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Mathematics Methods of Shape-Preserving Spline Approximation
Posted on 2010-04-13
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Author: Boris I. Kvasov
Publisher: World Scientific Publishing Company (2000) Binding: Hardcover, 338 pages pricer: $82.00 ISBN-10: 9810240104 editorialreviews 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.
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