Merge the four faces belonging to a tetrahedron

Hi,I have the element information of a mesh

but the mesh is too sparse. I extract all the faces of the mesh element and apply loop refinement for encryption

loop refinement extracts the midpoint of each face and generates a new triangle

but only generates a three-dimensional matrix

How do I merge the faces of a three-dimensional matrix into a new tetrahedron by index？

Answer 1

[Matt J]

The process you've described doesn't uniquely determine what the new tetrahedron decomposition should be. However, you could use delaunayn on your augmented list of vertices (the original vertices plus the new ones) to generate one possible decomposition.

[Chenglin Li]

The delaunayn function doesn't seem to add points, it just does delaunay partitioning and can't refine the mesh.

[Matt J]

No, it doesn't add points. It's your job to add the points. But once you've done so, the delaunay partitioning should become finer, similar to the example below where the adddition of the point (0.5,0) results in an additional triangle.

xy1=[0 0; 1 0; 0 1];
xy2=[0.5,0;xy1];

delaunay(xy1)

ans = 1×3

2 3 1

delaunay(xy2)

ans = 2×3

2 1 4 1 3 4

[Chenglin Li]

But now that I've refined the tetrahedron and generated the new triangle, do I need this function?

[Matt J]

You've added new vertices, but the vertex connection list has not been revised to form new, smaller tetrahedrons. delaunayn will do that.