python矢量算法-三角形变化寻找对应点
1.算法需求描述
现有随机生成的两个三角形A与B，在三角形A中存在Pa，使用算法计算出三角形B中对应的点Pb
2.python代码
import numpy as np # 计算三角形A的面积
def area_triangle(vertices): return 0.5 * np.abs(np.dot(vertices[0] - vertices[1], vertices[1] - vertices[2])) # 计算重心坐标
def barycentric_coordinates(P, vertices): v0 = vertices[1] - vertices[0] v1 = vertices[2] - vertices[0] v2 = P - vertices[0] d00 = np.dot(v0, v0) d01 = np.dot(v0, v1) d11 = np.dot(v1, v1) d20 = np.dot(v2, v0) d21 = np.dot(v2, v1) denom = d00 * d11 - d01 * d01 v = (d11 * d20 - d01 * d21) / denom w = (d00 * d21 - d01 * d20) / denom u = 1.0 - v - w return np.array([u, v, w])
def generate_random_triangle():# 随机生成三个点作为三角形的顶点vertices = np.random.rand(3, 2) # 生成三个点，每个点有两个坐标值return vertices
def generate_random_point_in_triangle(triangle):# 生成两个随机数r1, r2 = np.random.rand(2)# 通过重心坐标法生成点sqrt_r1 = np.sqrt(r1)u = 1 - sqrt_r1v = r2 * sqrt_r1w = 1 - u - v# 计算点的坐标point = u * triangle[0] + v * triangle[1] + w * triangle[2]return point
import matplotlib.pyplot as plt# 定义三角形的三个顶点坐标
source_A = generate_random_triangle()
target_B = generate_random_triangle()# 定义点P在三角形A内的坐标
PA = generate_random_point_in_triangle(source_A) # 计算点P在三角形A中的重心坐标
PA_coords = barycentric_coordinates(PA, source_A) # 使用重心坐标在三角形B中找到对应的点Pt
PB = PA_coords[0] * target_B[0] + PA_coords[1] * target_B[1] + PA_coords[2] * target_B[2] print("Pt的坐标是:", PB)# 绘制图形
plt.figure(figsize=(8, 6))# 绘制A_arr构成的平面
plt.fill([point[0] for point in source_A], [point[1] for point in source_A], color='blue', alpha=0.2, label='A_arr Plane')# 绘制B_arr中的点
plt.fill([point[0] for point in target_B], [point[1] for point in target_B], color='red', label='B_arr Points')# 绘制source_P和target_P
plt.scatter(PA[0], PA[1], color='green', marker='o', label='Source Point')
plt.scatter(PB[0], PB[1], color='orange', marker='o', label='Target Point')# 标记顶点顺序
for i, point in enumerate(source_A):plt.text(point[0], point[1], str(i + 1), fontsize=12, color='black', ha='right', va='bottom')for i, point in enumerate(target_B):plt.text(point[0], point[1], str(i + 1), fontsize=12, color='black', ha='right', va='bottom')plt.xlabel('X')
plt.ylabel('Y')
plt.title('Visualization of Points and Plane')
plt.legend()
plt.grid(True)
plt.show()3.计算结果
