Automatic shape control of triangular B-splines of arbitrary topology

Journal of Computer Science and Technology

Volumn 21, Issue 2, 2006, Pages 232-237

  He, Ying ^a   Gu, Xian Feng ^a   Qin, Hong ^a  

^a Stony Brook University   (United States)

Author keywords

Arbitrary topology; Fairing algorithm; Triangular B splines

Indexed keywords

ARBITRARY TOPOLOGY; FAIRING ALGORITHMS; TRIANGULAR B-SPLINES;

COMPUTATION THEORY; DATABASE SYSTEMS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; SET THEORY; TOPOLOGY; TRIANGULATION;

SPLINES;

EID: 33645943389     PISSN: 10009000     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11390-006-0232-4     Document Type: Article

References (20)

1. Dahmen W, Micchelli C A, Seidel H P. Blossoming begets B-spline bases built better by B-patches. Mathematics of Computation, 1992, 59(199): 97-115.
2. Pfeifle R, Seidel H P. Spherical triangular B-splines with application to data fitting. Computer Graphics Forum, 1995, 14(3): 89-96.
3. He Y, Gu X, Qin H. Rational spherical splines for genus zero shape modeling. In Proc. International Conference on Shape Modeling and Applications (SMI'05), Boston, USA, 2005, pp.82-91.
4. Gu X, He Y, Qin H. Manifold splines. In Proc. ACM Symposium on Solid and Physical Modeling (SPM'05), Boston, USA, 2005, pp.27-38.
5. C de Boor. Splines as Linear Combinations of B-Splines. A survey, In Approximation Theory II, Academic Press, 1976, pp.1-47.
6. Ramshaw L. Blossom are polar forms. Computer Aided Geometric Design, 1989, 6(4): 323-358.
7. Seidel H P. Symmetric recursive algorithms for surfaces: B-patches and the de Boor algorithm for polynomials over triangles. Constr. Approx., 1991, 7: 257-279.
8. Fong P, Seidel H P. An implementation of multivariate B-spline surfaces over arbitrary triangulations. In Proc. Graphics Interface (GI'92), Vancouver, Canada, 1992, pp.1-10.
9. Greiner G, Seidel H P. Modeling with triangular B-splines. IEEE Computer Graphics and Applications, 1994, 14(2): 56-60.
10. Pfeifle R, Seidel H P. Fitting triangular B-splines to functional scattered data. In Proc. Graphics Interface (GI'9&), Quebec, Canada, 1995, pp.26-33.
11. Gormaz R, Laurent P J. Some results on blossoming and multivariate B-splines. Multivariate Approximation: From CAGD to Wavelets, World Sci. Publishing, 1993, pp.147-165.
12. Franssen M, Veitkamp R C, Wesselink W. Efficient evaluation of triangular B-spline surfaces. Computer Aided Geometric Design, 2000, 17(9): 863-877.
13. He Y, Qin H. Surface reconstruction with triangular B-splines. In Proc. Geometric Modeling and Processing (GMP'04), Beijing, China, 2004, pp.279-290.
14. Neamtu M. Bivariate simplex B-splines: A new paradigm. In Proc. the 17th Spring Conference on Computer Graphics (SCCG'01), Budmerice, Slovakia, 2001, pp.71-78.
15. Alfeld P, Neamtu M, Schumaker L L. Bernstein-Bézier polynomials on spheres and sphere-like surfaces. Computer Aided Geometric Design, 1996, 13(4): 333-349.
16. Alfeld P, Neamtu M, Schumaker L L. Fitting scattered data on sphere-like surfaces using spherical splines. J. Comput. Appl. Math., 1996, 73(1-2): 5-43.
17. Neamtu M. Homogeneous simplex splines. J. Comput. Appl. Math., 1996, 73(1-2): 173-189.
18. Gu X, Yau S T. Global conformal surface parameterization. In Proc. the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SOP'03), Aachen, Germany, 2003, pp.127-137.
19. Gormaz R. B-Spline Knot-Line Elimination and Bézier Continuity Conditions. Curves and Surfaces in Geometric Design, MA: A K Peters, Wellesley, 1993, pp.209-216.
20. Seidel H P. Polar Forms and Triangular B-Spline Surfaces. Euclidean Geometry and Computers, 2nd Edition, World Scientific Publishing Co., 1994, pp.235-286.