Advertisement

Piecewise Rational Manifold Surfaces with Sharp Features

  • G. Della Vecchia
  • B. Jüttler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5654)

Abstract

We present a construction of a piecewise rational free-form surface of arbitrary topological genus which may contain sharp features: creases, corners or cusps. The surface is automatically generated from a given closed triangular mesh. Some of the edges are tagged as sharp ones, defining the features on the surface. The surface is \(\mathcal C^s\) smooth, for an arbitrary value of s, except for the sharp features defined by the user. Our method is based on the manifold construction and follows the blending approach.

Keywords

Manifold surface sharp features smooth piecewise rational free-form surface arbitrary topological genus geometric continuity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Attene, M., Falcidieno, B., Rossignac, J., Spagnuolo, M.: Sharpen and bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling. IEEE Transactions on Visualization and Computer Graphics 11(2), 181–192 (2005)CrossRefGoogle Scholar
  2. 2.
    Biermann, H., Martin, I., Zorin, D., Bernardini, F.: Sharp features on multiresolution subdivision surfaces. In: Proc. Pacific Graphics, pp. 140–149 (2001)Google Scholar
  3. 3.
    Cotrina-Navau, J., Pla-Garcia, N.: Modeling surfaces from meshes of arbitrary topology. Computer Aided Geometric Design 17(7), 643–671 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Della Vecchia, G., Jüttler, B., Kim, M.-S.: A construction of rational manifold surfaces of arbitrary topology and smoothness from triangular meshes. Computer Aided Geometric Design 25(9), 801–815 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    DeRose, T., Kass, M., Truong, T.: Subdivision surfaces in character animation. In: Proc. SIGGRAPH, pp. 85–94. ACM, New York (1998)Google Scholar
  6. 6.
    Grimm, C., Hughes, J.: Modeling surfaces of arbitrary topology using manifolds. In: Proc. Siggraph, pp. 359–368. ACM Press, New York (1995)Google Scholar
  7. 7.
    Gu, X., He, Y., Jin, M., Luo, F., Qin, H., Yau, S.-T.: Manifold splines with single extraordinary point. In: Proc. Solid and Physical modeling, pp. 61–72. ACM Press, New York (2007)Google Scholar
  8. 8.
    Gu, X., He, Y., Qin, H.: Manifold splines. In: Proc. Solid and Physical Modeling, pp. 27–38. ACM Press, New York (2005)Google Scholar
  9. 9.
    Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W.: Piecewise smooth surface reconstruction. In: Proc. SIGGRAPH, pp. 295–302. ACM, New York (1994)Google Scholar
  10. 10.
    Hubeli, A., Gross, M.: Multiresolution feature extraction from unstructured meshes. In: IEEE Visualization (2001)Google Scholar
  11. 11.
    Khodakovsky, A., Schröder, P.: Fine level feature editing for subdivision surfaces. In: Proc. Shape Modelling Appl., pp. 203–211. ACM, New York (1999)Google Scholar
  12. 12.
    Ling, R., Wang, W., Yan, D.: Fitting sharp features with Loop subdivision surfaces. Comput. Graph. Forum 27(5), 1383–1391 (2008)CrossRefGoogle Scholar
  13. 13.
    Loop, C., DeRose, T.D.: A multisided generalization of Bézier surfaces. ACM Trans. Graph. 8(3), 204–234 (1989)CrossRefzbMATHGoogle Scholar
  14. 14.
    Loop, C., DeRose, T.D.: Generalized B-spline surfaces of arbitrary topology. In: Proc. SIGGRAPH, pp. 347–356. ACM Press, New York (1990)Google Scholar
  15. 15.
    Loop, C.: Smooth spline surfaces over irregular meshes. In: Proc. SIGGRAPH, pp. 303–310. ACM Press, New York (1994)Google Scholar
  16. 16.
    Cotrina Navau, J., Pla Garcia, N., Vigo Anglada, M.: A generic approach to free form surface generation. In: Proc. Solid Modeling and Applications, pp. 35–44. ACM Press, New York (2002)Google Scholar
  17. 17.
    Peters, J.: C 2 free–form surfaces of degree (3,5). Computer Aided Geometric Design 19, 113–126 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Peters, J.: Geometric continuity. In: Farin, G., Hoschek, J., Kim, M.-S. (eds.) Handbook of Computer Aided Geometric Design. Elsevier, Amsterdam (2002)Google Scholar
  19. 19.
    Peters, J., Reif, U.: Subdivision surfaces. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  20. 20.
    Prautzsch, H.: Freeform splines. Computer Aided Geometric Design 14(3), 201–206 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Reif, U.: TURBS - topologically unrestricted rational B-splines. Constructive Approximation 14, 57–77 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Sabin, M.A., Cashman, T.J., Augsdorfer, U.H., Dodgson, N.A.: Bounded curvature subdivision without eigenanalysis. In: Martin, R., Sabin, M.A., Winkler, J.R. (eds.) Mathematics of Surfaces 2007. LNCS, vol. 4647, pp. 391–411. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Yang, H., Jüttler, B.: Evolution of T-spline level sets for meshing non-uniformly sampled and incomplete data. The Visual Computer 24, 435–448 (2008)CrossRefGoogle Scholar
  24. 24.
    Ying, L., Zorin, D.: A simple manifold-based construction of surfaces of arbitrary smoothness. Proc. Siggraph, ACM Transactions on Graphics 23(3), 271–275 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • G. Della Vecchia
    • 1
  • B. Jüttler
    • 1
  1. 1.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria

Personalised recommendations