GPU-based Conformal Flow on Surfaces

Technical Report
Accurately simulating fluid dynamics on arbitrary surfaces is of significance in graphics, digital entertainment, and engineering applications. This paper aims to improve the efficiency and enhance interactivity of the simulation without sacrificing its accuracy. We develop a GPU-based fluid solver that is applicable for curved geometry. We resort to the conformal (i.e., angle-preserving) structure to parameterize a surface in order to simplify differential operators used in Navier-Stokes and other partial differential equations. Our conformal flow method integrates fluid dynamics with Riemannian metric over curved geometry. Another significant benefit is that a conformal parameterization naturally facilitates the automatic conversion of mesh geometry into a collection of regular geometry images well suited for modern graphics hardware pipeline. Our algorithm for mapping general genus zero meshes to conformal cubic maps is rigorous, efficient, and completely automatic. performance. The proposed framework is very general and can be used to solve other types of PDEs on surfaces while taking advantage of GPU acceleration.