Problem 45220. Find triangles from edge

Created by Nicolas Douillet

Solve Later

{"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 is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[e = [2, 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>and T a tetrahedron</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[T = [1, 2, 3;...\n 1, 3, 4;...\n 1, 2, 4;...\n 2, 3, 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>then the output of the function is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[S = [1, 2, 4;...\n 2, 3, 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>since both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Conditions :</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>If the edge is not part of any triangle in the list, the function must of course return the empty set, [].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Edges are symmetric :</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>[e1, e2] is the same edge as [e2, e1]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Order of rows / edges in the output doesn't matter.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Triangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 &lt; t2 &lt; t3.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Every</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>indices are positive, distinct integers.</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 is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if<pre class="language-matlab">e = [2, 4]
</pre>and T a tetrahedron<pre class="language-matlab">T = [1, 2, 3;...
 1, 3, 4;...
 1, 2, 4;...
 2, 3, 4]
</pre>then the output of the function is<pre class="language-matlab">S = [1, 2, 4;...
 2, 3, 4]
</pre>since both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].Conditions :<ul><li>If the edge is not part of any triangle in the list, the function must of course return the empty set, [].</li><li>Edges are symmetric : [e1, e2] is the same edge as [e2, e1]</li><li>Order of rows / edges in the output doesn't matter.</li><li>Triangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 &lt; t2 &lt; t3.</li><li>Every indices are positive, distinct integers.</li></ul>

Solve

Solution Stats

22 Solutions
15 Solvers

Last Solution submitted on Mar 20, 2023

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Nicolas Douillet on 3 Dec 2019

Info : T is actually a triangulation -list of triangles-, in which each index corresponding to the row index of a vertex in another list -a vertices list-, it is a widely used technique used to store and write triangular meshes in mesh processing. Here below the example is a tetrahedron -4 facets-.

Nicolas Douillet on 3 Dec 2019

I actually realize this problem looks like a lot to my second problem, "Find a common edge" ( https://fr.mathworks.com/matlabcentral/cody/problems/45218-find-a-common-edge ) ...

Problem Recent Solvers15

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 45220. Find triangles from edge

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Problem 45220. Find triangles from edge

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players