Communications in Information & Systems

GPU-based Conformal Flow on Surfaces

Kyle Hegeman, Michael Ashikhmin, Hongyu Wang, Hong Qin, and Xianfeng Gu

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Abstract

Accurately simulating fluid dynamics on arbitrary surfaces is of significance in graph- ics, 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 parameter- ization 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. The proposed framework is very general and can be used to solve other types of PDEs on surfaces while taking advantage of GPU acceleration.

Article information

Source
Commun. Inf. Syst. Volume 9, Number 2 (2009), 197-212.

Dates
First available in Project Euclid: 24 December 2009

Permanent link to this document
http://projecteuclid.org/euclid.cis/1261671388

Zentralblatt MATH identifier
05692375

Mathematical Reviews number (MathSciNet)
MR2606089

Citation

Hegeman, Kyle; Ashikhmin, Michael; Wang, Hongyu; Qin, Hong; Gu, Xianfeng. GPU-based Conformal Flow on Surfaces. Communications in Information & Systems 9 (2009), no. 2, 197--212. http://projecteuclid.org/euclid.cis/1261671388.


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