Planar C2 cubic spline interpolation under geometric boundary conditions

Ginnis, AI; Kaklis, PD

dc.contributor.author	Ginnis, AI	en
dc.contributor.author	Kaklis, PD	en
dc.date.accessioned	2014-03-01T01:18:13Z
dc.date.available	2014-03-01T01:18:13Z
dc.date.issued	2002	en
dc.identifier.issn	0167-8396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14868
dc.subject	Bessel end conditions	en
dc.subject	C2 cubic spline interpolation	en
dc.subject	Curve design	en
dc.subject	End conditions	en
dc.subject	G2 cubic spline interpolation	en
dc.subject	Geometric boundary conditions	en
dc.subject	Not-a-knot end conditions	en
dc.subject	Quadratic boundary conditions	en
dc.subject	Type-I end conditions	en
dc.subject	Type-II end conditions	en
dc.subject.classification	Computer Science, Software Engineering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Computer aided design	en
dc.subject.other	Interpolation	en
dc.subject.other	Vectors	en
dc.subject.other	Geometric boundary conditions	en
dc.subject.other	Computational geometry	en
dc.title	Planar C2 cubic spline interpolation under geometric boundary conditions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0167-8396(02)00091-2	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0167-8396(02)00091-2	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	This paper deals with the problem of C-2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to necessary and sufficient conditions for all possible boundary-data configurations. A robust scheme for the numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples. (C) 2002 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Computer Aided Geometric Design	en
dc.identifier.doi	10.1016/S0167-8396(02)00091-2	en
dc.identifier.isi	ISI:000176195300004	en
dc.identifier.volume	19	en
dc.identifier.issue	5	en
dc.identifier.spage	345	en
dc.identifier.epage	363	en