Feature Preserving Parameterization for Quadrilateral Mesh Generation Based on Ricci Flow and Cross Field

Abstract

We propose a new method to generate surface quadrilateral mesh by calculating a globally defined parameterization with feature constraints. In the field of quadrilateral generation with features, the cross field methods are well-known because of their superior performance in feature preservation. The methods based on metrics are popular due to their sound theoretical basis, especially the Ricci flow algorithm. The cross field methods’ major part, the Poisson equation, is challenging to solve in three dimensions directly. When it comes to cases with a large number of elements, the computational costs are expensive while the methods based on metrics are on the contrary. In addition, an appropriate initial value plays a positive role in the solution of the Poisson equation, and this initial value can be obtained from the Ricci flow algorithm. So we combine the methods based on metric with the cross field methods. We use the discrete dynamic Ricci flow algorithm to generate an initial value for the Poisson equation, which speeds up the solution of the equation and ensures the convergence of the computation. Numerical experiments show that our method is effective in generating a quadrilateral mesh for models with features, and the quality of the quadrilateral mesh is reliable.