Methods of Shape-preserving Spline Approximation

Released on by Boris I. Kvasov
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  • Methods of Shape-preserving Spline Approximation Book Detail

  • Author : Boris I. Kvasov
  • Release Date : 2000
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 360
  • ISBN 13 : 9789810240103
  • File Size : 22,22 MB
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Methods of Shape-preserving Spline Approximation by Boris I. Kvasov PDF Summary

Book Description: 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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Interpolating Cubic Splines

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A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-spa