G1-smooth branching surface construction from cross sections

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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

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