ABSTRACT
This course provides an overview of CGAL geometric algorithms and data structures. We start with a presentation the objectives and scope of the CGAL open source project. The three next parts cover SIGGRAPH topics: (1) CGAL for point set processing, including denoising, outlier removal, smoothing, resampling, curvature estimation, shape detection and surface reconstruction, (2) CGAL for polygon mesh processing, including Boolean operations, deformation, skeletonization, segmentation, hole filling, isotropic remeshing, simplification, and (3) CGAL for mesh generation, including surface and volume mesh generation, from either 3D images, implicit functions or surface meshes.
Supplemental Material
- http://www.cgal.org/Google Scholar
- Ruwen Schnabel, Roland Wahl, and Reinhard Klein. Efficient ransac for point-cloud shape detection. In Computer graphics forum, volume 26, pages 214--226. Wiley Online Library, 2007.Google Scholar
- David Cohen-Steiner and Tran Kai Frank Da. A greedy Delaunay-based surface reconstruction algorithm. The Visual Computer, 20:4--16, 2004. Google ScholarDigital Library
- Olga Sorkine and Marc Alexa. As-rigid-as-possible surface modeling. In ACM International Conference Proceeding Series, volume 257, pages 109--116. Citeseer, 2007. Google ScholarDigital Library
- Isaac Chao, Ulrich Pinkall, Patrick Sanan, and Peter Schröder. A simple geometric model for elastic deformations. In ACM SIGGRAPH 2010 papers, SIGGRAPH '10, pages 38:1--38:6. ACM, 2010. Google ScholarDigital Library
- Andrea Tagliasacchi, Ibraheem Alhashim, Matt Olson, and Hao Zhang. Mean curvature skeletons. Computer Graphics Forum (Proceedings of the Symposium on Geometry Processing), 31(5):1735--1744, 2012. Google ScholarDigital Library
- L. Shapira, A. Shamir, and D. Cohen-Or. Consistent mesh partitioning and skeletonisation using the shape diameter function. The Visual Computer, 24(4):249--259, 2008. Google ScholarDigital Library
- M. Botsch and L. Kobbelt. A remeshing approach to multiresolution modeling. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, pages 185--192. ACM, 2004. Google ScholarDigital Library
- Shi-Qing Xin and Guo-Jin Wang. Improving chen and han's algorithm on the discrete geodesic problem. ACM Trans. Graph., 28(4):104:1--104:8, September 2009. Google ScholarDigital Library
- J. Chen and Y. Han. Shortest paths on a polyhedron. Internat. J. Comput. Geom. Appl., 6:127--144, 1996.Google ScholarCross Ref
- Joseph S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647--668, 1987. Google ScholarDigital Library
- Jonathan R. Shewchuk. Tetrahedral mesh generation by Delaunay refinement. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 86--95, 1998. Google ScholarDigital Library
- Pierre Alliez, David Cohen-Steiner, Mariette Yvinec, and Mathieu Desbrun. Variational tetrahedral meshing. ACM Transactions on Graphics, 24:617--625, 2005. SIGGRAPH '2005 Conference Proceedings. Google ScholarDigital Library
- Julie Digne, Jean-Michel Morel, Charyar-Mehdi Souzani, and Claire Lartigue. Scale space meshing of raw data point sets. Computer Graphics Forum, 30(6):1630--1642, 2011.Google ScholarCross Ref
- Michael Kazhdan, M. Bolitho, and Hugues Hoppe. Poisson Surface Reconstruction. In Symp. on Geometry Processing, pages 61--70, 2006. Google ScholarDigital Library
Index Terms
- CGAL: the computational geometry algorithms library
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