Isotopic approximations and interval solids

dc.contributor.author	Sakkalis, T	en
dc.contributor.author	Peters, TJ	en
dc.contributor.author	Bisceglio, J	en
dc.date.accessioned	2014-06-06T06:46:02Z
dc.date.available	2014-06-06T06:46:02Z
dc.date.issued	2004	en
dc.identifier.issn	00104485	en
dc.identifier.uri	http://dx.doi.org/10.1016/j.cad.2004.01.008	en
dc.identifier.uri	http://62.217.125.90/xmlui/handle/123456789/2769
dc.subject	Ambient isotopy	en
dc.subject	Computational topology	en
dc.subject	Interval solids	en
dc.subject	Offsets and deformations	en
dc.subject	Reverse engineering	en
dc.subject	Surface reconstruction	en
dc.subject.other	Algorithms	en
dc.subject.other	Animation	en
dc.subject.other	Approximation theory	en
dc.subject.other	Computational geometry	en
dc.subject.other	Computer graphics	en
dc.subject.other	Computer simulation	en
dc.subject.other	Mathematical models	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Reverse engineering	en
dc.subject.other	Topology	en
dc.subject.other	Ambient isotopy	en
dc.subject.other	Computational topology	en
dc.subject.other	Interval solids	en
dc.subject.other	Offsets and deformation	en
dc.subject.other	Surface reconstruction	en
dc.subject.other	Computer aided design	en
dc.title	Isotopic approximations and interval solids	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1016/j.cad.2004.01.008	en
heal.publicationDate	2004	en
heal.abstract	Given a nonsingular compact two-manifold F without boundary, we present methods for establishing a family of surfaces which can approximate F so that each approximant is ambient isotopic to F. The methods presented here offer broad theoretical guidance for a rich class of ambient isotopic approximations, for applications in graphics, animation and surface reconstruction. They are also used to establish sufficient conditions for an interval solid to be ambient isotopic to the solid it is approximating. Furthermore, the normals of the approximant are compared to the normals of the original surface, as these approximating normals play prominent roles in many graphics algorithms. The methods are based on global theoretical considerations and are compared to existing local methods. Practical implications of these methods are also presented. For the global case, a differential surface analysis is performed to find a positive number ρ so that the offsets Fo(±ρ) of F at distances ±ρ are nonsingular. In doing so, a normal tubular neighborhood, F(ρ), of F is constructed. Then, each approximant of F lies inside F(ρ). Comparisons between these global and local constraints are given. © 2004 Elsevier Ltd. All rights reserved.	en
heal.journalName	CAD Computer Aided Design	en
dc.identifier.issue	11	en
dc.identifier.volume	36	en
dc.identifier.doi	10.1016/j.cad.2004.01.008	en
dc.identifier.spage	1089	en
dc.identifier.epage	1100	en