Constructing smooth branching surfaces 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.date.accessioned 2014-03-01T02:43:59Z
dc.date.available 2014-03-01T02:43:59Z
dc.date.issued 2006 en
dc.identifier.uri http://hdl.handle.net/123456789/31593
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.other Branching surfaces en
dc.subject.other Cross sections en
dc.subject.other G1 surfaces en
dc.subject.other Hole filling en
dc.subject.other Reconstruction en
dc.subject.other Shape preserving interpolation en
dc.subject.other Skinning en
dc.subject.other Computer programming languages en
dc.subject.other Estimation en
dc.subject.other Interpolation en
dc.subject.other Problem solving en
dc.subject.other Trimming en
dc.subject.other Surface structure en
dc.title Constructing smooth branching surfaces from cross sections en
heal.type conferenceItem en
heal.identifier.primary 10.1145/1128888.1128910 en
heal.identifier.secondary http://dx.doi.org/10.1145/1128888.1128910 en
heal.publicationDate 2006 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 script M sign-contours on the (i+1)-plane, is based on combining skinning with trimming and hole filling. More specifically, we firstly construct a G1 surrounding curve of all script M sign-contours on the (i+1)-plane, consisting of contour portions connected with linear segments, the so-called bridges. Next, we build a surface that skins the i-plane contour with the (i+1)-plane surrounding curve and trim suitably along the bridges. 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 to split the configuration into two ""one-to-many"" problems. The methodology, implemented as a C++ Rhino v3.0 plug-in, is illustrated via a synthetic example. © 2006 ACM. en
heal.journalName Proceedings SPM 2006 - ACM Symposium on Solid and Physical Modeling en
dc.identifier.doi 10.1145/1128888.1128910 en
dc.identifier.volume 2006 en
dc.identifier.spage 161 en
dc.identifier.epage 170 en

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