Ico球面细分缺失

在处理Ico球面细分时，有时会出现缺失的问题。这是由于细分过程中某些边或顶点的分裂被跳过或错误处理导致的。以下是一种可能的解决方法，其中包含代码示例：

import numpy as np

def subdivide(vertices, indices, subdivisions):
    for _ in range(subdivisions):
        new_vertices = []
        new_indices = []

        for i in range(len(indices)//3):
            v1 = vertices[indices[i*3]]
            v2 = vertices[indices[i*3+1]]
            v3 = vertices[indices[i*3+2]]

            # Calculate midpoints
            mid1 = (v1 + v2) / 2
            mid2 = (v2 + v3) / 2
            mid3 = (v3 + v1) / 2

            # Normalize midpoints
            mid1 /= np.linalg.norm(mid1)
            mid2 /= np.linalg.norm(mid2)
            mid3 /= np.linalg.norm(mid3)

            # Append new vertices
            new_vertices.extend([v1, v2, v3, mid1, mid2, mid3])

            # Calculate new indices
            index = i * 6
            new_indices.extend([
                indices[index], indices[index+3], indices[index+5],
                indices[index+3], indices[index+1], indices[index+4],
                indices[index+5], indices[index+4], indices[index+2],
                indices[index+3], indices[index+4], indices[index+5],
            ])

        vertices = np.array(new_vertices)
        indices = np.array(new_indices)

    return vertices, indices

# Example usage
# Define icosahedron vertices and indices
icosahedron_vertices = np.array([
    [0, 0, -1],
    [0, 0, 1],
    [-1, 0.5, 0],
    [1, 0.5, 0],
    [-1, -0.5, 0],
    [1, -0.5, 0],
    [0.5, 0, -1],
    [-0.5, 0, -1],
    [0.5, 0, 1],
    [-0.5, 0, 1],
    [0, 1, 0.5],
    [0, 1, -0.5],
    [0, -1, 0.5],
    [0, -1, -0.5],
    [-0.5, 0.5, 0],
    [0.5, 0.5, 0],
    [-0.5, -0.5, 0],
    [0.5, -0.5, 0],
    [0, 0.5, -0.5],
    [0, -0.5, -0.5],
    [0, 0.5, 0.5],
    [0, -0.5, 0.5],
])

icosahedron_indices = np.array([
    0, 2, 6,
    0, 6, 7,
    0, 7, 3,
    0, 3, 1,
    0, 1, 2,
    1, 3, 9,
    3, 7, 10,
    7, 6, 11,
    6, 2, 8,
    2, 1, 5,
    4, 5, 9,
    4, 9, 11,
    4, 11, 10,
    4, 10, 8,
    4, 8, 5,
    5, 8, 2,
    9, 5, 1,
    11, 9, 3,
    10, 11, 7,
    8, 10, 6,
])

# Subdivide 3 times
subdivisions = 3
subdivided_vertices, subdivided_indices = subdivide(icosahedron_vertices, icosahedron_indices, subdivisions)

这段代码使用numpy库实现了Ico球面的细分。subdivide函数接受球面的初始顶点和索引数组，以及细分次数。它通过迭代将每个三角形分裂成四个新