Quad Mesh Density Control using Optimal Transport

Surface quadrilateral mesh generation plays a fundamental role in CAD/CAE fields. It is crucial to control the density of the meshing structures in practice. In this work, a novel method for controlling the density of quad meshes is proposed based on the Optimal Transport (OT) theory. This method has a rigorous mathematical foundation and efficient and robust computational algorithms. It provides the designers with the flexibility to control the meshing density by prescribing arbitrary probability density functions on the surface. This work demonstrates the efficiency and efficacy of the method using topological disk models, in principle, the method can be generalized to surfaces with arbitrary topologies.