Conformal equivalence of triangle meshes

SIGGRAPH'08: International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 Papers 2008

Volumn , Issue , 2008, Pages

  Springborn, Boris ^a   Schröder, Peter ^b   Pinkall, Ulrich ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Cone singularities; Conformal equivalence; Conformal parameterization; Discrete differential geometry; Discrete riemannian metric; Texture mapping

Indexed keywords

CONE SINGULARITIES; CONFORMAL EQUIVALENCE; CONFORMAL PARAMETERIZATION; DISCRETE DIFFERENTIAL GEOMETRY; DISCRETE RIEMANNIAN METRIC; TEXTURE MAPPING;

COMPUTER GRAPHICS; EQUIVALENCE CLASSES; INTERACTIVE COMPUTER GRAPHICS; PARAMETERIZATION; TEXTURES; TRIANGULATION;

CONFORMAL MAPPING;

EID: 57649112319     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (39)

1. BALAY, S., BUSCHELMAN, K., EIJKHOUT, V, GROPP, W D., KAUSHIK, D., KNEPLEY, M. G., MCINNES, L. C, SMITH, B. E, AND ZHANG, H. 2007. PETSc Users Manual. Tech. Rep. ANL-95/11 (Revision 2.3.3), Argonne National Laboratory, http://www.mcs.anl. gov/petsc/.
2. BEN-CHEN, M., GOTSMAN, C, AND BUNIN, G. 2008. Conformal Flattening by Curvature Prescription and Metric Scaling. Comp. Graph. Forum 27, 2, 449-458.
3. BENSON, S., MCINNES, L. C, MORÉ, J., MUNSON, T, AND SARICH, J. 2007. TAO User Manual. Tech. Rep. ANL/MCS-TM-242 (Revision 1.9), Argonne National Laboratory, http://www.mcs.anl. gov/tao.
4. BOBENKO, A. L., AND SPRINGBORN, B. A. 2004. Variational Principles for Circle Patterns and Koebe's Theorem. Trans. Amer. Math. Soc. 356, 2, 659-689.
5. BOBENKO, A. I., AND SURIS, Y. B., 2005. Discrete Differential Geometry. Consistency as Integrability. Preprint arXiv:math/ 0504358vl. To appear in Graduate Studies in Mathematics of the AMS.
6. BOWERS, P L., AND HURDAL, M. K. 2003. Planar Conformal Mappings of Piecewise Flat Surfaces. In Vis. and Math. III. Springer, 3-34.
7. CHOW, B., AND LUO, E 2003. Combinatorial Ricci Flows on Surfaces. J. Diff. Geom. 63, 1, 97-129.
8. COLIN DE VERDIÉRE, Y 1991. Un Principe Variationnel pour les Empilements de Cercles. Invent. Math. 104, 655-669.
9. DESBRUN, M., MEYER, M., AND ALLIEZ, P 2002. Intrinsic Param-eterizations of Surface Meshes. Comp. Graph. Forum 21, 3, 209-218.
10. DUFFIN, R. J. 1956. Basic Properties of Discrete Analytic Functions. Duke Math. J. 23, 335-363.
11. DUFFIN, R. 1959. Distributed and Lumped Networks. J. Math. Mech. [continued as Indiana Univ. Math. J.] 8, 793-826.
12. ERICKSON, J., AND WHITTLESEY, K. 2005. Greedy Optimal Homotopy and Homology Generators. In Proc. ACM/SIAM Symp. on Disc. Alg., SIAM, 1038-1046.
13. FLOATER, M. S., AND HORMANN, K. 2005. Surface Parameterization: a Tutorial and Survey. In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization. Springer, 157-186.
14. GU, X., AND YAU, S.-T. 2003. Global Conformal Surface Parameterization. In Proc. Symp. Geom. Proc., Eurographics, 127-137.
15. GU, X., GORTLER, S. J., AND HOPPE, H. 2002. Geometry Images. ACM Trans. Graph. 21, 3, 355-361.
