用matlab编写计算二十面体细分成球的坐标

二十面体细分成球的坐标可以通过以下步骤实现：

定义二十面体的顶点坐标和面的连接关系。
根据面的连接关系，计算出每个面的中心点坐标。
将每个面划分成三角形，计算出每个三角形的顶点坐标。
将每个三角形的顶点坐标与相邻三角形的顶点坐标进行插值，得到新的顶点坐标。
重复上述步骤，直到细分次数达到要求。

以下是一份matlab代码示例：

% 定义二十面体的顶点坐标和面的连接关系 phi = (1 + sqrt(5)) / 2; vertices = [ 0, 1, phi; 0, 1, -phi; 0, -1, phi; 0, -1, -phi; 1, phi, 0; 1, -phi, 0; -1, phi, 0; -1, -phi, 0; phi, 0, 1; phi, 0, -1; -phi, 0, 1; -phi, 0, -1; ]; faces = [ 1, 5, 8; 1, 8, 4; 1, 4, 10; 1, 10, 6; 1, 6, 5; 2, 11, 7; 2, 7, 9; 2, 9, 3; 2, 3, 12; 2, 12, 11; 3, 9, 5; 3, 5, 6; 3, 6, 10; 3, 10, 12; 3, 12, 8; 4, 8, 12; 4, 12, 10; 4, 10, 6; 4, 6, 11; 4, 11, 8; 5, 9, 7; 5, 7, 8; 6, 5, 9; 6, 9, 3; 7, 11, 12; 7, 12, 8; ];

% 细分次数 n = 3;

% 计算每个面的中心点坐标 face_centers = zeros(size(faces, 1), 3); for i = 1:size(faces, 1) face_vertices = vertices(faces(i, :), :); face_centers(i, :) = mean(face_vertices); end

% 计算每个三角形的顶点坐标 for i = 1:n new_vertices = zeros(0, 3); new_faces = zeros(0, 3); for j = 1:size(faces, 1) face_vertices = vertices(faces(j, :), :); face_center = face_centers(j, :); v1 = face_vertices(1, :); v2 = face_vertices(2, :); v3 = face_vertices(3, :); v12 = (v1 + v2) / 2; v23 = (v2 + v3) / 2; v31 = (v3 + v1) / 2; new_vertices = [new_vertices; v1; v2; v3; v12; v23; v31; face_center]; new_faces = [new_faces; ... size(new_vertices, 1) - 5, size(new_vertices, 1) - 3, size(new_vertices, 1); ... size(new_vertices, 1) - 4, size(new_vertices, 1) - 2, size(new_vertices, 1) - 3; ... size(new_vertices, 1) - 3, size(new_vertices, 1) - 1, size(new_vertices, 1) - 2; ... size(new_vertices, 1) - 5, size(new_vertices, 1), size(new_vertices, 1) - 1; ... ]; end vertices = new_vertices; faces = new_faces; face_centers = zeros(size(faces, 1), 3); for j = 1:size(faces, 1) face_vertices = vertices(faces(j, :), :); face_centers(j, :) = mean(face_vertices); end end

% 输出结果 scatter3(vertices(:,1), vertices(:,2), vertices(:,3), 'filled'); axis equal;