A discrete methodology for controlling the sign of curvature and torsion for NURBS

Ginnis, AI; Karousos, EI; Kaklis, PD

dc.contributor.author	Ginnis, AI	en
dc.contributor.author	Karousos, EI	en
dc.contributor.author	Kaklis, PD	en
dc.date.accessioned	2014-03-01T02:45:52Z
dc.date.available	2014-03-01T02:45:52Z
dc.date.issued	2009	en
dc.identifier.issn	0010-485X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32438
dc.subject	Curvature	en
dc.subject	Curves	en
dc.subject	Knot insertion	en
dc.subject	NURBS	en
dc.subject	Torsion	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	Curvature	en
dc.subject.other	Curves	en
dc.subject.other	Knot insertion	en
dc.subject.other	NURBS	en
dc.subject.other	Torsion	en
dc.subject.other	Topology	en
dc.subject.other	Torsional stress	en
dc.subject.other	Splines	en
dc.title	A discrete methodology for controlling the sign of curvature and torsion for NURBS	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/s00607-009-0053-8	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00607-009-0053-8	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration. © 2009 Springer-Verlag.	en
heal.publisher	SPRINGER WIEN	en
heal.journalName	Computing (Vienna/New York)	en
dc.identifier.doi	10.1007/s00607-009-0053-8	en
dc.identifier.isi	ISI:000270649000005	en
dc.identifier.volume	86	en
dc.identifier.issue	2-3	en
dc.identifier.spage	117	en
dc.identifier.epage	129	en