A GPU-based Method for Generating quasi-Delaunay Triangulations based on Edge-flips

Cristobal A. Navarro, Eliana Scheihing, Nancy Hitschfeld-Kahler

2013

Abstract

The Delaunay edge-flip technique is a practical method for transforming any existing triangular mesh S into a mesh T(S) that satisfies the Delaunay condition. In this paper we present an iterative GPU-based method capable of improving triangulations under the Delaunay criteria. This method is based on the edge-flip technique and its implementation is fully integrable with the OpenGL rendering pipeline. Since the algorithm uses an e value to handle co-circular or close to co-circular point configurations, we can not guarantee that all triangles fulfill the Delaunay condition. However, we have compared the triangulations generated by our method with the ones generated by the Triangle software and by the CGAL library and we obtained less than 0.05% different triangles. Based on our experimental results, we report speedups from 14× to 50× against Lawson’s sequential algorithm and of approximately 3× against the O(nlog n) CGAL’s and Triangle’s constructive algorithms while processing bad quality triangulations.

Paper Citation

in Harvard Style

Navarro C., Hitschfeld-Kahler N. and Scheihing E. (2013). A GPU-based Method for Generating quasi-Delaunay Triangulations based on Edge-flips . In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013) ISBN 978-989-8565-46-4, pages 27-34. DOI: 10.5220/0004281900270034

in Bibtex Style

@conference{grapp13,
author={Cristobal A. Navarro and Nancy Hitschfeld-Kahler and Eliana Scheihing},
title={A GPU-based Method for Generating quasi-Delaunay Triangulations based on Edge-flips},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)},
year={2013},
pages={27-34},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004281900270034},
isbn={978-989-8565-46-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)
TI - A GPU-based Method for Generating quasi-Delaunay Triangulations based on Edge-flips
SN - 978-989-8565-46-4
AU - Navarro C.
AU - Hitschfeld-Kahler N.
AU - Scheihing E.
PY - 2013
SP - 27
EP - 34
DO - 10.5220/0004281900270034