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Helix splines as an example of affine Tchebycheffian splines

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Abstract

The present paper summarizes the theory of affine Tchebycheffian splines and presents an interesting affine Tchebycheffian free-form scheme, the “helix scheme”. The curve scheme provides exact representations of straight lines, circles and helix curves in an arc length parameterization. The corresponding tensor product surfaces contain helicoidal surfaces, surfaces of revolution and patches on all types of quadrics. We also show an application to the construction of planarC 2 motions interpolating a given set of positions. Because the spline curve segments are calculated using a subdivision algorithm, many algorithms, which are of fundamental importance in the B-spline technique, can be applied to helix splines as well. This paper should demonstrate how to create an affine free-form scheme fitting to certain special applications.

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Authors and Affiliations

  1. Institut für Geometrie, Technische Universität Wien, A-1040, Wien, Austria

    Helmut Pottmann & Michael G. Wagner

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  1. Helmut Pottmann
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  2. Michael G. Wagner
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Pottmann, H., Wagner, M.G. Helix splines as an example of affine Tchebycheffian splines. Adv Comput Math 2, 123–142 (1994). https://doi.org/10.1007/BF02519039

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