Problem 45262. Remove duplicated vertices

Created by Nicolas Douillet

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>First input V_in is a vertices list (X Y Z coordinates) which may contain duplicata (identical rows).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Second input T_in is the corresponding</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://fr.mathworks.com/help/matlab/ref/triangulation.html\"><w:r><w:t>triangulation</w:t></w:r></w:hyperlink><w:r><w:t> , in which each integer represents the row index of the vertex in the list V_in.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>First output</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>V_out</w:t></w:r><w:r><w:t> -the easiest to compute- is the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>list of vertices without duplicata.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Second output</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>T_out</w:t></w:r><w:r><w:t> is a bit more tricky to compute : once you get rid of duplicated vertices, you of course have to update their</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>corresponding indices in the triangulation</w:t></w:r><w:r><w:t> array. The resulting table is T_out which</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>admit no duplicated triangle.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>NB :</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>triangle orientations in T_out doesn't matter : [i1 i2 i3] is the same as [i3 i2 i1] for instance</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example on a regular octahedron included in the unit sphere :</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[V_in = [0 0 1;...\n sqrt(2) sqrt(2) 0;...\n -sqrt(2) sqrt(2) 0;...\n 0 0 1;... \n -sqrt(2) -sqrt(2) 0;...\n sqrt(2) sqrt(2) 0;...\n sqrt(2) -sqrt(2) 0;...\n 0 0 -1];\n\nT_in = [1, 2, 3;...\n 1, 3, 5;...\n 4, 5, 7;...\n 2, 4, 7;...\n 2, 3, 8;...\n 3, 5, 8;...\n 5, 7, 8;...\n 2, 7, 8];\n\nV_out = [0 0 1;...\n sqrt(2) sqrt(2) 0;...\n -sqrt(2) sqrt(2) 0;... \n -sqrt(2) -sqrt(2) 0;... \n sqrt(2) -sqrt(2) 0;...\n 0 0 -1];\n\nT_out = [1, 2, 3;... \n 1, 2, 5;... \n 1, 3, 4;...\n 1, 4, 5;... \n 2, 3, 6;...\n 2, 5, 6;...\n 3, 4, 6;...\n 4, 5, 6];]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>That's all folks ! (for today at least)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Good work Matlab bro ! :)</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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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Last Solution submitted on Oct 14, 2020

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Nicolas Douillet 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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