Chapter 6: Discrete conformal mappings via circle patterns

ACM SIGGRAPH 2005 Courses, SIGGRAPH 2005

Volumn , Issue , 2005, Pages

  Kharevych, Liliya ^a   Springborn, Boris ^b   Schröder, Peter ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Circle patterns; Conformal parameterizations; Discrete analytic functions; Discrete differential geometry; Meshing; Texture mapping

Indexed keywords

COMPUTER GRAPHICS; GEOMETRY; INTERACTIVE COMPUTER GRAPHICS; MAPPING; NUMERICAL METHODS;

ANALYTIC FUNCTIONS; CIRCLE PATTERNS; CONFORMAL PARAMETERIZATIONS; DISCRETE DIFFERENTIAL GEOMETRY; MESHING; TEXTURE MAPPING;

CONFORMAL MAPPING;

EID: 84866489621     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1198555.1198665     Document Type: Conference Paper

References (21)

1. BOBENKO, A. I., AND SPRINGBORN, B. A. 2004. Variational Principles for Circle Patterns and Koebe's Theorem. Transactions of the American Mathematical Society 356, 659-689.
2. BOWERS, P. L., AND HURDAL, M. K. 2003. Planar Conformal Mappings of Piecewise Flat Surfaces. In Visualization and Mathematics III, Springer-Verlag, Berlin, H.-C. Hege and K. Polthier, Eds., Mathematics and Visualization, 3-34. Papers from the 3rd International Workshop held in Berlin, May 22-25, 2002.
3. BRÄGGER, W. 1992. Kreispackungen und Triangulierungen. Enseign. Math. 38, 201-217.
4. COLIN DE VERDIÈRE, Y. 1991. Un principe variationnel pour les empilements de cercles. Invent. Math. 104, 655-669.
5. COLLINS, C., AND STEPHENSON, K. 2003. A Circle Packing Algorithm. Computational Geometry: Theory and Applications 25, 233-256.
6. DESBRUN, M., MEYER, M., AND ALLIEZ, P. 2002. Intrinsic Parameterizations of Surface Meshes. Computer Graphics Forum (Proceedings of Eurographics 2002) 21, 3, 209-218.
7. GRÜNBAUM, B. 2003. Convex polytopes, second ed., vol. 221 of Graduate Texts in Mathematics. Springer-Verlag, New York.
8. GU, X., AND YAU, S.-T. 2003. Global Conformal Surface Parameterization. In Symposium on Geometry Processing, Eurographics/ACM SIGGRAPH, 127-137.
9. HIRANI, A. N. 2003. Discrete Exterior Calculus. PhD thesis, California Institute of Technology.
10. JIN, M., WANG, Y., YAU, S.-T., AND GU, X. 2004. Optimal Global Conformal Surface Parameterizations. In Proceedings of IEEE Visualization, IEEE, 267-274.
11. LEIBON, G. 2002. Characterizing the Delaunay Decompositions of Compact Hyperbolic Surfaces. Geom. Topol. 6, 361-391.
12. LÉVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. 2002. Least Squares Conformal Maps for Automatic Texture Atlas Generation. ACM Transactions on Graphics 21, 3, 362-371.
13. MERCAT, C. 2001. Discrete Riemann Surfaces and the Ising Model. Communications in Mathematical Physics 218, 1, 177-216.
14. MOSEK, 2005. Constrained Quadratic Minimization Software. http://www.mosek.com/. Version 3.1r42.
15. PINKALL, U., AND POLTHIER, K. 1993. Computing Discrete Minimal Surfaces and Their Conjugates. Experimental Mathematics 2, 1, 15-36.
16. RIVIN, I. 1994. Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume. Annals of Mathematics 139, 3, 553-580.
17. RODIN, B., AND SULLIVAN, D. 1987. The Convergence of Circle Packings to the Riemann Mapping. J. Differential Geom. 26, 2, 349-360.
18. SHEFFER, A., AND DE STURLER, E. 2000. Surface Parameterization for Meshing by Triangulation Flattening. In Proceedings of the 9th International Meshing Roundtable, Sandia National Labs, 161-172.
19. SHEFFER, A., LÉVY, B., MOGILNITSKI, M., AND BOGOMYAKOV, A. 2004. ABF++: Fast and Robust Angle Based Flattening. ACM Transactions on Graphics. To appear.
20. THURSTON, W. P. 1980. The Geometry and Topology of Three-Manifolds. Available at http://www.msri.org/publications/books/gt3m/.
21. THURSTON, W. P. 1985. The finite Riemann mapping theorem. Invited talk at the symposium on the occasion of the proof of the Bieberbach conjecture held at Purdue University, March 1985.