Abstract
Smoothing is only one of the processes we generally have to apply to acquired geometry. This chapter discusses several other important algorithms connected by virtue of being simple greedy processes where we improve the mesh by local changes to the mesh connectivity.
First, we discuss the popular scheme for mesh simplification due to Garland and Heckbert where edges are iteratively contracted according to a cost function stored in a priority queue. Next, we discuss various algorithms for improvement of meshes based on flipping an edge separating two triangles to the other diagonal of the quadrilateral formed by the two triangles. Greedy schemes may again be applied for mesh flip optimization, but we also consider the method of simulated annealing.
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
References
Schroeder, W.J., Zarge, J.A., Lorensen, W.E.: Decimation of triangle meshes. Comput. Graph. 26(2), 65–70 (1992)
Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. Graph. 23(3), 905–914 (2004)
Yan, D.M., Liu, Y., Wang, W.: Quadric surface extraction by variational shape approximation. In: Geometric Modeling and Processing-GMP 2006, pp. 73–86 (2006)
Kälberer, F., Nieser, M., Polthier, K.: QuadCover-surface parameterization using branched coverings. Comput. Graph. Forum 26(3), 375–384 (2007)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings of the 24th Annual Conference on Computer Graphics and interactive Techniques, pp. 209–216 (1997)
Zelinka, S., Garland, M.: Permission grids: practical, error-bounded simplification. ACM Trans. Graph. 21(2), 207–229 (2002)
Hoppe, H.: Progressive meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 99–108. ACM, New York (1996)
Garland, M.: Quadric-based polygonal surface simplification. Ph.D. thesis, Georgia Institute of Technology (1999)
Shewchuck, J.R.: Lecture notes on delaunay mesh generation. Technical report, UC Berkeley (1999). http://www.cs.berkeley.edu/~jrs/meshpapers/delnotes.ps.gz
Dyn, N., Hormann, K., Kim, S.-J., Levin, D.: Optimizing 3d triangulations using discrete curvature analysis. In: Mathematical Methods for Curves and Surfaces, Oslo, 2000, pp. 135–146. Vanderbilt University, Nashville (2001)
Bærentzen, J.A.: Optimizing 3d triangulations to recapture sharp edges. Technical report, Technical University of Denmark, Informatics and Mathematical Modelling, Image Analysis and Computer Graphics (2006). http://www2.imm.dtu.dk/pubdb/p.php?4689
Hoffmann, C.M.: Geometric and Solid Modeling. Morgan Kaufmann, San Mateo (1989)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Schumaker, L.L.: Computing optimal triangulations using simulated annealing. In: Selected Papers of the International Symposium on Free-form Curves and Free-form Surfaces, pp. 329–345. Elsevier, Amsterdam (1993). doi:10.1016/0167-8396(93)90045-5
Paulsen, R.R., Baerentzen, J.A., Larsen, R.: Markov random field surface reconstruction. In: IEEE Transactions on Visualization and Computer Graphics, pp. 636–646 (2009)
Botsch, M., Kobbelt, L.: A remeshing approach to multiresolution modeling. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP’04, pp. 185–192. ACM, New York (2004)
Botsch, M., Kobbelt, L., Pauly, M., Alliez, P., Levy, B.: Polygon Mesh Processing. AK Peters, Wellesley (2010)
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Mesh optimization. In: Proc. ACM SIGGRAPH 93 Conf Comput Graphics and Proceedings of the ACM SIGGRAPH’93 Conference on Computer Graphics, pp. 19–25 (1993)
Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W.: Piecewise smooth surface reconstruction. In: Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, pp. 295–302. ACM, New York (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag London
About this chapter
Cite this chapter
Bærentzen, J.A., Gravesen, J., Anton, F., Aanæs, H. (2012). Simplifying and Optimizing Triangle Meshes. In: Guide to Computational Geometry Processing. Springer, London. https://doi.org/10.1007/978-1-4471-4075-7_11
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4075-7_11
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4074-0
Online ISBN: 978-1-4471-4075-7
eBook Packages: Computer ScienceComputer Science (R0)