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Residue and Implicitization Problem for Rational Surfaces

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

The implicitization problem of rational surfaces is a central challenge in computational aided geometric design. We propose a new algorithm to solve it, based on the residue calculus in the general multivariate setting. The proposed approach allows us to treat surfaces with base points (without geometric hypothesis on the zero-locus of base points). The efficiency of the method is illustrated by some examples computed with maple software. We also give another application of the residue calculus to the computation of offsets of rational parametric surfaces.

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Authors and Affiliations

  1. UMR CNRS 6621, UNSA, Parc Varose, BP 71, 06108 Nice, France

    Mohamed Elkadi

  2. GALAAD, INRIA, 93, 06902, Sophia-Antipolis, France

    Bernard Mourrain

Authors
  1. Mohamed Elkadi
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  2. Bernard Mourrain
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Correspondence to Mohamed Elkadi.

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Keywords: Implicitization, Multivariable residue calculus, Bezoutian matrix.

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Elkadi, M., Mourrain, B. Residue and Implicitization Problem for Rational Surfaces. AAECC 14, 361–379 (2004). https://doi.org/10.1007/s00200-003-0139-z

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  • DOI: https://doi.org/10.1007/s00200-003-0139-z

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