A Relaxation Method for Surface-Conforming Prisms

This paper presents a method for computing thin layers of high-quality, triangular prisms that conform to surfaces that are specified as level sets of an implicit function. Triangular prisms are important in circumstances where volumetric meshes need to capture the geometries materials with thin layers–i.e. that are smooth relative to their thickness–or where, as in fluid mechanics simulations, solutions perpendicular to boundaries exhibit boundary layer complexities that exceed that of the bounding surfaces. “High-quality” triangular prisms exhibit a roughly linear structure, with nearly regular triangles at the ends and side faces that are nearly perpendicular to the triangular faces. The proposed method relies on an iterative relaxation of point samples, which we call dynamic particles, that simultaneously regularize inter-point distance on the surfaces while shortening distances to corresponding points on a nearby offset surface, which establishes the layer. This paper describes the method and results on meshes of medical data sets that model human vasculature.