Curves and surfaces

Description

Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory.  Read more... Abstract: Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory Content: Front Cover Curves and Surfaces Copyright Page Table of Contents PREFACE CONTRIBUTORS Chapter 1. Parametrization for Data Approximation 1. Introduction 2. Local Taylor Expansion of the Curve 3. Criteria 4. Application to Approximation with B-Splines References Chapter 2. A Vector Spline Approximation With Application to Meteorology 1. Introduction 2. The Minimization Problem 3. Solution of P &lt U+00dc&gt , &lt U+00dd&gt 4. Limit Problems 5. Numerical Results References Chapter 3. Kernel Estimation in Change-Point Hazard Rate Models 1. Introduction 2. The Model 3. Main Results. 4. Simulation Results and Concluding RemarksReferences Chapter 4. Spline Manifolds 1. Introduction 2. Basic Tools 3. A Fundamental Result 4. Spline Manifolds 5. P(D)-positive Vectorial Distributions 6. Extension of P(D)-spline References Chapter 5. Use of Simulated Annealing to Construct Triangular Facet Surfaces 1. Introduction 2. Optimal Triangulations 3. Locally Optimal Triangulations and Edge Swapping 4. Simulated Annealing 5. An Example 6. Conclusions References Chapter 6. G1 and G2 Continuity Between (SBR) Surfaces 1. Geometric Framework. 2. Analytical Conditions3. Geometric Continuity Between Two Rectangular (SBR) References Chapter 7. Ray Tracing Rational Parametric Surfaces 1. Introduction 2. Implicitization 3. Intersection Problem 4. Discussion References Chapter 8. Energy-Based Segmentation of Sparse Range Data Abstract 1. Segmentation: Introduction and Background 2. Definition of the Model of World Surfaces 3. Experimentation References Chapter 9. Error Estimates for Multiquadric Interpolation 1. Introduction and Statement of Main Result 2. Proof of Theorem 1 References. Chapter 10. A Geometrical Analysis for a Data Compression of 3D Anatomical Structures1. Introduction 2. Data Format 3. Feature Extraction 4. Data Compression 5. Contour Reconstruction 6. Conclusion References Chapter 11. Ck Continuity of (SBR) Surfaces 1. Framework 2. Rectangular (SBR) Surfaces 3. Triangular (SBR) Surfaces References Chapter 12. A Note on Piecewise Monotonie Bivariate Interpolation 1. Introduction 2. Outline of the Algorithm 3. Conclusions References Chapter 13. Real-Time Signal Analysis with Quasi-Interpolatory Splines and Wavelets. 1. Introduction2. Spline Sampling of Digital Signals 3. Wavelet Signal Decomposition 4. Wavelet Signal Reconstruction References Chapter 14. Polynomial Expansions for Cardinal Interpolants and Orthonormal Wavelets 1. Introduction 2. The Case of Real &lt U+005a&gt 3. The Case of Complex &lt U+005a&gt 4. Construction of Quasi-Interpolation Operators References Chapter 15. Realtime Pipelined Spline Data Fitting for Sketched Curves 1. Introduction 2. Background 3. Data Reduction 4. Pipelining the Algorithm 6. Remarks References Chapter 16. Remarks on Digital Terrain Modelling Accuracy.