Authors:
Cristobal A. Navarro
1
;
Eliana Scheihing
2
and
Nancy Hitschfeld-Kahler
1
Affiliations:
1
Universidad de Chile, Chile
;
2
Universidad Austral de Chile, Chile
Keyword(s):
Delaunay Triangulations, Edge-flip Technique, Parallel Realtime Applications, CUDA, OpenGL, GPGPU.
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Fundamental Methods and Algorithms
;
Geometric Computing
;
Geometry and Modeling
;
High-Performance Computing and Parallel Rendering
;
Modeling and Algorithms
;
Rendering
;
Surface Modeling
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.
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