Algorithm 783. Pcp2Nurb  smooth surfacing with bicubic Bsplines  J. Peters
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Название: 
Algorithm 783. Pcp2Nurb  smooth surfacing with bicubic Bsplines 
Автор: 
J. Peters 
Категория: 
Информатика. Компьютеры

Тип: 
Книга 
Дата: 
22.02.2009 12:39:42 
Скачано: 
57 
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Описание: 
Unrestricted control polyhedra facilitate modeling freeform surfaces of arbitrary topology and local patchlayout by allowing гаsided, possibly nonplanar, facets and mvalent vertices. By cutting off edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a planarcut polyhedron. A planarcut polyhedron is a generalization of the wellknown tensorproduct control structure. The routine Pcp2Nurb in turn translates planarcut polyhedra to a collection of foursided linearly trimmed bicubic Bsplines and untrimmed biquadratic Bsplines. The routine can thus serve as central building block for overcoming topological constraints in the mathematical modeling of smooth surfaces that are stored, transmitted, and rendered using only the standard representation in industry. Specifically, on input of a ninepoint subnet of a planarcut polyhedron, the routine outputs a trimmed bicubic NURBS patch. If the subnet does not have geometrically redundant edges, this patch joins smoothly with patches from adjacent subnets as a foursided piece of a regular C1 surface. The patch integrates smoothly with untrimmed biquadratic tensorproduct surfaces derived from subnets with tensorproduct structure. Sharp features can be retained in this representation by using geometrically redundant edges in the planarcut polyhedron. The resulting surface follows the outlines of the planarcut polyhedron in the manner traditional tensorproduct splines follow the outline of their rectilinear control polyhedron. In particular, it stays in the local convex hull of the planarcut polyhedron.
Categories and Subject Descriptors: D.3.2 [Programming Languages]: Language Classifications—C; G.l.l [Interpolation]: Spline and Piecewise Polynomial Interpolation; G.1.2 [Approximation]: Spline and Piecewise Polynomial Approximation; 1.3.5 [Computational Geometry and Object Modeling]: Boundary Representations; Surface Representations
General Terms: Algorithms
Additional Key Words and Phrases: Arbitrary patch layout, arbitrary surface topology, biquadratic tensorproduct Bsplines, C1 surface, freeform surface, Matlab, NURBS, planarcut polyhedron, trimmed bicubic Bsplines 
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