Using a biarc filter to compute curvature extremes of NURBS curves |
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Authors: | Les A Piegl Khairan Rajab Volha Smarodzinava Kimon P Valavanis |
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Affiliation: | (1) Department of Computer Science and Engineering, University of South Florida, Tampa, FL 33620, USA;(2) Department of Electrical and Computer Engineering, University of Denver, Denver, CO 80208, USA |
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Abstract: | A method to compute curvature minima and maxima of parametric curves (represented in NURBS format) is presented in this paper.
Since the curvature changes vary rapidly along the path of (even smooth) curves, a biarc filter is employed to approximate
the curvature function with a piecewise constant function. This allows the isolation of curvature extreme values that are
found within-engineering tolerances via repeated biarc approximation followed by golden section search. Because the derivative
of the curvature is numerically very unstable, only optimization without derivatives is feasible. However, given the excellent
isolation property of biarc filters, curvature extremes are found within 10–20 steps even for high accuracy requirements ranging
from 10−4 to 10−6. |
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