Mathematical Methods in Computer Aided Geometric Design II

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.

Contenu

Preface
Participants
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