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An Approach for Embedding Regular Analytic Shapes with Subdivision Surfaces

  • Abdulwahed Abbas
  • Ahmad Nasri
  • Weiyin Ma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)

Abstract

This paper presents an approach for embedding regular analytic shapes within subdivision surfaces. The approach is illustrated through the construction of compound Spherical-Catmull-Clark subdivision surfaces. It starts with a subdivision mechanism that can generate a perfect sphere. This mechanism stems from the geometric definition of the sphere shape. Thus, it comes with a trivial proof that the target of the construction is what it is. Furthermore, the similarity of this mechanism to the Catmull-Clark subdivision scheme is exploited to embed spherical surfaces within Catmull-Clark Surfaces, which holds a great potential for many practical applications.

Keywords

Subdivision Scheme Limit Curve Regular Shape Freeform Surface Subdivision Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abbas, A., Nasri, A.: A Generalized Scheme for the Interpolation Of Arbitrarily Intersecting Curves by Subdivision Surfaces. IJCC Journal Japan (2005)Google Scholar
  2. 2.
    Beets, K., Claes, J., Van Reeth, F.: A Subdivision Scheme to Model Surfaces with Spherelike Features. In: WSCG, pp. 103–108 (2005)Google Scholar
  3. 3.
    Catmull, E., Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10, 350–355 (1978)CrossRefGoogle Scholar
  4. 4.
    Chaikin, G.: An algorithm for high-speed curve generation. Computer Graphics and Image Processing 3, 346–349 (1974)CrossRefGoogle Scholar
  5. 5.
    Chalmovianský, P., Jüttler, B.: A Circle-preserving Subdivision Scheme Based on Local Algebraic Fits. Neubauer, A., Schicho, J. (eds.) (November, 2003)Google Scholar
  6. 6.
    Doo, D., Sabin, M.: Behaviors of recursive division surfaces near extraordinary points. Computer-Aided Design 10, 356–360 (1978)CrossRefGoogle Scholar
  7. 7.
    Dyn, N., Levin, D., Gregory, J.A.: A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graph., 9(2), 160–169 (1990)MATHCrossRefGoogle Scholar
  8. 8.
    Levin, A.: Combined Subdivision Schemes, Ph.D. Thesis, Tel Aviv University (2000)Google Scholar
  9. 9.
    Li, G., Ma, W., Bao, H.: \(\sqrt{2}\) Subdivision for quadrilateral meshes. The Visual Computer 20(2-3), 180–198 (2004)CrossRefGoogle Scholar
  10. 10.
    Loop, C.: Smooth Subdivision Surfaces Based on Triangles, Master Thesis, University of Utah (1987)Google Scholar
  11. 11.
    Morin, G., Warren, J.D., Weimer, H.: A subdivision scheme for surfaces of revolution. Computer Aided Geometric Design 18(5), 483–502 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Nasri, A.H., van Overveld, C.W., Wyvill, B.: A Recursive Subdivision Algorithm for Piecewise Circular Spline. Computer Graphics Forum 20(1), 35–45 (2001)CrossRefGoogle Scholar
  13. 13.
    Nasri, A., Farin, G.: A subdivision algorithm for generating rational curves, Journal of Graphical Tools (AK Peters, USA) 3(1), 00–12 (2001)Google Scholar
  14. 14.
    Oswald, P., Schröder, P.: Composite primal/dual sqrt3-subdivision scheme. Computer Aided Geometric Design 20(2), 135–164 (2003)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sabin, M.A.: What is wrong with subdivision surfaces? In: Workshop on Industry Challenges in Geometric Modeling in CAD, March 17 - 18, Darmstadt University of Technology (2004)Google Scholar
  16. 16.
    Sabin, M.A., Dodgson, N.A.: A Circle Preserving Variant of the Four-Point Subdivision Scheme. In: Daelen, M., Morken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces, pp. 275–286. Nashboro Press, Brentwood, TN (2005)Google Scholar
  17. 17.
    Stam, J.: On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree. Computer Aided Geometric Design 18(5), 383–396 (2001)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Stam, J., Loop, C.: Quad/triangle subdivision. Computer Graphics Forum 22(1), 1–7 (2003)CrossRefGoogle Scholar
  19. 19.
    Warren, J., Schaefer, S.: A Factored Approach to Subdivision Surfaces. Computer Graphics & Applications 24, 74–81 (2004)CrossRefGoogle Scholar
  20. 20.
    Warren, J., Weimer, H.: Subdivision Methods for Geometric Design – a Constructive Approach. Morgan Kaufmann Publishers, San Francisco (2002)Google Scholar
  21. 21.
    Zorin, D., Schröder, P.: A unified framework for primal/dual quadrilateral subdivision scheme. Computer Aided Geometric Design 18(5), 429–454 (2001)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Abdulwahed Abbas
    • 1
  • Ahmad Nasri
    • 2
  • Weiyin Ma
    • 3
  1. 1.Department of Computer ScienceThe University of Balamand 
  2. 2.Department of Computer ScienceAmerican University of Beirut 
  3. 3.Dept. of Manufacturing Engr. & Engr. ManagementCity University of Hong Kong 

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