Summary
Polygonal meshes are used to model smooth surfaces in many applications. Often these meshes need to be remeshed for improving the quality, density or gradedness. We apply the Delaunay refinement paradigm to design a provable algorithm for isotropic remeshing of a polygonal mesh that approximates a smooth surface. The proofs provide new insights and our experimental results corroborate the theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Alliez, E. C. de Verdière, O. Devillers and M. Isenburg. Isotropic surface remeshing. Proc. Shape Modeling Internat. (2003).
N. Amenta and M. Bern. Surface reconstruction by Voronoi filtering. Discr. Comput. Geom. 22 (1999), 481–504.
N. Amenta, M. Bern and D. Eppstein. The crust and the β-skeleton: combinatorial curve reconstruction. Graphical Models and Image Processing, 60 (1998), 125–135.
N. Amenta, S. Choi, T. K. Dey and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. Applications 12 (2002), 125–141.
J.-D. Boissonnat and S. Oudot. Provably good surface sampling and approximation. Eurographics Sympos. Geom. Process. (2003), 9–18.
H.-L. Cheng, T. K. Dey, H. Edelsbrunner and J. Sullivan. Dynamic skin triangulation. Discrete Comput. Geom. 25 (2001), 525–568.
S.-W. Cheng, T. K. Dey, E. A. Ramos and T. Ray. Sampling and meshing a surface with guaranteed topology and geometry. Proc. 20th Annu. Sympos. Comput. Geom. (2004), 280–289.
S.-W. Cheng, T. K. Dey, E. A. Ramos and T. Ray. Quality meshing for polyhedra with small angles. Proc. 20th Annu. Sympos. Comput. Geom. (2004), 290–299.
L. P. Chew. Guaranteed-quality triangular meshes. Report TR-98-983, Comput. Sci. Dept., Cornell Univ., Ithaca, New York, (1989).
L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., (1993), 274–280.
T. K. Dey. Curve and surface reconstruction. Chapter in Handbook on Discrete and Computational Geometry, 2nd Edition (2004), eds. J. Goodman and J. O’Rourke, CRC press, Boca Raton, Florida.
T. K. Dey, G. Li and T. Ray. Polygonal surface remeshing with Delaunay refinement. Extended version, 2005. http://www.cse.ohiostate.edu/~tamaldey/papers.html.
H. Edelsbrunner and N. Shah. Triangulating topological spaces. Internat. J. Comput. Geom. Appl. 7 (1997), 365–378.
S. Pav and N. Walkington. A robust 3D Delaunay refinement algorithm. Proc. Intl. Meshing Roundtable (2004).
P. P. Pébay and T. J. Baker. Comparison of triangle quality measures. Proc. 10th Internat. Meshing Roundtable, Sandia National Laboratories, (2001), 327–340.
J. Ruppert. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms, 18, (1995), 548–585.
J. R. Shewchuk. Tetrahedral mesh generation by Delaunay refinement. Proc. 14th Annu. ACM Sympos. Comput. Geom., (1998), 86–95.
O. Sifri, A. Sheffer and C. Gotsman. Geodesic-based surface remeshing. Proc. Internat. Meshing Roundtable (2003).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dey, T.K., Li, G., Ray, T. (2005). Polygonal Surface Remeshing with Delaunay Refinement. In: Hanks, B.W. (eds) Proceedings of the 14th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29090-7_21
Download citation
DOI: https://doi.org/10.1007/3-540-29090-7_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25137-8
Online ISBN: 978-3-540-29090-2
eBook Packages: EngineeringEngineering (R0)