I am working with volumetric meshes - meshes that have vertices (0-cell), edges (1-cell), facets (2-cells) and volumes (3-cells) - and I'm interested in removing facets without breaking connectedness.

In other words, say my mesh has 1 connected component, and I don't want to remove a facet f if the resulting mesh has 2 (or more) connected components.

A simple approach is to count the number of connected component with and without f, with a breadth/depth-first search (wikipedia.org/wiki/Component_(graph_theory)). But I don't care how many components there are before or after facet removal, I just don't want this number to change. Any way of estimating the number of connected components looks like a waste of computation time.

My intuition is that a necessary (but not sufficient) condition for the removal of a facet f to possibly "break" connectedness is that both sides of f lie in the same volume, while the removal a facet f' whose incident volumes are two different volumes cannot modify the connectedness of the mesh.

Am I wrong ?

Below is an illustration of a case where the removal of the facet in red would result in two connected components (the little cube inside the big cube). Note that there is no 2-border in this case.

enter image description here



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.