On Designing GPU Algorithms with Applications to Mesh Refinement

TL;DR

This paper introduces a set of GPU design rules and presents new algorithms for mesh refinement that significantly outperform existing methods in speed while maintaining mesh quality, enabling real-time applications.

Contribution

It proposes a novel set of GPU algorithm design rules and develops mesh refinement algorithms that are an order of magnitude faster than current state-of-the-art methods.

Findings

Algorithms run an order of magnitude faster than existing methods.

Mesh quality is comparable to current state-of-the-art.

Reduces mesh refinement time from hours to minutes.

Abstract

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D constrained, 3D constrained and 3D Restricted Delaunay refinement problems respectively. Our algorithms take a 2D planar straight line graph (PSLG) or 3D piecewise linear complex (PLC) $\mathcal{G}$ as input, and generate quality meshes conforming or approximating to $\mathcal{G}$. The implementation of our algorithms shows that they are the first to run an order of magnitude faster than current state-of-the-art counterparts in sequential and parallel manners while using similar numbers of Steiner points to produce triangulations of comparable qualities. It thus reduces the computing time of mesh refinement from possibly hours to a few seconds or minutes for possible use in interactive graphics applications.