Does edges work with 3D delaunayTriangulation?

Hi,

I have been doing some work with 3D triangulation and the edges command runs with a 3D delaunayTriangulation as the input, but I am unsure if the list of edges it outputs fully encapsulates every connection found with the delaunayTriangulation command.

I was just wondering if anyone can confirm that when you input a 3D delaunayTriangulation, the edges command will sucesfully produce a list of all connections found. The edges page only has an example for 2D triangulation. I would assume it would also do 3D, but some outputs I have had appear to not have all the connections, hence my concern.

Apologies if this has been answered elsewhere, I could not see any other posts on this.

https://au.mathworks.com/help/matlab/ref/triangulation.edges.html?

If it does not, how would one get a list of all connections produced by a delaunayTriangulation ?

Kind Regards,

Aidan.

Answer 1

[Avni Agrawal]

Hi Aidan,

I understand that you are trying to use edges with 3 Delaunay triangulation. To do the same in MATLAB, it should list all the unique edges in the triangulation. If it seems like some edges are missing, it could be due to visualization challenges or the specific characteristics of the Delaunay triangulation.

For ensuring you have all connections, you can manually extract edges from the `ConnectivityList` of the `delaunayTriangulation` object. Here's a simplified example:

% Assuming 'points' is your array of 3D points
DT = delaunayTriangulation(points);

% Extract the list of all tetrahedra
tetrahedra = DT.ConnectivityList;

% Generating all edges from the tetrahedra
edges = unique(sort([tetrahedra(:,[1,2]); tetrahedra(:,[1,3]); tetrahedra(:,[1,4]);
    tetrahedra(:,[2,3]); tetrahedra(:,[2,4]); tetrahedra(:,[3,4])], 2), 'rows');

'edges' now contains all unique edges in the triangulation

This method ensures you're manually checking all edges, which can help verify the completeness of the `edges` command's output.

I hope this helps.