Geodesic Mesh Processing¶
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This tour explores geodesic computations on 3D meshes.
warning off
addpath('toolbox_signal')
addpath('toolbox_general')
addpath('toolbox_graph')
addpath('toolbox_wavelet_meshes')
addpath('solutions/fastmarching_4_mesh')
Distance Computation on 3D Meshes¶
Using the fast marching on a triangulated surface, one can compute the distance from a set of input points. This function also returns the segmentation of the surface into geodesic Voronoi cells.
Load a 3D mesh.
name = 'elephant-50kv';
[vertex,faces] = read_mesh(name);
nvert = size(vertex,2);
Starting points for the distance computation.
nstart = 15;
pstarts = floor(rand(nstart,1)*nvert)+1;
options.start_points = pstarts;
No end point for the propagation.
clear options;
options.end_points = [];
Use a uniform, constant, metric for the propagation.
options.W = ones(nvert,1);
Compute the distance using Fast Marching.
options.nb_iter_max = Inf;
[D,S,Q] = perform_fast_marching_mesh(vertex, faces, pstarts, options);
Display the distance on the 3D mesh.
clf;
plot_fast_marching_mesh(vertex,faces, D, [], options);
Extract precisely the voronoi regions, and display it.
[Qexact,DQ, voronoi_edges] = compute_voronoi_mesh(vertex, faces, pstarts, options);
options.voronoi_edges = voronoi_edges;
plot_fast_marching_mesh(vertex,faces, D, [], options);