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The polynomial approximation Issues Rational Curves and Surfaces

Author: MengXiangGuo
Tutor: WangRenHong
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Rational curves Rational Surfaces Interval B (?) Zier curve Interval B (?) Zier Surfaces Hybrid algorithm Hermitie algorithm
CLC: O241.5
Type: Master's thesis
Year: 2003
Downloads: 123
Quote: 1
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Rational curves and surfaces as an important class of approximation functions have a wide range of applications in computer-aided design and manufacturing . In particular, as after NURBS been identified as the international standard , but also laid the dominance of rational functions in CAD . However, due to the complexity of the calculation and design needs , sometimes we need to use a polynomial function approximation of rational curves and surfaces . In approximation theory , rational formula of the classic polynomial approximation method the various interpolation operator approximation methods, such as Lagrange interpolation , Hermite interpolation and Bernstein polynomial approximation . These approximation methods or slow convergence or convergence is not guaranteed. Based on the actual needs of the curves and the concept of the interval surface approximation problems to do with it . The curves and interval surface interval analysis method of error analysis of the main tools in the field of numerical analysis , application and promotion in CAGD . Depth study of curves and surfaces with the interval by interval curves and surfaces approximation of curves and surfaces . In this paper , the first chapter introduces some of the knowledge of the polynomial approximation of rational curves and surfaces in the development of the research work and the range of curves and surfaces . The second chapter introduces previous work in this regard . Chapter rational curves interval polynomial approximation . Chapter IV introduces the rational surface interval polynomial approximation , first briefly based on the Taylor expansion do interval surface approximation , the latter is the main work of this paper -based optimization method , we get a better range surface approximation it is also an important part of this article .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Numerical approximation
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