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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Bicubic G1 Interpolation of Irregular Quad Meshes Using a 4-Split
verfasst von : Stefanie Hahmann, Georges-Pierre Bonneau, Baptiste Caramiaux
Erschienen in: Advances in Geometric Modeling and Processing
Verlag: Springer Berlin Heidelberg
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We present a piecewise bi-cubic parametric G
1
spline surface interpolating the vertices of any irregular quad mesh of arbitrary topological type. While tensor product surfaces need a chess boarder parameterization they are not well suited to model surfaces of arbitrary topology without introducing singularities. Our spline surface consists of tensor product patches, but they can be assembled with G
1
-continuity to model any non-tensor-product configuration. At common patch vertices an arbitrary number of patches can meet. The parametric domain is built by 4-splitting one unit square for each input quadrangular face. This key idea of our method enables to define a very low degree surface, that interpolates the input vertices and results from an explicit and local procedure : no global linear system has to be solved.