I am implementing an algorithm which produces a 4d mesh for a cylinder with a given 3d base. This means, I have a 3d mesh and I want to generate a 4d mesh for the corresponding space-time cylinder. Currently I am using netgen for 3d mesh. I am able to generate the 4d vertices and the new 4d elements (pentatopes). This is done by applying a sort of the element-wise procedure for each 3d element. However, I also need boundary elements (which are tetrahedrons in 4d case).
The problem is that the boundary elements of the 3d mesh as produced by netgen are not connected to the 3d elements. I just have a set of triangle indices.
But what I need is to know whether a given 3d element has some of its faces at the boundary (and which one). If I know this, I could use it in the element-wise procedure and create a list of 4d boundary elements as well. But by know I only have a list of 3d boundary elements which contains vertex indices for each boundary triangle of the 3d mesh.
Can anyone give a hint of how one can do that, probably with another meshing software, or somehow?
Or probably there is a software which can generate 4d meshes for a space-time cylinders with, e.g., 3d sphere as a base?
I would appreciate any comments.