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Least-Squares Fitting of Algebraic Spline Surfaces

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Abstract

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.

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Authors and Affiliations

  1. Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria

    Bert Jüttler

  2. ProSTEP GmbH, Dolivostr. 11, 64293, Darmstadt, Germany

    Alf Felis

Authors
  1. Bert Jüttler
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  2. Alf Felis
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Jüttler, B., Felis, A. Least-Squares Fitting of Algebraic Spline Surfaces. Advances in Computational Mathematics 17, 135–152 (2002). https://doi.org/10.1023/A:1015200504295

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