Mathematical methods in computer aided geometric design II / edited by Tom Lyche, Larry L. Schumaker.

Format:

Book

Contributor:

Lyche, Tom, editor.

Schumaker, Larry L., editor.

Language:

English

Subjects (All):

Geometry--Data processing--Congresses.

Geometry.

Physical Description:

1 online resource (649 p.)

Edition:

United Kingdom edition.

Place of Publication:

San Diego, California ; London, England : Academic Press, Inc., 1992.

Language Note:

English

Summary:

Mathematical Methods in Computer Aided Geometric Design II

Contents:

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 ofSurface-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. TransfiniteInterpolation; 6. Octree and Face Octree Representations

7. Discussion of These Modeling SchemesReferences; Chapter 5. A New Characterization of PlaneElastica; 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 ProvidePotential 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 theFactors 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 MultiresolutionAnalysis

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: Introductionof a CHpping Technique; 1. Introduction; 2. Clipping; 3. Singular Cases; 4. Examples; 5. Extension to Surfaces; 6. Conclusion; References

Chapter 12. Best Approximations of ParametricCurves by Splines

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4832-5798-3