16. JIN, M., KIM, J., AND GU, X. D. 2007. Discrete Surface Ricci Flow: Theory and Applications. In Mathematics of Surfaces 2007, R. Martin, M. Sabin, and J. Winkler, Eds., Vol. 4647 of lecture Notes in Computer Science. Springer, 209-232.
17. KÄLBERER, E, NIESER, M., AND POLTHIER, K. 2007. QuadCover- Surface Parameterization using Branched Coverings. Comp. Graph. Forum 26, 3, 375-384.
18. KHAREVYCH, L., SPRINGBORN, B., AND SCHRÖ DER, P 2006. Discrete Conformal Mappings via Circle Patterns. ACM Trans. Graph. 25, 2, 412-438.
19. LEIBON, G. 2002. Characterizing the Delaunay Decompositions of Compact Hyperbolic Surfaces. Geom. Topol. 6, 361-391.
20. LÉVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. 2002. Least Squares Conformal Maps for Automatic Texture Atlas Generation. ACM Trans. Graph. 21, 3, 362-371.
21. LEWIN, L. 1981. Polylogarithms and Associated Functions. North Holland.
22. LUO, E 2004. Combinatorial Yamabe Flow on Surfaces. Commun. Contemp. Math. 6, 765-780.
23. MACLEOD, A. J. 1996. ALGORITHM 757: MISCFUN, a Software Package to Compute Uncommon Special Functions. ACM Trans. Math. Softw. 22, 3, 288-301.
24. MERCAT, C. 2001. Discrete Riemann Surfaces and the Ising Model. Comm. in Math. Physics 218, 1, 177-216.
25. MILNOR, J. 1982. Hyperbolic Geometry: The First 150 Years. Bul. Amer. Math. Soc. 6, 1, 9-24.
26. PINKALL, U., AND POLTHIER, K. 1993. Computing Discrete Minimal Surfaces and Their Conjugates. Experiment. Math. 2, 1, 15-36.
27. RAY, N., LI, W C, LÉVY, B., SHEFFER, A., AND ALLIEZ, P 2006. Periodic Global Parameterization. ACM Trans. Graph. 25, 4, 1460-1485.
28. RIVIN, I, 1994. Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume. Ann. of Math. (2) 139, 553-580.
29. SHEFFER, A., AND HART, J. C. 2002. Seamster: Inconspicuous Low-Distortion Texture Seam Layout. In Proc. IEEE Vis., IEEE Comp. Soc, 291-298.
30. SHEFFER, A., LÉ B., MOGILNITSKY, M., AND BOGOMYAKOV, A. 2005. ABF++ : Fast and Robust Angle Based Flattening. ACM Trans. Graph. 24, 2, 311-330.
31. SHEFFER, A., PRAUN, E., AND ROSE, K. 2006. Mesh Parameterization Methods and their Applications. Found. Trends Comput. Graph. Vis. 2, 2, 105-171.
32. SPRINGBORN, B. 2005. A Unique Representation of Polyhedral Types. Centering via Möbius Transformations. Math. Z. 249, 513-517.
33. STEIHAUG, T. 1983. The Conjugate Gradient Method and Trust Regions in Large Scale Optimization. SIAM J. Numer. Anal. 20, 3, 626-637.
34. STEPHENSON, K. 2003. Circle Packing: A Mathematical Tale. Notices Amer. Math. Soc. 50, 11, 1376-1388.
35. STEPHENSON, K. 2005. Introduction to Circle Packing. Cambridge University Press.
36. TONG, Y., ALLIEZ, P, COHEN-STEINER, D., AND DESBRUN, M. 2007. Designing Quadrangulations with Discrete Harmonic Forms. In Proc. Symp. Geom. Proc., Eurographics, 201-210.
37. TROYANOV, M. 1986. Les Surfaces Euclidiennes à Singularités Coniques. Enseign. Math. (2) 32, 79-94.
38. YANG, Y, KIM, J., LUO, K. HU, S., AND GU, D. 2008. Optimal Surface Parameterization Using Inverse Curvature Map. IEEE Trans. Vis. Comp. Graph, (to appear).
39. ZAYER, R., LÉVY, B., AND SEIDEL, H.-R 2007. Linear Angle Based Parameterization. In Proc. Symp. Geom. Proc, Eurographics, 135-141.