Mathematical Methods in Computer Aided Geometric Design II - 1st Edition - ISBN: 9780124605107, 9781483257983

Mathematical Methods in Computer Aided Geometric Design II

1st Edition

Editors: Tom Lyche Larry L. Schumaker
eBook ISBN: 9781483257983
Imprint: Academic Press
Published Date: 23rd June 1992
Page Count: 644
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Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway.

This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets.

This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Table of Contents



Symmetrizing Multiaffine Polynomials

Norm Estimates for Inverses of Distance Matrices

Numerical Treatment of Surface-Surface-Intersection and Contouring

Modeling Closed Surfaces: A Comparison of Existing Methods

A New Characterization of Plane Elastica

POLynomials, POLar Forms, and InterPOLation

Pyramid Patches Provide Potential Polynomial Paradigms

Implicitizing Rational Surfaces with Base Points by Applying Perturbations and the Factors of Zero Theorem

Wavelets and Multiscale Interpolation

Decomposition of Splines

A Curve Intersection Algorithm with Processing of Singular Cases: Introduction of a Clipping Technique

Best Approximations of Parametric Curves by Splines

An Approximately G1 Cubic Surface Interpolant

On the G2 Continuity of Piecewise Parametric Surfaces

Stationary and Non-Stationary Binary Subdivision Schemes

MQ-Curves are Curves in Tension

Offset Approximation Improvement by Control Point Perturbation

Curves and Surfaces in Geometrical Optics

Evaluation and Properties of the Derivative of a NURBS Curve

Hybrid Cubic Bézier Triangle Patches

Modelling Geological Structures Using Splines

Wonderful Triangle: A Simple, Unified, Algorithmic Approach to Change of Basis Procedures in Computer Aided Geometric Design

An Arbitrary Mesh Network Scheme Using Rational Splines

Bézier Curves and Surface Patches on Quadrics

Monotonicity Preserving Interpolation Using C2 Rational Cubic Bézier Curves

Minimization of Interpolating Spline Curves with Bounded Derivatives

On Piecewise Quadratic G2 Approximation and Interpolation

Non-Affine Blossoms and Subdivision for Q-Splines

On a Class of Data Parametrizations: Variations on a Theme of Epstein, II

Wavelets and Image Compression

Lower Bounds on the Dimension of Bivariate Spline Spaces and Generic Triangulations

Geometric Contact of Order p Between Two Surfaces

On Non-Parametric Constrained Interpolation

Tensor Product Slices

Construction of Smooth Surfaces by Piecewise Tensor Product Polynomials

The Virtues of Cyclides in CAGD

Simple Surfaces Have No Simple C1 Parametrization

Some Tools for Quasi-Interpolation on Cardinal Grids

Discrete Bezier Curves and Surfaces

Rational Geometric Curve Interpolation

Curvature Properties of Parametric Triangular Bézier Patches

Offsets of Polynomial Bézier Curves: Hermite Approximation with Error Bounds

Representing Piecewise Polynomials as Linear Combinations of Multivariate B-Splines

An Explicit Derivation of Discretely Shaped Beta-Spline Basis Functions of Arbitrary Order

Discrete Convolution Schemes

A Method of Removing the Singularities from Gregory Surfaces

Bivariate Spline Approximation by Penalized Least Squares

Interpolation with g-Splines


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© Academic Press 1992
Academic Press
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About the Editor

Tom Lyche

Larry L. Schumaker

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