Constructing smooth branching surfaces from cross sections

Gabrielides, NC; Ginnis, AI; Kaklis, PD

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	https://dspace.lib.ntua.gr/xmlui/handle/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