Skip to main content
SpringerLink
Log in

Automatic Shape Control of Triangular B-Splines of Arbitrary Topology

  • Surface Modeling and Computational Geometry
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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.

    MathSciNet  Google Scholar 

  2. Pfeifle R, Seidel H P. Spherical triangular B-splines with application to data fitting. Computer Graphics Forum, 1995, 14(3): 89–96.

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  10. 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.

  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, Veltkamp R C, Wesselink W. Efficient evaluation of triangular B-spline surfaces. Computer Aided Geometric Design, 2000, 17(9): 863–877.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  17. Neamtu M. Homogeneous simplex splines. J. Comput. Appl. Math., 1996, 73(1-2): 173–189.

    Article  MATH  MathSciNet  Google Scholar 

  18. 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.

  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.

    Google Scholar 

  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.

Download references

Author information

Authors and Affiliations

  1. Center for Visual Computing (CVC) and Department of Computer Science, Stony Brook University, Stony Brook, NY, 11790-4400, U.S.A.

    Ying He, Xian-Feng Gu & Hong Qin

Authors
  1. Ying He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xian-Feng Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying He.

Additional information

A preliminary version of this paper appeared in Proc. Pacific Graphics 2005, Macau.

Ying He is a Ph.D. candidate in Computer Science Department at Stony Brook University. He obtained his B.S. and M.S. degrees in electrical engineering from Tsinghua University in 1997 and 2000, respectively. His research interests include computer graphics, computer aided geometric design, scientific visualization, computer vision and medical imaging. His current research projects focus on spline-based shape and solid modeling.

Xian-Feng Gu is an assistant professor in computer science at Stony Brook University. He earned his Ph.D. degree in computer science from Harvard University in 2003. He won the NSF CAREER award in 2004. His research interests are computer graphics, computer vision and medical imaging. His major work includes geometry images, global conformal surface parameterization, manifold splines, hyperbolic and projective structures on surface and computational conformal geometry.

Hong Qin is an associate professor of Computer Science Department at Stony Brook University. In 1997, Professor Qin was awarded NSF CAREER Award from the National Science Foundation (NSF). In December, 2000, Professor Qin received Honda Initiation Grant Award. In April, 2001, Professor Qin was selected as an Alfred P. Sloan Research Fellow by the Sloan Foundation. His areas of expertise include geometric modeling, graphics, physics-based simulation, computer aided geometric design, and human-computer interaction. At present, he is an associate editor of IEEE Transactions on Visualization and Computer Graphics (TVCG) and he is also on the editorial board of The Visual Computer (International Journal of Computer Graphics). In 2005, he co-chaired the 23rd Computer Graphics International Conference (CGI 2005).

Rights and permissions

Reprints and permissions

About this article

Cite this article

He, Y., Gu, XF. & Qin, H. Automatic Shape Control of Triangular B-Splines of Arbitrary Topology. J Comput Sci Technol 21, 232–237 (2006). https://doi.org/10.1007/s11390-006-0232-4

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11390-006-0232-4

Keywords

Search

Navigation