Automatic Shape Control of Triangular B-Splines of Arbitrary Topology
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Triangular B-splines are powerful and flexible in modeling a broader class of geometric objects defined over arbitrary, non-rectangular domains. Despite their great potential and advantages in theory, practical techniques and computational tools with triangular B-splines are less-developed. This is mainly because users have to handle a large number of irregularly distributed control points over arbitrary triangulation. In this paper, an automatic and efficient method is proposed to generate visually pleasing, high-quality triangular B-splines of arbitrary topology. The experimental results on several real datasets show that triangular B-splines are powerful and effective in both theory and practice.
- 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.
- Pfeifle R, Seidel H P. Spherical triangular B-splines with application to data fitting. Computer Graphics Forum, 1995, 14(3): 89–96. CrossRef
- 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.
- 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.
- C de Boor. Splines as Linear Combinations of B-Splines. A survey, In Approximation Theory II, Academic Press, 1976, pp.1–47.
- Ramshaw L. Blossom are polar forms. Computer Aided Geometric Design, 1989, 6(4): 323–358. CrossRef
- 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. CrossRef
- 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.
- Greiner G, Seidel H P. Modeling with triangular B-splines. IEEE Computer Graphics and Applications, 1994, 14(2): 56–60. CrossRef
- Pfeifle R, Seidel H P. Fitting triangular B-splines to functional scattered data. In Proc. Graphics Interface (GI′95), Quebec, Canada, 1995, pp.26–33.
- 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.
- Franssen M, Veltkamp R C, Wesselink W. Efficient evaluation of triangular B-spline surfaces. Computer Aided Geometric Design, 2000, 17(9): 863–877. CrossRef
- He Y, Qin H. Surface reconstruction with triangular B-splines. In Proc. Geometric Modeling and Processing (GMP′04), Beijing, China, 2004, pp.279–290.
- 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.
- 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. CrossRef
- 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. CrossRef
- Neamtu M. Homogeneous simplex splines. J. Comput. Appl. Math., 1996, 73(1-2): 173–189. CrossRef
- Gu X, Yau S T. Global conformal surface parameterization. In Proc. the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SGP′03), Aachen, Germany, 2003, pp.127–137.
- 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.
- Seidel H P. Polar Forms and Triangular B-Spline Surfaces. Euclidean Geometry and Computers, 2nd Edition, World Scientific Publishing Co., 1994, pp.235–286.
- Automatic Shape Control of Triangular B-Splines of Arbitrary Topology
Journal of Computer Science and Technology
Volume 21, Issue 2 , pp 232-237
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- triangular B-splines
- arbitrary topology
- fairing algorithm
- Industry Sectors