The projective linear transition map for constructing smooth surfaces

SMI 2010 - International Conference on Shape Modeling and Applications, Proceedings

Volumn , Issue , 2010, Pages 124-130

  Peters, Jörg ^a   Fan, Jianhua ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Free form spline surface; Gs geometric continuity; Non zero genus; Quad meshes; Reparameterization; Topology; Unique rational linear transition map

Indexed keywords

GEOMETRIC CONTINUITY; LINEAR TRANSITIONS; NON-ZERO GENUS; QUAD MESHES; REPARAMETERIZATION; SPLINE SURFACES;

TOPOLOGY;

SPLINES;

EID: 77956445923     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMI.2010.26     Document Type: Conference Paper

References (11)

1. X. Gu, Y. He, M. Jin, F. Luo, H. Qin, and S.-T. Yau, "Manifold splines with a single extraordinary point," Computer-Aided Design, vol.40, no.6, pp. 676-690, 2008. [Online]. Available: http://dx.doi.org/10.1016/j.cad. 2008.01.008
2. J. W. Milnor, "On the existence of a connection with curvature zero," Comm. Math. Helv., vol.32, no.1, p. 215223, 1958.
3. wiki, "Uniformization theorem," 2009, http://en.wikipedia.org/ wiki/Uniformizationtheorem.
4. J. Peters, "Geometric continuity," in Handbook of Computer Aided Geometric Design. Elsevier, 2002, pp. 193-229.
5. K. Karčiauskas and J. Peters, "Assembling curvature continuous surfaces from triangular patches," SMI 26/105, Computers and Graphics, 2009.
6. L. Ying and D. Zorin, "A simple manifold-based construction of surfaces of arbitrary smoothness," ACM Transactions on Graphics, vol.23, no.3, pp. 271-275, Aug. 2004.
7. C. T. Loop and S. Schaefer, "G2 tensor product splines over extraordinary vertices," Comput. Graph. Forum, vol.27, no.5, pp. 1373-1382, 2008. [Online]. Available: http://dx.doi.org/10.1111/j.1467-8659.2008.01277.x
8. J. Peters and J. Fan, "On the complexity of smooth spline surfaces from quad meshes," Computer- Aided Geometric Design, vol.27, pp. 96-105, 2009, doi:10.1016/j.cagd.2009.09.003.
9. J. M. Hahn, "Geometric continuous patch complexes," Computer Aided Geometric Design, vol.6, no.1, pp. 55-67, 1989.
10. T. Hermann, J. Peters, and T. Strotman, "Constraints on curve networks suitable for G2 interpolation," Dept of CISE, University of Florida, Tech. Rep. REP-2010-2490, feb 2010.
11. J. Wallner and H. Pottmann, "Spline orbifolds," in Curves and Surfaces with Applications in CAGD, A. L. Méhauté, C. Rabut, and L. L. Schumaker, Eds., 1998, pp. 445-464.