\[
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Mesh Simplification
This tour explore the simplication of a highly detailed mesh into a coarser one.
Contents
Installing toolboxes and setting up the path.
You need to download the following files: signal toolbox, general toolbox and graph toolbox.
You need to unzip these toolboxes in your working directory, so that you have toolbox_signal, toolbox_general and toolbox_graph in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path);
Then you can add the toolboxes to the path.
getd('toolbox_signal/');
getd('toolbox_general/');
getd('toolbox_graph/');
Random Edge Contraction
Simplest way to perform mesh simplification is through edge collapse. Each step replaces two vertex joined by an edge by a
single vertex, and removes the edge.
Load a model.
name = 'venus';
options.name = name;
[vertex,faces] = read_mesh(name);
n = size(vertex,2);
Display full quality.
plot_mesh(vertex,faces,options);
shading faceted;
Initialize the simplification.
faces1 = faces;
vertex1 = vertex;
Compute the collection of edges.
edges = compute_edges(faces1);
nedges = size(edges,2);
Select an edge. Here selection is done at random.
k = floor(rand*(nedges-1))+1;
e = edges(:,k);
Change the vertex location, and remove one of the two vertices.
vertex1(:,e(1)) = mean( vertex1(:,e),2 );
vertex1(:,e(2)) = Inf;
Change the face indexing.
faces1(faces1==e(2)) = e(1);
a = sum( diff(sort(faces1))==0 );
faces1(:,a>0) = [];
Exercice 1: (check the solution) Perform iterative collapse to reach p = round(2*n/3) vertices.
exo1;
Exercice 2: (check the solution) As a post processing, find a way to remove from faces1 and vertex1 the unecessary information (remove vertex and faces that are not used).
exo2;
Error Driven Edge Contraction
To ameliorate the quality of the output mesh, it is necessary to order to select the edge to collapse according to some quality
priority.
Exercice 3: (check the solution) Perform iterative collapse to reach p = round(2*n/3) vertices. Use an ordering of the edge by their length.
exo3;
Exercice 4: (check the solution) Try to use other criteria.
exo4;