Advances in Computational Mathematics

, Volume 17, Issue 1–2, pp 135–152 | Cite as

Least-Squares Fitting of Algebraic Spline Surfaces

  • Bert Jüttler
  • Alf Felis
Article

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.

algebraic surface spline surface surface fitting least-squares fitting reverse engineering 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Bert Jüttler
    • 1
  • Alf Felis
    • 2
  1. 1.Johannes Kepler UniversityLinzAustria
  2. 2.ProSTEP GmbHDarmstadtGermany

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