GPU-based Conformal Flow on Surfaces
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