Determine boundary faces from tetrahedral mesh

Alec Jacobson

April 20, 2011

weblog/

Here's a matlab function that takes a list of tetrahedron indices (4 indices to a row) and finds the triangles that are on the surface of the volume. It does this simply by finding all of the faces that only occur once.

function F = boundary_faces(T)
  % BOUNDARY_FACES
  % F = boundary_faces(T)
  % Determine boundary faces of tetrahedra stored in T
  %
  % Input:
  %  T  tetrahedron index list, m by 4, where m is the number of tetrahedra
  %
  % Output:
  %  F  list of boundary faces, n by 3, where n is the number of boundary faces
  %

  % get all faces
  allF = [ ...
    T(:,1) T(:,2) T(:,3); ...
    T(:,1) T(:,3) T(:,4); ...
    T(:,1) T(:,4) T(:,2); ...
    T(:,2) T(:,4) T(:,3)];
  % sort rows so that faces are reorder in ascending order of indices
  sortedF = sort(allF,2);
  % determine uniqueness of faces
  [u,m,n] = unique(sortedF,'rows');
  % determine counts for each unique face
  counts = accumarray(n(:), 1);
  % extract faces that only occurred once
  sorted_exteriorF = u(counts == 1,:);
  % find in original faces so that ordering of indices is correct
  F = allF(ismember(sortedF,sorted_exteriorF,'rows'),:);
end

With this you can easily determine the vertices of a tetmesh that are on the boundary:

% V are your vertex positions, T are your tet indices
% get boundary faces
F = boundary_faces(T);
% get boundary vertices
b = unique(F(:));
subplot(1,2,1);
% plot boundary positions
plot3(V(b,1),V(b,2),V(b,3),'.');
subplot(1,2,2);
% plot just  boundary faces
trisurf(F,V(:,1),V(:,2),V(:,3),'FaceAlpha',0.3)