Bounding the Distance between 2D Parametric Bézier Curves and their Control Polygon

M. I. Karavelas (), P. D. Kaklis () and K. V. Kostas ()
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M. I. Karavelas: University of Notre Dame, Dept. Computer Science and Engineering
P. D. Kaklis: National Technical University of Athens, Dept. Naval Arch. & Mar. Eng.
K. V. Kostas: National Technical University of Athens, Dept. Naval Arch. & Mar. Eng.

A chapter in Geometric Modelling, 2004, pp 117-128 from Springer

Abstract: Abstract Employing the techniques presented by Nairn, Peters and Lutterkort in [1], sharp bounds are firstly derived for the distance between a planar parametric Bézier curve and a parameterization of its control polygon based on the Greville abscissae. Several of the norms appearing in these bounds are orientation dependent. We next present algorithms for finding the optimal orientation angle for which two of these norms become minimal. The use of these bounds and algorithms for constructing polygonal envelopes of planar polynomial curves, is illustrated for an open and a closed composite Bézier curve.

Keywords: Parametric Bézier curves; control polygon; polygonal envelopes; bounding region; optimal-orientation bounds; collision detection; 65D07; 65D17; 68U07 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0587-0_10

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DOI: 10.1007/978-3-7091-0587-0_10

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