Problem 45257. Find neighbor triangle indices

Created by Nicosahedron

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First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).Given a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. A triangle is neighbor to another triangle if they share exactly one edge.For instance if<pre class="language-matlab">T = [1 2 4;...
 2 3 4;...
 5 6 8;...
 6 7 8;...
 1 2 5;...
 2 5 6;...
 2 3 6;...
 3 6 7;...
 3 4 7;...
 4 7 8;...
 4 1 8;...
 1 8 5]
</pre>and t = 3, then the function should return<pre class="language-matlab">L = [4, 6, 12]'
</pre>since rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.Hypothesis :- Since a triangle is not considered neighbor of itself, t should not be part of L.- Order doesn't matter, but T must be a column vector containing all the neighbor triangle -row- indices (except itself then) once only. No duplicata is admitted.- Edges are symmetric : [e1, e2] is the same edge as [e2, e1]- Every indices are positive, distinct integers.

First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).

Given a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. *A triangle is neighbor to another triangle if they share exactly one edge.*

For instance if

T = [1 2 4;...
       2 3 4;...
       5 6 8;...
       6 7 8;...
       1 2 5;...
       2 5 6;...
       2 3 6;...
       3 6 7;...
       3 4 7;...
       4 7 8;...
       4 1 8;...
       1 8 5]

and t = 3, then the function should return

L = [4, 6, 12]'

since rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.

Hypothesis :

- Since a triangle is not considered neighbor of itself, *t should not be part of L.*

- Order doesn't matter, but *T must be a column vector containing all the neighbor* triangle -row- indices (except itself then) once only. *No duplicata is admitted.*

- *Edges are symmetric : [e1, e2] is the same edge as [e2, e1]*

- Every indices are positive, distinct integers.

Solve

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Last Solution submitted on Oct 25, 2021

Last 200 Solutions

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Problem Tags

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 45257. Find neighbor triangle indices

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