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Advances in Computational Mathematics

, Volume 2, Issue 1, pp 1–21 | Cite as

NURBS approximation of surface/surface intersection curves

  • Chandrajit L. Bajaj
  • Guoliang Xu
Article

Abstract

We use a combination of both symbolic and numerical techniques to construct degree boundedC k -continuous, rational B-spline ε-approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points, we use the classical Newton power series factorizations to determine the distinct branches of the space intersection curve. In addition to singular points, we obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achievesC k continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided.

Keywords

Singular Point Algebraic Curf Newton Iteration Algebraic Surface Intersection 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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Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Chandrajit L. Bajaj
    • 1
  • Guoliang Xu
    • 2
  1. 1.Department of Computer SciencePurdue UniversityWest LafayetteUSA
  2. 2.Computer CenterChinese Academy of SciencesBeijingPR China

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