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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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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DOI: https://doi.org/10.1023/A:1015200504295