Helix splines as an example of affine Tchebycheffian splines |
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Authors: | Helmut Pottmann Michael G Wagner |
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Institution: | 1. Institut für Geometrie, Technische Universit?t Wien, A-1040, Wien, Austria
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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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Keywords: | Free-form curve B-spline Tchebycheffian spline blossoming tensor product surface screw motion helix helicoidal surface quadric surface motion design |
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