Blending Polyhedral Edge Clusters
This paper presents an efficient method for blending edge clusters on polyhedra, where an edge cluster means a set of polyhedral edges connected together by polyhedral vertices. It extends the vertex-first algorithm in (P. Zhou, W.H. Qian, A vertex-first parametric algorithm for polyhedron blending, Computer-Aided Design 41 812–824(2009)) from a single vertex to several vertices with relevant edges together, so that a tensor product or multisided Bézier surface can blend an edge cluster of diverse configurations. This is achieved simply by placing the control points of the Bézier surface on the vertices and edges properly. If the clusters can not cover the whole polyhedron, the left C0 corner points can be handled by Hartmann method. Thus the complete Gg (geometrically continuous up to order g) blending surfaces can be produced faster. Their shapes can be adjusted by utilizing certain freedoms of placing the control points. The implementation of this method is demonstrated with various practical examples.
KeywordsMultivariate bernstein polynomials Multisided bézier surfaces S-patches Vertex blending Geometric continuity
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