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Constructive Theory and Algorithm for Blending Several Implicit Algebraic Surfaces

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Computer Algebra and Geometric Algebra with Applications (IWMM 2004, GIAE 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3519))

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Abstract

Blending implicit algebraic surfaces has long been a hard work due to the complex calculations and the lack of effective algorithms. In this paper, we present a recursive method to derive the existence conditions and expressions of the blending surface for an arbitrary number of quadratic surfaces based on the blending surface for few quadratic surfaces. The existence conditions can be described in terms of geometric parameters of the given quadratic surfaces, which makes them easy to check. This greatly simplifies the calculations. Finally, some examples are presented.

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Author information

Authors and Affiliations

  1. The Information Electronic Engineering School, Shandong Institute of Business and Technology, 264005, Yantai, China

    Yurong Li

  2. Key Laboratory of Symbolic Computation and Knowledge Engineering in JLU Ministry of Education, 130012, Changchun, China

    Na Lei, Shugong Zhang & Guochen Feng

  3. Institute of Mathematics, Jilin University, 130012, Changchun, China

    Shugong Zhang & Guochen Feng

Authors
  1. Yurong Li
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  2. Na Lei
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  3. Shugong Zhang
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  4. Guochen Feng
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Editor information

Editors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, CAS, P.O. Box, 100080, Beijing, P.R. China

    Hongbo Li

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, U.S.A.

    Peter J. Olver

  3. Institute of Computer Science, Christian-Albrecht-University, 24098, Kiel, Germany

    Gerald Sommer

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© 2005 Springer-Verlag Berlin Heidelberg

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Li, Y., Lei, N., Zhang, S., Feng, G. (2005). Constructive Theory and Algorithm for Blending Several Implicit Algebraic Surfaces. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_9

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  • DOI: https://doi.org/10.1007/11499251_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26296-1

  • Online ISBN: 978-3-540-32119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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