Problem 45218. Find a common edge

Created by Mathworlds

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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 is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie</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> ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.</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[e = [2 3]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>the output is the vector</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[row_idx = [1 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>since [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>edge [b a] is the same as edge [a b]</w:t></w:r><w:r><w:t> so must be the corresponding outputs). If the edge 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 e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie e1 &lt; e2 ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.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">e = [2 3]
</pre>the output is the vector<pre class="language-matlab">row_idx = [1 4]
</pre>since [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that edge [b a] is the same as edge [a b] so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.

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Last Solution submitted on Dec 05, 2020

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Mathworlds on 1 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-.

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Problem 45218. Find a common edge

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