⚡ add some mathematical method for object Line3

mbcp/mp_math/line.py

@@ -0,0 +1,88 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/6 下午12:57
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : line.py
+@Software: PyCharm
+"""
+from typing import overload, TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from .point import Point3
+
+
+class Line3:
+    def __init__(self, a: float, b: float, c: float, d: float):
+        """
+        三维空间中的直线。
+        :param a:
+        :param b:
+        :param c:
+        :param d:
+        """
+        self.a = a
+        self.b = b
+        self.c = c
+        self.d = d
+
+    def __str__(self):
+        return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
+
+    def get_perpendicular(self, point: "Point3") -> "Line3":
+        """
+        获取直线经过指定点p的垂线。
+        :param point: 指定点p，直线外的点
+        :return: 垂直于self且过点p的直线
+        """
+        a = -self.b
+        b = self.a
+        c = 0
+        d = -(a * point.x + b * point.y + self.c * point.z)
+        return Line3(a, b, c, d)
+
+    def get_intersection(self, line: "Line3") -> "Point3":
+        """
+        获取两条直线的交点。
+        :param line:
+        :return:
+        """
+        normal1 = (self.b, -self.a, 0)
+        normal2 = (-line.b, line.a, 0)
+
+        if self.is_parallel(line):
+            raise ValueError("Lines are parallel and do not intersect.")
+
+        if self.is_collinear(line):
+            raise ValueError("Lines are collinear and do not have a single intersection point.")
+
+        if not self.is_coplanar(line):
+            raise ValueError("Lines are not coplanar and do not intersect.")
+
+        a1, b1, c1, d1 = self.a, self.b, self.c, self.d
+        a2, b2, c2, d2 = line.a, line.b, line.c, line.d
+
+        t = (b1 * (c2 * d1 - c1 * d2) - b2 * (c1 * d1 - c2 * d2)) / (b1 * c2 - b2 * c1)
+
+        x = self.a * t + self.b * (-d1 / self.b)
+        y = -self.b * t + self.a * (d1 / self.a)
+        z = 0
+
+        return Point3(x, y, z)
+
+    def is_parallel(self, line: "Line3") -> bool:
+        # 直线平行的条件是它们的法向量成比例
+        return self.a * line.b == self.b * line.a and self.c * line.b == self.d * line.a
+
+    def is_collinear(self, line: "Line3") -> bool:
+        # 直线共线的条件是它们的法向量成比例且常数项也成比例
+        return self.is_parallel(line) and (self.d * line.b - self.b * line.d) / (self.a * line.b - self.b * line.a) == 0
+
+    def is_coplanar(self, line: "Line3") -> bool:
+        # 两条直线共面的条件是它们的方向向量和法向量的叉乘为零向量
+        direction1 = (-self.c, 0, self.a)
+        direction2 = (line.c, -line.b, 0)
+        cross_product = direction1[0] * direction2[1] - direction1[1] * direction2[0]
+        return cross_product == 0

mbcp/mp_math/point.py

@@ -1,7 +1,7 @@
 from typing import overload, TYPE_CHECKING
 
-if TYPE_CHECKING:
+if TYPE_CHECKING:     # type: ignore
-    from mcpe.mp_math.vector import Vector3
+    from .vector import Vector3
 
 
 class Point3:

mbcp/mp_math/vector.py

@@ -1,7 +1,7 @@
 from typing import overload, TYPE_CHECKING
 
-if TYPE_CHECKING:
+if TYPE_CHECKING:  # type: ignore
-    from mcpe.mp_math.point import Point3
+    from .point import Point3
 
 
 class Vector3:
@@ -47,6 +47,12 @@ class Vector3:
         ...
 
     def __sub__(self, other):
+        """
+        V - P -> P
+        V - V -> V
+        :param other:
+        :return:
+        """
         if isinstance(other, Vector3):
             return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
         elif isinstance(other, Point3):
@@ -55,9 +61,13 @@ class Vector3:
             raise TypeError(f"unsupported operand type(s) for -: 'Vector3' and '{type(other)}'")
 
     def __rsub__(self, other: Point3):
+        """
+        P - V -> P
+        :param other:
+        :return:
+        """
+
         if isinstance(other, Point3):
             return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
-        elif isinstance(other, Vector3):
-            return Vector3(other.x - self.x, other.y - self.y, other.z - self.z)
         else:
             raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

mcpe/mp_math/line.py

@@ -1,66 +0,0 @@
-# -*- coding: utf-8 -*-
-"""
-Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
-
-@Time    : 2024/8/6 下午12:57
-@Author  : snowykami
-@Email   : snowykami@outlook.com
-@File    : line.py
-@Software: PyCharm
-"""
-from typing import overload, TYPE_CHECKING
-
-if TYPE_CHECKING:
-    from mcpe.mp_math.point import Point3
-    from mcpe.mp_math.vector import Vector3
-
-
-class Line3:
-    def __init__(self, a: float, b: float, c: float, d:float):
-        """
-        三维空间中的直线。
-        :param a:
-        :param b:
-        :param c:
-        :param d:
-        """
-        self.a = a
-        self.b = b
-        self.c = c
-        self.d = d
-
-    def __str__(self):
-        return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
-
-    def get_perpendicular(self, p: "Point3") -> "Line3":
-        """
-        获取直线经过指定点p的垂线。
-        :param p: 指定点p，直线外的点
-        :return: 垂直于self且过点p的直线
-        """
-        a = -self.b
-        b = self.a
-        c = 0
-        d = -(a * p.x + b * p.y + self.c * p.z)
-        return Line3(a, b, c, d)
-
-    def get_intersection(self, l: "Line3") -> "Point3":
-        """
-        获取两空间直线的交点。
-        :param l: 另一条直线，不平行于self，不共线，且共面
-        :return: 交点
-        """
-        # 平行检测
-        if ...:
-            ...
-        # 共线检测
-        if ...:
-            ...
-        # 不共线检测
-        if ...:
-            ...
-
-
-
-
-