Bounding the distance between 2D parametric Bézier curves and their control polygon

Karavelas, MI; Kaklis, PD; Kostas, KV

dc.contributor.author	Karavelas, MI	en
dc.contributor.author	Kaklis, PD	en
dc.contributor.author	Kostas, KV	en
dc.date.accessioned	2014-03-01T02:42:31Z
dc.date.available	2014-03-01T02:42:31Z
dc.date.issued	2004	en
dc.identifier.issn	0010-485X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31029
dc.subject	Bounding region	en
dc.subject	Collision detection	en
dc.subject	Control polygon	en
dc.subject	Optimal-orientation bounds	en
dc.subject	Parametric Bézier curves	en
dc.subject	Polygonal envelopes	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	Algorithms	en
dc.subject.other	Computer simulation	en
dc.subject.other	Control systems	en
dc.subject.other	Linear equations	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Polynomials	en
dc.subject.other	Bounding region	en
dc.subject.other	Collision detection	en
dc.subject.other	Control polygon	en
dc.subject.other	Optimal orientation bounds	en
dc.subject.other	Parametric Bézier curves	en
dc.subject.other	Polygonal envelops	en
dc.subject.other	Curve fitting	en
dc.title	Bounding the distance between 2D parametric Bézier curves and their control polygon	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/s00607-003-0051-1	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00607-003-0051-1	en
heal.language	English	en
heal.publicationDate	2004	en
heal.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.	en
heal.publisher	SPRINGER-VERLAG WIEN	en
heal.journalName	Computing (Vienna/New York)	en
dc.identifier.doi	10.1007/s00607-003-0051-1	en
dc.identifier.isi	ISI:000221453100011	en
dc.identifier.volume	72	en
dc.identifier.issue	1-2	en
dc.identifier.spage	117	en
dc.identifier.epage	128	en