Geodesic Mesh Processing

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This tour explores geodesic computations on 3D meshes.

In [2]:
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.

In [3]:
name = 'elephant-50kv';
[vertex,faces] = read_mesh(name);
nvert = size(vertex,2);

Starting points for the distance computation.

In [4]:
nstart = 15;
pstarts = floor(rand(nstart,1)*nvert)+1;
options.start_points = pstarts;

No end point for the propagation.

In [5]:
clear options;
options.end_points = [];

Use a uniform, constant, metric for the propagation.

In [6]:
options.W = ones(nvert,1);

Compute the distance using Fast Marching.

In [7]:
options.nb_iter_max = Inf;
[D,S,Q] = perform_fast_marching_mesh(vertex, faces, pstarts, options);

Display the distance on the 3D mesh.

In [8]:
clf;
plot_fast_marching_mesh(vertex,faces, D, [], options);

Extract precisely the voronoi regions, and display it.

In [9]:
[Qexact,DQ, voronoi_edges] = compute_voronoi_mesh(vertex, faces, pstarts, options);
options.voronoi_edges = voronoi_edges;
plot_fast_marching_mesh(vertex,faces, D, [], options);

Exercise 1

Using |options.nb_iter_max|, display the progression of the propagation.

In [10]:
exo1()