Transfinite surface interpolation over irregular n-sided domains

CAD Computer Aided Design

Volumn 43, Issue 11, 2011, Pages 1330-1340

  Várady, Tamás ^a   Rockwood, Alyn ^b   Salvi, Péter ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

Blending functions; Computer aided design; Curves and surfaces; n sided patches; Transfinite surface interpolation

Indexed keywords

BLENDING FUNCTION; BOUNDARY CURVES; COMPUTER-AIDED GEOMETRIC DESIGN; CONVEX DOMAINS; CURVES AND SURFACES; DISTANCE-BASED; LOCAL EFFECTS; N-SIDED PATCHES; NETWORK BASED DESIGNS; PARAMETERIZATION METHOD; RESEARCH TOPICS; SHAPE ARTIFACTS; SURFACE INTERPOLATION; TRANSFINITE SURFACE INTERPOLATION; VERTEX BLENDING;

BLENDING; COMPUTER AIDED DESIGN;

INTERPOLATION;

EID: 80054713546     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2011.08.028     Document Type: Article

References (28)

1. G. Farin Curves and surfaces for CAGD: a practical guide 5th ed. 2002 Morgan Kaufmann Publishers Inc. San Francisco (CA, USA)
2. T.W. Sederberg, J. Zheng, A. Bakenov, and A. Nasri T-splines and T-NURCCs, SIGGRAPH'03 2003 ACM New York (NY, USA) p. 47784
3. Coons SA. Surfaces for computer-aided design of space forms. Tech. rep. Cambridge (MA, USA): Massachusetts Institute of Technology; 1967.
4. W.J. Gordon Spline blended surface interpolation through curve networks Journal of Mathematics and Mechanics 18 10 1969 931 952
5. T. Varady Survey and new results in n-sided patch generation Proceedings on mathematics of surfaces II 1988 Clarendon Press New York (NY, USA) 203 235
6. Malraison P. A bibliography for n-sided surfaces. In: Mathematics of surfaces (VIII), information geometers. Winchester (UK); 1998. p. 41930.
7. P. Charrot, and J.A. Gregory A pentagonal surface patch for computer aided geometric design Computer Aided Geometric Design 1 1 1984 87 94 (Pubitemid 16494160)
8. J.A. Gregory N-sided surface patches The mathematics of surfaces 1986 Oxford University Press USA 217 232
9. M. Sabin Non-rectangular surfaces patches suitable for inclusion in a B-spline surface Eurographics'83 1983 North Holland 57 70
10. M. Sabin Some negative results in n sided patches Computer-Aided Design 18 1 1986 38 44
11. D. Storry, and A. Ball Design of an n-sided surface patch from Hermite boundary data Computer Aided Geometric Design 6 2 1989 111 120
12. K. Kato Generation of n-sided surface patches with holes Computer-Aided Design 23 10 1991 676 683
13. T. Varady Overlap patches: a new scheme for interpolating curve networks with n-sided regions Computer Aided Geometric Design 8 1 1991 7 27
14. D. Plowman, and P. Charrot A practical implementation of vertex blend surfaces using an n-sided patch Proceedings of the 6th IMA conference on the mathematics of surfaces 1996 Clarendon Press New York (NY, USA) 67 78
15. M. Hosaka, and F. Kimura Non-four-sided patch expressions with control points Computer Aided Geometric Design 1 1 1984 75 86 (Pubitemid 16494159)
16. C.T. Loop, and T.D. DeRose A multisided generalization of Bézier surfaces ACM Transactions on Graphics 8 1989 204 234
17. C.T. Loop, and T.D. DeRose Generalized B-spline surfaces of arbitrary topology Proceedings of the 17th annual conference on computer graphics and interactive techniques, SIGGRAPH'90 1990 ACM New York (NY, USA) 347 356
18. M. Sabin Transfinite surface interpolation Proceedings of the 6th IMA conference on the mathematics of surfaces 1996 Clarendon Press New York (NY, USA) 517 534
19. K. Kato n-sided surface generation from arbitrary boundary edges P.-J. Laurent, P. Sablonnire, L.L. Schumaker, Curve and surface design: Saint-Malo 1999, innovations in applied mathematics 2000 Vanderbilt University Press Nashville (TN) 173 181
20. Sabin M. Further transfinite surface developments. In: Mathematics of surfaces (VIII), information geometers. Winchester (UK); 1998. p. 16173.
21. K. Gao, and A. Rockwood Multi-sided attribute based modeling R. Martin, H. Bez, M. Sabin, Mathematics of surfaces XI Lecture notes in computer science vol. 3604 2005 Springer Berlin (Heidelberg) 219 232
22. C 2 polygonal surface patch Computer Aided Geometric Design 6 1989 69 75
23. J.A. Gregory, V.K.H. Lau, and J. Zhou Smooth parametric surfaces and n-sided patches W. Dahmen, M. Gasca, C.A. Micchelli, Computation of curves and surfaces 1990 Kluwer Academic Publishers 499 528
24. M.S. Floater Mean value coordinates Computer Aided Geometric Design 20 1 2003 19 27
25. K. Hormann, and M.S. Floater Mean value coordinates for arbitrary planar polygons ACM Transactions on Graphics 25 2006 1424 1441 (Pubitemid 44917211)
26. T. Ju, S. Schaefer, and J. Warren Mean value coordinates for closed triangular meshes ACM Transactions on Graphics 24 2005 561 566
27. Floater MS, Schulz C. Pointwise radial minimization: Hermite interpolation on arbitrary domains. In: Proceedings of the symposium on geometry processing, SGP'08, Eurographics association. Switzerland; 2008. p. 150512.
28. J. Manson, and S. Schaefer Moving least squares coordinates Computer Graphics Forum 29 5 2010 1517 1524