Mathematical Methods in Computer Aided Geometric Design - 1st Edition - ISBN: 9780124605152, 9781483257808

Mathematical Methods in Computer Aided Geometric Design

1st Edition

Editors: Tom Lyche Larry L. Schumaker
eBook ISBN: 9781483257808
Imprint: Academic Press
Published Date: 28th June 1989
Page Count: 628
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Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers.

This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles.

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

Table of Contents



Scattered Data Interpolation in Three or More Variables

Some Applications of Discrete Dm Splines

Spline Elastic Manifolds

Geometry Processing: Curvature Analysis and Surface-Surface Intersection

Three Examples of Dual Properties of Bézier Curves

What is the Natural Generalization of a Bézier Curve?

Convexity and a Multidimensional Version of the Variation Diminishing Property of Bernstein Polynomials

Gröbner Basis Methods for Multivariate Splines

On Finite Element Interpolation Problems

The Design of Curves and Surfaces by Subdivision Algorithms

A Data Dependent Parametrization for Spline Approximation

On the Evaluation of Box Splines

Smooth Piecewise Quadric Surfaces

Inserting New Knots Into Beta-Spline Curves

Recursive Subdivision and Iteration in Intersections and Related Problems

Rational Curves and Surfaces

Hierarchical Segmentations of Algebraic Curves and Some Applications

An Algorithm for Shape Preserving Parametric Interpolating Curves with G2 Continuity

Knot Selection for Parametric Spline Interpolation

Splines and Estimation of Nonlinear Parameters

On Beta-Continuous Functions and Their Application to the Construction of Geometrically Continuous Curves and Surfaces

Algebraic Aspects of Geometric Continuity

Shape Preserving Representations

Geometric Continuity

Curvature Continuous Triangular Interpolants

Box-Spline Surfaces

Parallelization of the Subdivision Algorithm for Intersection of Bézier Curves on the FPS T20

Composite Quadrilateral Finite Elements of Class Cr

A Knot Removal Strategy for Scattered Data in R2

Interpolation Systems and the Finite Element Method

Uniform Bivariate Hermite Interpolation

A Survey of Applications of an Affine Invariant Norm

An Algorithm for Smooth Interpolation to Scattered Data in R2

Some Remarks on Three B-Spline Constructions

Modified B-Spline Approximation for Quasi-Interpolation or Filtering

Design Tools for Shaping Spline Models

A Process Oriented Design Method for Three-Dimensional CAD Systems

Open Questions in the Application of Multivariate B-Splines

On Global GC2 Convexity Preserving Interpolation of Planar Curves by Piecewise Bézier Polynomials

Best Interpolation with Free Nodes by Closed Curves

Segmentation Operators on Coons' Patches

A General Subdivision Theorem for Bézier Triangles

Cardinal Interpolation with Translates of Shifted Bivariate Box-Splines

Approximation of Surfaces Constrained by a Differential Equation Using Simplex Splines

A Construction for VC1 Continuity of Rational Bézier Patches


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© Academic Press 1989
Academic Press
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About the Editor

Tom Lyche

Larry L. Schumaker

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