## Shape Preserving Representations in Computer-aided Geometric DesignContents: Introduction to Bezier and spline curves; Interpolation, shape control and shape properties; Shape properties of normalised totally positive bases; Bases with optimal shape preserving properties; Stability and error analysis of shape preserving representations; Blossoming and CAGD algorithms; A geometric approach to variation diminishing free-form curve schemes; Multivariate Bernstein polynomials, convexity and related shape properties; Shape properties of tensor-product Bernstein polynomials; Techniques for fair and shape-preserving surface fitting with tensor-product B-splines; Trigonometric B-basis for defining curves and surfaces; Trigonometric splines; a survey with new results. |

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### Contents

Bases with optimal shape preserving properties J M Pena | 63 |

Stability and error analysis of shape preserving | 85 |

Blossoming and CAGD algorithms M L Mazure | 99 |

Copyright | |

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### Other editions - View all

Shape Preserving Representations in Computer-aided Geometric Design Juan M. Peņa Limited preview - 1999 |

### Common terms and phrases

affine combination Aided Geometric Design algorithm approximation B-spline surfaces bases Bernstein basis Bernstein polynomials Bezier curves Bezier surfaces blossom Carnicer Casteljau algorithm Chapter Chebyshev space coefficients collocation matrices Computer Aided Geometric condition number control points control polygon convex hull convexity conditions corner cutting algorithm corresponding Curves and Surfaces Definition denote derivatives example Gasca Gaussian elimination given hyperplane integer interpolation property intersection knot insertion linear linearly independent Lyche Math matrix monotonicity preserving n-tuple Neville elimination nonnegative functions nonsingular normal curve normalized B-basis normalized totally positive obtain osculating parametric surfaces Pena polynomial function polynomials of degree positively oriented preserves the orientation Proof Proposition rational curves recurrence relation resp satisfying Schumaker Section sequence shape preserving properties shape preserving representations shape properties sign-regular spline curves spline functions surface fitting system of functions tensor-product Theorem totally positive basis totally positive matrices trigonometric B-splines trigonometric polynomials variation diminishing property vector space