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dc.contributor.authorCotrina Navau, Josep
dc.contributor.authorPla García, Núria
dc.contributor.authorVigo Anglada, Marc
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Telemàtica
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.identifier.citationCotrina, J., Pla, N., Vigo, M. "N-sided patches with B-spline boundaries". 2001.
dc.description.abstractWe present a method to construct a patch of parametric surface of degree k+1 that fills a n-sided hole, with bigger than 2, and whose boundary coincides with a B-Spline, thus, the resulting patch can be easily connected with given B-Spline surfaces with fixed continuity conditions. The method is based on the generic approach by the same authors to con-struct free form surfaces, which gives a family of practical schemes to design surfaces from an arbitrary given mesh, using the differentiable manifold the-ory. The proposal uses a star shaped mesh which describes a generic n-hole and a surface in a neighborhood of the hole. From this mesh, a set of charts is defined, one associated to each vertex or face of the mesh, depending on the parity of the input parameter k. A basis function and a control point is defined from each chart, and the surface is obtained as a baricentric combination of the control points using the defined basis functions. The main advantages of the method are the following: arbitrary order k continuity conditions can be imposed; the involved hole can have an arbitrary number of sides and arbitrary shape (convex or not) the simplicity of the construction process gives an easy and flexible method; and finally, the surface near the boundary is a B-Spline with piecewise uniform knot sequences and whose control points are vertices of the given mesh. Implementation details to evaluate a surface point are given, showing that the de Boor algorithm can be exploited for efficiency.
dc.format.extent21 p.
dc.subjectÀrees temàtiques de la UPC::Informàtica::Infografia
dc.subject.otherN-sided patches
dc.subject.otherB-spline boundaries
dc.subject.otherde Boor algorithm
dc.subject.otherComputer graphics
dc.titleN-sided patches with B-spline boundaries
dc.typeExternal research report
dc.contributor.groupUniversitat Politècnica de Catalunya. WNG - Grup de xarxes sense fils
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorCotrina, J.; Pla, N.; Vigo, M.

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