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Mathematical Methods in Computer Aided Geometric Design
Tom Lyche,Larry L. Schumaker
- 628 pages
- English
- PDF
- Only available on web
Mathematical Methods in Computer Aided Geometric Design
Tom Lyche,Larry L. Schumaker
About This Book
Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers. This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles. This book will prove useful to mathematicians and advance mathematics students.
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Table of contents
- Front Cover
- Mathematical Methods in Computer Aided Geometric Design
- Copyright Page
- Table of Contents
- PREFACE
- PARTICIPANTS
- Chapter 1. Scattered Data Interpolation in Three or More Variables
- Chapter 2. Some Applications of Discrete Dm Splines
- Chapter 3. Spline Elastic Manifolds
- Chapter 4. Geometry Processing: Curvature Analysis and Surface-Surface Intersection
- Chapter 5. Three Examples of Dual Properties of Bézier Curves
- Chapter 6. What is the Natural Generalization of a Bézier Curve?
- Chapter 7. Convexity and a Multidimensional Version of the Variation Diminishing Property of Bernstein Polynomials
- Chapter 8. Gröbner Basis Methods for Multivariate Splines
- Chapter 9. On Finite Element Interpolation Problems
- Chapter 10. The Design of Curves and Surfaces by Subdivision Algorithms
- Chapter 11. A Data Dependent Parametrization for Spline Approximation
- Chapter 12. On the Evaluation of Box Splines
- Chapter 13. Smooth Piecewise Quadric Surfaces
- CHapter 14. Inserting New Knots Into Beta-Spline Curves
- Chapter 15. Recursive Subdivision and Iteration in Intersections and Related Problems
- Chapter 16. Rational Curves and Surfaces
- Chapter 17. Algebraic Aspects of Geometric Continuity
- Chapter 18. Shape Preserving Representations
- Chapter 19. Geometric Continuity
- Chapter 20. Curvature Continuous Triangular Interpolants
- Chapter 21. Box-Spline Surfaces
- Chapter 22. Parallelization of the Subdivision Algorithm for Intersection of Bézier Curves on the FPS T20
- Chapter 23. Composite Quadrilateral Finite Elements of Class C
- Chapter 24. Interpolation Systems and the Finite Element Method
- Chapter 25. Uniform Bivariate Hermite Interpolation
- Chapter 26. A Survey of Applications of an Affine Invariant Norm
- Chapter 27. An Algorithm for Smooth Interpolation to Scattered Data in R
- Chapter 28. Some Remarks on Three B-Spline Constructions
- Chapter 29. Modified B-Spline Approximation for Quasi-Interpolation or Filtering
- Chapter 30. Design Tools for Shaping Spline Models
- Chapter 31. A Process Oriented Design Method for Three-dimensional CAD Systems
- Chapter 32. Open Questions in the Application of Multivariate B-splines
- Chapter 33. On Global GC2 Convexity Preserving Interpolation of Planar Curves by Piecewise Bézier Polynomials
- Chapter 34. Best Interpolation with Free Nodes by Closed Curves
- Chapter 35. Segmentation Operators on Coons' Patches
- Chapter 36. neral Subdivision Theorem for Bézier Triangles
- Chapter 37. Cardinal Interpolation with Translates of Shifted Bivariate Box-Splines
- Chapter 38. Approximation of Surfaces Constrained by a Differential Equation Using Simplex Splines
- Chapter 39. A Construction for VC1 Continuity of Rational Bézier Patches
- References