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, radia. Read more...
Abstract: 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, radia
Content: Front Cover
Mathematical Methods in Computer Aided Geometric Design II
Copyright Page
Table of Contents
PREFACE
PARTICIPANTS
Chapter 1. Symmetrizing Multiaffine Polynomials
1. Introduction and Motivation
2. Cubics
3. Quartics, Quintics, and Sextics
4. Observations on Conversion to B-spline Form
5. Open Questions
References
Chapter 2. Norm Estimates for Inverses of Distance Matrices
1. Introduction
2. The Univariate Case for the Euclidean Norm
3. The Multivariate Case for the Euclidean Norm
4. Fourier Transforms and Bessel Transforms. 5. The Least Upper Bound for Subsets of the Integer GridReferences
Chapter 3. Numerical Treatment of Surface-Surface Intersection and Contouring
1. Introduction
2. Lattice Evaluation (2D Grid-Methods)
3. Marching Based on Davidenko's Differential Equation
4. Marching Based on Taylor Expansion
5. Conclusion and Future Extensions
References
Chapter 4. Modeling Closed Surfaces: A Comparison of Existing Methods
1. Introduction
2. Subdivision Schemes
3. Discrete Interpolation
4. Algebraic Interpolation
5. Transfinite Interpolation
6. Octree and Face Octree Representations. 7. Discussion of These Modeling SchemesReferences
Chapter 5. A New Characterization of Plane Elastica
1. Introduction
2. A Characterization of Elástica by their Curvature Function
3. A Characterizing Representation Theorem
References
Chapter 6. POLynomials, POLar Forms, and InterPOLation
1. Introduction
2. Algebraic Definition of Polar Curves
3. Interpolation
4. Conclusion and a Few Historical Remarks
Chapter 7. Pyramid Patches Provide Potential Polynomial Paradigms
1. Introduction
2. Linear Independence of Families of Lineal Polynomials
3. B-patches for Hn(IRs). 4. Other Pyramid Schemes5. B-patches for IIn (IRs)
6. Degree Raising, Conversion and Subdivision for B-patches
References
Chapter 8. Implicitizing Rational Surfaces with Base Points by Applying Perturbations and the Factors of Zero Theorem
1. Introduction
2. Mathematical Preliminaries
3. The Factors of Zero Theorem
4. Implicitization with Base Points Using the Dixon Resultant
5. An Implicitization Example
6. Conclusion and Open Problems
References
Chapter 9. Wavelets and Multiscale Interpolation
1. Introduction
2. Wavelets and Multiresolution Analysis. 3. Fundamental Scaling Functions4. Symmetric and Compactly Supported Scaling Functions
5. Subdivision Schemes
6. Regularity
References
Chapter 10. Decomposition of Splines
1. Introduction
2. Decomposition
3. Decomposing Splines
4. Box Spline Decomposition
5. Data Reduction by Decomposition
References
Chapter 11. A Curve Intersection Algorithm with Processing of Singular Cases: Introduction of a CHpping Technique
1. Introduction
2. Clipping
3. Singular Cases
4. Examples
5. Extension to Surfaces
6. Conclusion
References.
