手动实现bowyer-watson算法的python代码

以下是基于Bowyer-Watson算法的Python代码实现：

import math

class Vertex:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __hash__(self):
        return hash((self.x, self.y))

class Triangle:
    def __init__(self, vertex1, vertex2, vertex3):
        self.vertices = [vertex1, vertex2, vertex3]

    def __eq__(self, other):
        return set(self.vertices) == set(other.vertices)

    def __hash__(self):
        return hash((self.vertices[0], self.vertices[1], self.vertices[2]))

    def get_circumcenter(self):
        A = self.vertices[0]
        B = self.vertices[1]
        C = self.vertices[2]
        a = (B.x - A.x)**2 + (B.y - A.y)**2
        b = (C.x - B.x)**2 + (C.y - B.y)**2
        c = (A.x - C.x)**2 + (A.y - C.y)**2
        s = 2 * (a * b + b * c + c * a) - (a**2 + b**2 + c**2)
        px = (a * (b + c - a) * A.x + b * (c + a - b) * B.x + c * (a + b - c) * C.x) / s
        py = (a * (b + c - a) * A.y + b * (c + a - b) * B.y + c * (a + b - c) * C.y) / s
        return Vertex(px, py)

class DelaunayTriangulation:
    def __init__(self, vertices):
        self.vertices = vertices
        self.triangles = []

        # 计算超级三角形
        max_x = max(vertex.x for vertex in self.vertices)
        max_y = max(vertex.y for vertex in self.vertices)
        min_x = min(vertex.x for vertex in self.vertices)
        min_y = min(vertex.y for vertex in self.vertices)

        dx = max(max_x - min_x, max_y - min_y)
        mid_x = min_x + dx / 2
        mid_y = min_y + dx / 2

        self.super_triangle = Triangle(
            Vertex(mid_x - 20 * dx, mid_y - dx),
            Vertex(mid_x, mid_y + 20 * dx),
            Vertex(mid_x + 20 * dx, mid_y - dx)
        )

        self.triangles.append(self.super_triangle)

        # 插入所有的点
        for vertex in self.vertices:
            bad_triangles = []
            for triangle in self.triangles:
                if self.in_circumcircle(triangle, vertex):
                    bad_triangles.append(triangle)

            polygon = []
            for triangle in bad_triangles:
                for v in triangle.vertices:
                    if v not in vertex and self.is_edge_shared_by_triangles(v, vertex, bad_triangles):
                        polygon.append((v, vertex))

            for triangle in bad_triangles:
                self.triangles.remove(triangle)

            for edge in polygon:
                self.triangles.append(Triangle(edge[0], edge[1], vertex))

    def in_circumcircle(self, triangle, vertex):
        circle_center = triangle.get_circumcenter()
        radius = math.sqrt((circle_center.x - triangle.vertices[0].x)**2 + (circle_center.y - triangle.vertices[0].y)**2)
        distance = math.sqrt((circle_center.x - vertex.x)**2 + (circle_center.y - vertex.y)**2)
        return distance <= radius

    def is_edge_shared_by_triangles(self, vertex1, vertex2, triangles):
        edge_count = 0
        for triangle in triangles:
            if vertex1 in triangle.vertices and vertex2 in triangle.vertices:
                edge_count += 1
        return edge_count == 2

    def get_triangles(self):
        triangles = []
        for triangle in self.triangles:
            if not any(vertex in self.super_triangle.vertices for vertex in triangle.vertices):
                triangles.append(triangle)
        return triangles

该代码使用了三角形和顶点的类来表示数据，以及Bowyer-Watson算法来进行三角剖分。在主函数中，可以通过创建一个DelaunayTriangulation对象并传入一个顶点列表来获取三角形列表。