G1-smooth branching surface construction from cross sections

Gabrielides, NC; Ginnis, AI; Kaklis, PD; Karavelas, MI

dc.contributor.author	Gabrielides, NC	en
dc.contributor.author	Ginnis, AI	en
dc.contributor.author	Kaklis, PD	en
dc.contributor.author	Karavelas, MI	en
dc.date.accessioned	2014-03-01T01:26:23Z
dc.date.available	2014-03-01T01:26:23Z
dc.date.issued	2007	en
dc.identifier.issn	0010-4485	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18053
dc.subject	Branching Surfaces	en
dc.subject	Cross sections	en
dc.subject	Design	en
dc.subject	G1 surfaces	en
dc.subject	Hole filling	en
dc.subject	Reconstruction	en
dc.subject	Shape-preserving interpolation	en
dc.subject	Skinning	en
dc.subject	Trimming	en
dc.subject.classification	Computer Science, Software Engineering	en
dc.subject.other	Data structures	en
dc.subject.other	Object oriented programming	en
dc.subject.other	Problem solving	en
dc.subject.other	Vector quantization	en
dc.subject.other	Data symmetries	en
dc.subject.other	Hermite problems	en
dc.subject.other	Hole filling	en
dc.subject.other	Surface topography	en
dc.title	G1-smooth branching surface construction from cross sections	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cad.2007.05.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cad.2007.05.004	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	This paper proposes a framework for constructing G1 surfaces that interpolate data points on parallel cross sections, consisting of simple disjoined and non-nested contours, the number of which may vary from plane to plane. Using appropriately estimated cross tangent vectors at the given points, we split the problem into a sequence of local Hermite problems, each of which can be one of the following three types: ""one-to-one"", ""one-to-many"" or ""many-to-many"". The solution of the ""one-to-many"" branching problem, where one contour on the i-plane is to be connected to M<sub/> contours on the (i + 1)-plane, is based on combining skinning with trimming and hole filling. More specifically, we first construct a C1 surrounding curve of all M<sub/> contours on the (i + 1)-plane. Next, we build the so-called surrounding surface that skins the i-plane contour with the (i + 1)-plane surrounding curve, and trim suitably along parts of the surrounding curve that connect contours. The resulting multi-sided hole is covered with quadrilateral Gordon-Coons patches that possess G1 continuity. For this purpose, we develop a hole-filling technique that employs shape-preserving guide curves and is able to preserve data symmetries. The ""many-to-many"" problem is handled by combining the ""one-to-many"" methodology with a zone-separation technique, that achieves splitting the ""many-to-many"" problem into two ""one-to-many"" problems. The methodology, implemented as a C++ Rhino v3.0 plug-in, is illustrated via two synthetic data sets and in the context of two realistic design examples. Finally, the paper concludes with discussing ongoing work towards improving the robustness and the applicability of the method regarding the surrounding curve construction step. © 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	CAD Computer Aided Design	en
dc.identifier.doi	10.1016/j.cad.2007.05.004	en
dc.identifier.isi	ISI:000248639300003	en
dc.identifier.volume	39	en
dc.identifier.issue	8	en
dc.identifier.spage	639	en
dc.identifier.epage	651	en