Problem 45219. Find edges from a vertex

Created by Nicosahedron

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. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example if inputs are</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 4 2 ;...\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>and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[i = 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 is the 3 x 2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[matrix edg_list= [1 4;...\n 3 4;...\n 2 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>since vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :</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>size(edg_list) = [number of edges, 2]</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 row of it is an edge at the format [e1, e2], sorted in ascending order, i.e.</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>e1 &lt; e2</w:t></w:r><w:r><w:t>, and e1, e2 positive integers.</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>Each edge is present once and only once, no duplicated edge admitted</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:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If the vertex is not in the list, the function must of course return the empty set.</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. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.For example if inputs are<pre class="language-matlab">T = [1 2 3 ;...
 1 3 4 ;...
 1 4 2 ;...
 2 3 4]
</pre>and<pre class="language-matlab">i = 4
</pre>then the output is the 3 x 2<pre class="language-matlab">matrix edg_list= [1 4;...
 3 4;...
 2 4]
</pre>since vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :<ul><li>size(edg_list) = [number of edges, 2]</li><li>Every row of it is an edge at the format [e1, e2], sorted in ascending order, i.e. e1 &lt; e2, and e1, e2 positive integers.</li><li>Each edge is present once and only once, no duplicated edge admitted</li><li>Order of rows / edges in the output doesn't matter .</li></ul>If the vertex is not in the list, the function must of course return the empty set.

Solve

Solution Stats

17 Solutions
9 Solvers

Last Solution submitted on Apr 27, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Nicosahedron 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-.

Problem Recent Solvers9

Problem Tags

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

Community Treasure Hunt

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

Start Hunting!

Problem 45219. Find edges from a vertex

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers9

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Problem 45219. Find edges from a vertex

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers9

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players