Topology-preserving triangulation simplification algorithm by edge contraction

Triangulation is widely used to represent models of real objects in digital form, and often, in order to get the desired model, we need to triangulate it from data of another kind, for example, from a voxel model. There are methods that allow one to do it, but the resulting triangulation does not always have the desired quality. One way to solve this problem is triangulation simplification algorithms. However, they have disadvantages; in particular, in some cases they can destroy the model topology during the simplification process, which leads to the rejection of the simplification of the tetrahedral mesh in some local area. In this paper, we will consider the naive method of triangulation simplification using edge contraction, its shortcomings, and propose its modification that allows us to contract any edges without topology violations.