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NURBS approximation of surface/surface intersection curves

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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.

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Authors and Affiliations

  1. Department of Computer Science, Purdue University, 47907, West Lafayette, IN, USA

    Chandrajit L. Bajaj

  2. Computer Center, Chinese Academy of Sciences, 100080, Beijing, PR China

    Guoliang Xu

Authors
  1. Chandrajit L. Bajaj
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  2. Guoliang Xu
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Additional information

Supported in part by NSF Grants CCR 92.22467, DMS 91-01424, AFOSR Grant F49620-10138 and NASA Grant NAG-1-1473.

Supported in part by K.C. Wong Education Foundation, Hong Kong.

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Bajaj, C.L., Xu, G. NURBS approximation of surface/surface intersection curves. Adv Comput Math 2, 1–21 (1994). https://doi.org/10.1007/BF02519033

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