High quality compatible triangulations

Compatible meshes are isomorphic meshings of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons, sometimes requiring extra (Steiner) vertices. Experimental results show that for typical real-life inputs, the number of Steiner vertices introduced is very small. However, having a small number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e. they do not have well-shaped triangles. We show how to increase the quality of these triangulations by adding Steiner vertices in a compatible manner, using remeshing and mesh smoothing techniques. The total scheme results in high-quality compatible meshes with a small number of triangles. These meshes may then be morphed to obtain the intermediate triangulated sections of a sweep, if needed.