MESHEDGEGEODESICDISTANCES Calculates distances between vertices on 3d triangulated mesh

Usage Notes

• Time taken on fsLR downsampled meshes: 5k, 1.5 seconds; 10k, 6 seconds; 32k, 50 seconds
• You can select a subset of the vertices to be used as sources/targets, or a maximum radius within which to compute distances. However using both concurrently is not (yet) supported.

Examples

[x,y] = meshgrid(1:20,1:30); x=x(:); y=y(:); z=ones(size(x)); f=delaunay(x,y); v=[x,y,z]; d = meshEdgeGeodesicDistances(v,f); figure; for ii = 1:21:400; nexttile; patch('Vertices', v, 'Faces', f, 'FaceColor', 'interp', 'FaceVertexCData', d(:,ii), 'EdgeColor', 'k'); hold on; scatter3(v(ii,1), v(ii,2), v(ii,3), 50, 'red', 'filled'); axis square equal tight off; view(3); colorbar; end;
[x,y] = meshgrid(1:20); x=x(:); y=y(:); z=10*sin(x)+0.1*(y-10).^2; f=delaunay(x,y); v=[x,y,z]; d = meshEdgeGeodesicDistances(v,f); figure; for ii = 1:40:400; nexttile; patch('Vertices', v, 'Faces', f, 'FaceColor', 'interp', 'FaceVertexCData', d(:,ii), 'EdgeColor', 'k'); hold on; scatter3(v(ii,1), v(ii,2), v(ii,3), 50, 'red', 'filled'); axis square equal tight off; view(3); colorbar; end;
[v,f] = torusMesh(10); d = meshEdgeGeodesicDistances(v,f); figure; for ii = 1:8:90; nexttile; patch('Vertices', v, 'Faces', f, 'FaceColor', 'interp', 'FaceVertexCData', d(:,ii), 'EdgeColor', 'k'); hold on; scatter3(v(ii,1), v(ii,2), v(ii,3), 50, 'red', 'filled'); axis square equal tight off; view(3); colorbar; end;
[v,f] = torusMesh(200); d = meshEdgeGeodesicDistances(v,f); figure; for ii = 1:900:9900; nexttile; patch('Vertices', v, 'Faces', f, 'FaceColor', 'interp', 'FaceVertexCData', d(:,ii), 'EdgeColor', 'none'); hold on; scatter3(v(ii,1), v(ii,2), v(ii,3), 50, 'red', 'filled'); axis square equal tight off; view(3); colorbar; end;

[v,f] = equilateralMesh(20); d = meshEdgeGeodesicDistances(v,f,[],[],1.01); assert(all(sum(isnan(d))==7));
[v,f] = torusMesh(40); d = meshEdgeGeodesicDistances(v,f,[],[],1); figure; for ii = 1:100:1200; nexttile; patch('Vertices', v, 'Faces', f, 'FaceColor', 'interp', 'FaceVertexCData', d(:,ii), 'EdgeColor', 'none'); axis image; colorbar; end

TODO

• docs

Authors

Mehul Gajwani, Monash University, 2024