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Article: Interpolation on quadric surfaces with rational quadratic spline curves

TitleInterpolation on quadric surfaces with rational quadratic spline curves
Authors
Issue Date1997
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagd
Citation
Computer Aided Geometric Design, 1997, v. 14 n. 3, p. 207-230 How to Cite?
AbstractGiven a sequence of points {Xi}n i=1 on a regular quadric S: XT AX = 0 ⊂ double-struck E signd, d ≥ 3, we study the problem of constructing a G1 rational quadratic spline curve lying on S that interpolates {Xi}n i=1. It is shown that a necessary condition for the existence of a nontrivial interpolant is (XT 1 AX2)(XT i AXi+1) > 0, i = 1, 2, . . . , n - 1. Also considered is a Hermite interpolation problem on the quadric S: a biarc consisting of two conic arcs on S joined with G1 continuity is used to interpolate two points on S and two associated tangent directions, a method similar to the biarc scheme in the plane (Bolton, 1975) or space (Sharrock, 1987). A necessary and sufficient condition is obtained on the existence of a biarc whose two arcs are not major elliptic arcs. In addition, it is shown that this condition is always fulfilled on a sphere for generic interpolation data.
Persistent Identifierhttp://hdl.handle.net/10722/152261
ISSN
2015 Impact Factor: 1.092
2015 SCImago Journal Rankings: 1.024
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Wen_US
dc.contributor.authorJoe, Ben_US
dc.date.accessioned2012-06-26T06:36:49Z-
dc.date.available2012-06-26T06:36:49Z-
dc.date.issued1997en_US
dc.identifier.citationComputer Aided Geometric Design, 1997, v. 14 n. 3, p. 207-230en_US
dc.identifier.issn0167-8396en_US
dc.identifier.urihttp://hdl.handle.net/10722/152261-
dc.description.abstractGiven a sequence of points {Xi}n i=1 on a regular quadric S: XT AX = 0 ⊂ double-struck E signd, d ≥ 3, we study the problem of constructing a G1 rational quadratic spline curve lying on S that interpolates {Xi}n i=1. It is shown that a necessary condition for the existence of a nontrivial interpolant is (XT 1 AX2)(XT i AXi+1) > 0, i = 1, 2, . . . , n - 1. Also considered is a Hermite interpolation problem on the quadric S: a biarc consisting of two conic arcs on S joined with G1 continuity is used to interpolate two points on S and two associated tangent directions, a method similar to the biarc scheme in the plane (Bolton, 1975) or space (Sharrock, 1987). A necessary and sufficient condition is obtained on the existence of a biarc whose two arcs are not major elliptic arcs. In addition, it is shown that this condition is always fulfilled on a sphere for generic interpolation data.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagden_US
dc.relation.ispartofComputer Aided Geometric Designen_US
dc.titleInterpolation on quadric surfaces with rational quadratic spline curvesen_US
dc.typeArticleen_US
dc.identifier.emailWang, W:wenping@cs.hku.hken_US
dc.identifier.authorityWang, W=rp00186en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0167-8396(96)00030-1-
dc.identifier.scopuseid_2-s2.0-0031123712en_US
dc.identifier.hkuros27221-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031123712&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume14en_US
dc.identifier.issue3en_US
dc.identifier.spage207en_US
dc.identifier.epage230en_US
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridBarry, J=11041516200en_US

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