Problem 45261. List every vertices neighbor indices
Input T is a triangulation.
The purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)
Output N must be a cell array since of course each vertex may have a different number of neighbors.
For example, for an input filled octahedron whom triangulation is
T = [1, 2, 3;... 1, 3, 4;... 1, 4, 5;... 1, 2, 5;... 2, 3, 6;... 3, 4, 6;... 4, 5, 6;... 2, 5, 6;... 2, 3, 4;... 2, 4, 5;... 1, 2, 4;... 2, 4, 6],
then the output N is a 6x1 cell array of integers row vectors, such that :
N(1,1) = {[2, 3, 4, 5]}; N(2,1) = {[1, 3, 4, 5, 6]}; N(3,1) = {[1, 2, 4, 6]}; N(4,1) = {[1, 2, 3, 5, 6]}; N(5,1) = {[1, 2, 4, 6]}; N(6,1) = {[2, 3, 4, 5]};
Indeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).
Hypothesis / conditions :
- a vertex is the neighbor of another if they are linked with an edge in at least one same triangle. A vertex is not neighbor of itself.
- Output N row order is crucial since row number actually corresponds to the vertex id / index.
- Output N cells content order doesn't matter, but it doesn't admit any duplicated index / value.
Tip : solving my previous problems, and especially query_vertex_neighbors will help you to fully understand and solve this one.
NB : the question of unreferenced vertices is not tacled here. We just supposed there are not.
Good work Matlab-bro ! :)
Solution Stats
Problem Comments
-
2 Comments
Pedagogic solution is available in position 2 (commented, same as solution 1 but more explicit thus suboptimal).
In problem 45261, my solution produces a cell array with the correct contents except that my vectors are columns not rows as required in the solution tests. How do I change the contents of each cell from a column to row vector?
Solution Comments
Show commentsProblem Recent Solvers22
Suggested Problems
-
3711 Solvers
-
Maximum running product for a string of numbers
2198 Solvers
-
3616 Solvers
-
Sort numbers by outside digits
151 Solvers
-
Adding Cells with numbers defined as strings
79 Solvers
More from this Author9
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!