Mathematical methods in computer aided geometric design 2

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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, 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.