Problem 45262. Remove duplicated vertices

Created by Mathworlds

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First input V_in is a vertices list (X Y Z coordinates) which may contain duplicata (identical rows).Second input T_in is the corresponding <a href = "https://fr.mathworks.com/help/matlab/ref/triangulation.html">triangulation</a> , in which each integer represents the row index of the vertex in the list V_in.First output V_out -the easiest to compute- is the list of vertices without duplicata.Second output T_out is a bit more tricky to compute : once you get rid of duplicated vertices, you of course have to update their corresponding indices in the triangulation array. The resulting table is T_out which admit no duplicated triangle.NB : triangle orientations in T_out doesn't matter : [i1 i2 i3] is the same as [i3 i2 i1] for instanceExample on a regular octahedron included in the unit sphere :<pre class="language-matlab">V_in = [0 0 1;...
 sqrt(2) sqrt(2) 0;...
 -sqrt(2) sqrt(2) 0;...
 0 0 1;... 
 -sqrt(2) -sqrt(2) 0;...
 sqrt(2) sqrt(2) 0;...
 sqrt(2) -sqrt(2) 0;...
 0 0 -1];
</pre><pre class="language-matlab">T_in = [1, 2, 3;...
 1, 3, 5;...
 4, 5, 7;...
 2, 4, 7;...
 2, 3, 8;...
 3, 5, 8;...
 5, 7, 8;...
 2, 7, 8];
</pre><pre class="language-matlab">V_out = [0 0 1;...
 sqrt(2) sqrt(2) 0;...
 -sqrt(2) sqrt(2) 0;... 
 -sqrt(2) -sqrt(2) 0;... 
 sqrt(2) -sqrt(2) 0;...
 0 0 -1];
</pre><pre class="language-matlab">T_out = [1, 2, 3;... 
 1, 2, 5;... 
 1, 3, 4;...
 1, 4, 5;... 
 2, 3, 6;...
 2, 5, 6;...
 3, 4, 6;...
 4, 5, 6];
</pre>That's all folks ! (for today at least)Good work Matlab bro ! :)

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Mathworlds on 13 Jan 2020

This function is actually one basics of any mesh processing librairy / software.

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3d edge face facet find geometry index indices list mathematics mesh mesh processing surface triangle triangulation trimesh triplet vertex vertices

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Problem 45262. Remove duplicated vertices

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