生成网格并细化三角形的网格 [英] Generate mesh and refine mesh of triangles

问题描述

我需要找到一种方法来对三角形进行网格划分，然后使用细化"进行细化.我原始三角形的顶点存储在大小为nb_points * 2的矩阵内.我的人脸存储在 nb_faces * 3 矩阵中.每个面部的数据存储在nb_face * 1矩阵中.网格划分是通过使用三角形线段的中间对区域进行潜水来完成的.

示例:来源:

  vertices = [0 1;2 3;4 1;4 5]；面孔= [1 2 3;2 3 4];数据= [1 2]; 

啮合后预期结果:

  vertices = [0 1;2 3;4 1;4 5;1 2;3 2;2 1;3 4;4 3];面孔= [1 5 7;2 5 6;5 6 7;7 6 3;2 6 8;6 8 9;6 9 3;8 4 9];数据= [1 1 1 1 2 2 2 2]; 

我正在使用:

  FV.Vertices =顶点；FV.Faces =面孔；FV.FaceVertexCData =数据;数字;坚持，稍等;轴相等并网补丁(FV，'FaceColor'，'flat'); 

精度:我不想使用下面的函数，这些函数会导致过多的顶点和面:

• 您可以重复操作:

  I need to find a way to mesh triangles then to refine using refine. My vertices of my original triangles are stored inside a matrix of size nb_points * 2. My faces are stored in a nb_faces * 3 matrix. The data for each face is stored in a nb_face * 1 matrix. The meshing is done by diving the area using the middles of the segments of the triangles.

  Example : Origin :

  vertices = [0 1 ; 
              2 3 ; 
              4 1 ;
              4 5];
  faces = [1 2 3;
           2 3 4];
  data = [1 2]; 
  

  Result expected after meshing :

  vertices = [0 1; 
              2 3; 
              4 1;
              4 5;
              1 2;
              3 2;
              2 1;
              3 4;
              4 3];
  faces = [1 5 7;
           2 5 6;
           5 6 7;
           7 6 3;
           2 6 8;
           6 8 9;
           6 9 3;
           8 4 9];
  data = [1 1 1 1 2 2 2 2];
  

  I am displaying using :

  FV.Vertices = vertices; 
  FV.Faces = faces; 
  FV.FaceVertexCData = data;
  figure; hold on; axis equal; grid on;
  patch(FV,'FaceColor','flat');
  

  Precision : I do not want to use the following functions which gives way too many vertices and faces :

  • generateMesh()
  • refinemesh()

  The data are temperatures since this is a simulation of heat transfer.

  解决方案

  With a for loop it can be done quite easily, here is one solution:

  % Dummy data
  vertices = [0 1 ; 
              2 3 ; 
              4 1 ;
              4 5];
  faces = [1 2 3;
           2 3 4];
  data = [1 2]; 
  
  % Number of vertices
  vnum = size(vertices,1);
  
  % new faces empty vector
  nfaces = [];
  
  % triangular shift
  tshift = [2,-1,-1].';
  
  % Run the algorithm
  for ii = 1:size(faces,1)
      % For each triangle get the 3 pairs of vertices
      nsk = [faces(ii,1), faces(ii,2);faces(ii,2), faces(ii,3);faces(ii,3), faces(ii,1)];
      % Compute the center of each pair of vertices
      cmiddle = (vertices(nsk(:,1),:)+vertices(nsk(:,2),:))/2
      % Compute the new faces
      nfaces = [nfaces;[nsk(:,1),vnum+(ii*3-3+[1:3].'),vnum+(ii*3-3+[1:3].')+tshift];[(vnum+(ii*3-2)):(vnum+(ii*3))]]
      % Add the new vertices
      vertices = [vertices;cmiddle];
  end
  
  % Delete the duplicate vertices
  [vertices,~,ind] = unique(vertices,'rows');
  faces = ind(nfaces);
  
  % Plot
  figure; hold on; axis equal; grid on;
  patch('Faces',faces,'Vertices',vertices,'FaceVertexCData',kron(data,ones(1,4)).','FaceColor','flat')
  colorbar
  

  If you find a way to generate the nsk vector without for loop you could even get rid of the loop. This code will only work on triangle, but it can be adapted if needed.

  Result:

  You can repeat the operation:

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