Schicho J.  Rational parametrization of surfaces

Название: 
Rational parametrization of surfaces 
Автор: 
Schicho J. 
Категория: 
Математика

Тип: 
Книга 
Дата: 
04.01.2009 11:55:37 
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32 
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Описание: 
The reverse problem (given the three rational functions, find the equation) is called the implicitization problem. It has been investigated in Canny and Manocha (1992), Gao and Chou (1992), Kalkbrener (1990) and Chionh and Goldman (1992). An algorithm can be found in the С AS A package (Tran and Winkler, 1997).
There are tasks in computational geometry, for which the parametric representation is more convenient, and others for which the implicit representation is more convenient. A task in the second group is to decide whether a given point is lying on the surface. The first group contains tasks in which many points have to be produced fast. The parametric representation, especially parametrization by NURBSs (i.e. piecewise rational functions) is used for many applications in computer aided design and manufacture, such as reliable surface plotting and display, motion display (computing transformations), computing cutter offset surfaces, computing curvatures for shading and colouring, and many others (see also Bohm et al. (1984), Qiulin and Davies (1987) and Farin (1988)). Therefore, the parametrization problem is important. 
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