cls, p1: Point3, p2: Point3) -> Line3`
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工厂函数 由两点构造直线。
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**Arguments**:
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- p1: 点1
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- p2: 点2
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**Return**:
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- 直线
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@classmethod
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def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
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"""
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工厂函数 由两点构造直线。
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Args:
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p1: 点1
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p2: 点2
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Returns:
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直线
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"""
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direction = p2 - p1
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return cls(p1, direction)
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```
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</details>
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### *method* `__and__(self, other: Line3) -> Line3 | Point3 | None`
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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。
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**Arguments**:
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- other: 另一条直线
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**Return**:
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- 交点
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
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"""
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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。
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Args:
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other: 另一条直线
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Returns:
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交点
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"""
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if self.is_collinear(other):
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return self
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elif self.is_parallel(other) or not self.is_coplanar(other):
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return None
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else:
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return self.cal_intersection(other)
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```
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</details>
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### *method* `__eq__(self, other) -> bool`
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判断两条直线是否等价。
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v1 // v2 ∧ (p1 - p2) // v1
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**Arguments**:
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- other:
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<details>
|
||
<summary> <i>Source code</i> </summary>
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```python
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def __eq__(self, other) -> bool:
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"""
|
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判断两条直线是否等价。
|
||
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v1 // v2 ∧ (p1 - p2) // v1
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Args:
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other:
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Returns:
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"""
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return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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```
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</details>
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