Voronoi Filters for Simulation Enrichment

Abstract

The simulation of complex deformation problems often requires enrichment techniques that introduce local high-resolution detail on a generally coarse discretization. The use cases include spatial or temporal refinement of the discretization, the simulation of composite materials with phenomena occurring at different scales, or even codimensional simulation. We present an efficient simulation enrichment method for both local refinement of the discretization and codimensional effects. We dub our method Voronoi filters, as it combines two key computational elements. One is the use of kinematic filters to constrain coarse and fine deformations, and thus provide enrichment functions that are complementary to the coarse deformation. The other one is the use of a centroidal Voronoi discretization for the design of the enrichment functions, which adds high-resolution detail in a compact manner while preserving the rigid modes of coarse deformation. We demonstrate our method on simulation examples of composite materials, hybrid triangle-based and yarn-level simulation of cloth, or enrichment of flesh simulation with high-resolution detail.