Manifold splines with single extraordinary point

Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling

Volumn , Issue , 2007, Pages 61-72

  Gu, Xianfeng ^a,c   He, Ying ^a   Jin, Miao ^a,c   Luo, Feng ^b   Qin, Hong ^a,c   Yau, Shing Tung ^a,d  

^a NTU ^*

^b RUTGERS UNIVERSITY   (United States)

^c STONY BROOK UNIVERSITY   (United States)

^d HARVARD UNIVERSITY   (United States)

Author keywords

Affine structure; Differential geometry; Discrete ricci flow; Extraordinary point; Manifold splines; Metric

Indexed keywords

AFFINE STRUCTURES; DIFFERENTIAL GEOMETRY; EXTRAORDINARY POINTS; MANIFOLD SPLINES;

ALGORITHMS; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; REVERSE ENGINEERING; TOPOLOGY;

SPLINES;

EID: 35348877242     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1236246.1236258     Document Type: Conference Paper

References (19)

1. BOBENKO, A. L, AND SPRINGBORN, B. A. 2004. Variational principles for circle patterns and koebe's theorem. Trans. Amer. Math. Soc 356, 659-689.
2. CARNER, C., JIN, M., GU, X., AND QIN, H. 2005. Topologydriven surface mappings with robust feature alignment. In IEEE Visualization.
3. CHOW, B., AND LUO, F. 2003. Combinatorial Ricci flows on surfaces. J. Differential Geom. 63, 1, 97-129.
4. FLOATER, M. S., AND HORMANN, K. 2005. Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling, N. A. Dodgson, M. S. Floater, and M. A. Sabin, Eds., Mathematics and Visualization. Springer, Berlin, Heidelberg, 157-186.
5. GRIMM, C., AND HUGHES, J. F. 1995. Modeling surfaces of arbitrary topology using manifolds. In SIGGRAPH, 359-368.
6. GU, X., AND YAU, S.-T. 2003. Global conformal surface parameterization. In Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, 127-137.
7. GU, X., HE, Y, AND QIN, H. 2005. Manifold splines. In ACM Symposium on Solid and Physical Modeling, 27-38.
8. HAMILTON, R. S. 1988. The Ricci flow on surfaces. In Mathematics and general relativity (Santa Cruz, CA, 1986), vol.71 of Contemp. Math. Amer. Math. Soc., Providence, RI, 237-262.
9. HE, Y, GU, X., AND QIN, H. 2005. Fairing triangular B-splines of arbitrary topology. In Proceedings of Pacific Graphics '05 (short paper). 153-156.
10. HOPPE, H. 1998. Efficient implementation of progressive meshes. Computers & Graphics 22, 1, 27-36.
11. JIN, M., LUO, F., AND GU, X. 2006. Computing surface hyperbolic structure and real projective structure. In Symposium on Solid and Physical Modeling, 105-116.
12. KHAREVYCH, L., SPRINGBORN, B., AND SCHRÖDER, P. 2005. Cone singularities to the rescue: Mitigating area distorsion in discrete conformai. In ACM SIGGRAPH/Eurographics Symposium on Geometry Processing.
13. NI, X., GARLAND, M., AND HART, J. C. 2004. Fair morse functions for extracting the topological structure of a surface mesh. 613-622.
14. RAY, N., LI, W. C., LEVY, B., SHEFFER, A., AND ALLIEZ, P. 2006. Periodic global parameterization. ACM Transactions on Graphics.
15. RODIN, B., AND SULLIVAN, D. 1987. The convergence of circle packings to the Riemann mapping. J. Differential Geom. 26, 2, 349-360.
16. SEIDEL, H.-P. 1993. An introduction to polar forms. IEEE Comput. Graph. Appl. 13, 1, 38-16.
17. STEPHENSON, K. 2005. Introduction to circle packing. Cambridge University Press, Cambridge. The theory of discrete analytic functions.
18. THURSTON, W. 1982. Hyperbolic geometry and 3-manifolds. In Low-dimensional topology (Bangor, 1979), vol. 48 of London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 9-25.
19. YING, L., AND ZORIN, D. 2004. A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Trans. Graph. 23, 3, 211-215.