Methods of shape-preserving spline approximation
著者
書誌事項
Methods of shape-preserving spline approximation
World Scientific, c2000
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注記
Includes bibliographical references (p. 309-321) and index
内容説明・目次
内容説明
This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces.Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
目次
- Interpolation by polynomials and Lagrange splines
- cubic spline interpolation
- algorithms for computing 1-D and 2-D polynomial splines
- methods of montone and convex spline interpolation
- methods of shape-preserving spline interpolation
- local bases for generalized tension splines
- GB-splines of arbitrary order
- methods of shape preserving local spline approximation
- difference method for construction hyperbolic tension splines
- discrete generalized tension splines
- methods of shape preserving parametrization.
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