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Recursive Curves and Surfaces in Grassmann Space for Computer Modeling and Animation

  • Xiaonan Luo
  • Shujin Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3942)

Abstract

This study gives the new definition of the rational L curve and surface in Grassmann space, where convert these rational recursive curves and surfaces’ equations to normal polynomial. So we can use blossom algorithms and duality principle to deduce the derivative equations of these curves and surfaces. Thus, the rational L spline curve and surface are defined and constructed based on blossom algorithms and ensuring the continuity of L curve segment and surface patch. Next, we prove that rational L spline curve and surface are the generalization of many interpolation or approach parameter curves and surfaces (Lagrange, rational Lagrange, Bezier, rational Bezier, B spline, NURBS curves and surfaces, etc.). These recurrence curves and surfaces are used to establish the universal storage data file format for different CAD systems.

Keywords

Mobile Device Surface Patch Curve Segment Spline Curve NURBS Curve 
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.
    Luo, X.: Curves and Surfaces in Computer Aided Geometric Design. PHD dissertation. Dalian University of Technology (1992)Google Scholar
  2. 2.
    Luo, X., Nie, H., Li, Y., Luo, Z.: Recurrence Surfaces on Arbitrary Quadrilateral Mesh. Journal of Computational and Applied Mathematics 144, 221–232 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ramshaw, L.: Blossoming: a Connect-the-Dots Approach to Splines. Systems Research Center (1987)Google Scholar
  4. 4.
    Goldman, R.: Blossoming with Cancellation. Computer Aided Geometric Design 16, 671–689 (1999)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiaonan Luo
    • 1
  • Shujin Lin
    • 1
  1. 1.Computer Application InstituteSun Yat-sen UniversityGuangzhouChina

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