![](bg8.png)
Table 2: Detail of effective edge-flips and parallelism ratio at each iteration for the 3d examples.
Moai Horse Dragon Infinite
#iteration flipped excluded flipped excluded flipped excluded flipped excluded
1 1,786 3.88% 31,453 0.08% 106,101 6.63% 508,502 8.62%
2 215 1.83% 4,376 0.21% 22,608 4.08% 237,340 8.48%
3 41 4.66% 598 1.65% 4,455 5.86% 95,975 3.81%
4 3 0% 131 4.38% 995 1.49% 29,568 5.95%
5 1 0% 33 8.34% 207 1.43% 7,882 4.52%
6 10 0% 34 0% 2,844 1.6%
7 4 0% 1 0% 762 5.81%
8 1 0% 195 6.25%
9 40 0%
10 11 0%
Total flips 2,046 36,596 134,401 883,119
Our proposed implementation is useful for appli-
cations that need to quickly improvethe minimum an-
gle of triangulations and visualize a mesh at the same
time; dynamic terrain manipulation and tree stem de-
formations to name some examples. In the near fu-
ture, we will compare the in-circle test with the oppo-
site angle test used in this implementation. We also
want to test the algorithm with bad quality 3D surface
meshes.
ACKNOWLEDGEMENTS
This work was partially supported by Fondecyt
Project N
o
1120495.
REFERENCES
Antonopoulos, C. D., Ding, X., Chernikov, A., Blagojevic,
F., Nikolopoulos, D. S., and Chrisochoides, N. (2005).
Multigrain parallel Delaunay mesh generation: chal-
lenges and opportunities for multithreaded architec-
tures. In Proceedings of the 19th annual international
conference on Supercomputing, ICS ’05, pages 367–
376, New York, NY, USA. ACM.
Cao, T. T. (2010). Computing 2d Delaunay triangulation
using GPU. Manuscript in preparation.
Cervenansk´y, M., T´oth, Z., Starinsk´y, J., Ferko, A.,
and Sr´amek, M. (2010). Parallel GPU-based data-
dependent triangulations. Computers & Graphics,
34(2):125–135.
De Berg, M. (2000). Computational Geometry: Algo-
rithms and Applications. Springer-Verlag TELOS,
Santa Clara, CA, USA.
Edelsbrunner, H. (2001). Geometry and topology for mesh
generation (Cambridge monographs on applied and
computational mathematics).
Fortune, S. (1993). A note on Delaunay diagonal flips”.
Pattern Recognition Letters, 14(9):723 – 726.
Harada, T. (2011). A parallel constraint solver for a rigid
body simulation. In SIGGRAPH Asia 2011 Sketches,
SA ’11, pages 22:1–22:2, New York, NY, USA. ACM.
Healey, R. G., Minetar, M. J., and Dowers, S., editors
(1997). Parallel Processing Algorithms for GIS. Tay-
lor & Francis, Inc., Bristol, PA, USA.
Kohout, J. and Kolingerov´a, I. (2003). Parallel Delau-
nay triangulation based on circum-circle criterion. In
SCCG ’03: Proceedings of the 19th spring conference
on Computer graphics, pages 73–81, New York, NY,
USA. ACM.
Lawson, C. L. (1972). Transforming triangulations. Dis-
crete Mathematics, 3(4):365 – 372.
Navarro, C., Hitschfeld-Kahler, N., and Scheihing, E.
(2011). A parallel GPU-based algorithm for Delaunay
edge-flips. In Abstracts from 27th European Workshop
on Computational Geometry (EUROCG2011), pages
75–78. Morschach, Switzerland.
Nvidia (2011). NVIDIA CUDA Compute Unified Device
Architecture - Programming Guide.
Paul Chew, L. (1989). Constrained Delaunay triangulations.
Algorithmica, 4:97–108.
Rong, G., Tan, T.-S., Cao, T.-T., and Stephanus (2008).
Computing two-dimensional Delaunay triangulation
using graphics hardware. In I3D ’08: Proceedings of
the 2008 symposium on Interactive 3D graphics and
games, pages 89–97, New York, NY, USA. ACM.
Shewchuk, J. R. (1996). Triangle: Engineering a 2d quality
mesh generator and Delaunay triangulator. In ACM,
editor, First Workshop on Applied Computational Ge-
ometry, pages 124–133. (Philadelphia, Pennsylvania).
CGAL (2012). CGAL, Computational Geometry Algo-
rithms Library. http://www.cgal.org.
Tobler, R. F. and Maierhofer, S. (2006). A mesh data struc-
ture for rendering and subdivision. In WSCG ’2006:
Proceedings of WSCG (International Conference in
Central Europe on Computer Graphics, Visualization
and Computer Vision), pages 157–162.
GRAPP2013-InternationalConferenceonComputerGraphicsTheoryandApplications
34