Mathematical Methods in Computer Aided Geometric Design
eBook - PDF

Mathematical Methods in Computer Aided Geometric Design

  1. 628 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Mathematical Methods in Computer Aided Geometric Design

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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Yes, you can access Mathematical Methods in Computer Aided Geometric Design by Tom Lyche,Larry L. Schumaker in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780124605152
eBook ISBN
9781483257808
Topic
Mathematics
Subtopic
Geometry
Index
Mathematics

Table of contents

  1. Front Cover
  2. Mathematical Methods in Computer Aided Geometric Design
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. PARTICIPANTS
  7. Chapter 1. Scattered Data Interpolation in Three or More Variables
  8. Chapter 2. Some Applications of Discrete Dm Splines
  9. Chapter 3. Spline Elastic Manifolds
  10. Chapter 4. Geometry Processing: Curvature Analysis and Surface-Surface Intersection
  11. Chapter 5. Three Examples of Dual Properties of BĂ©zier Curves
  12. Chapter 6. What is the Natural Generalization of a BĂ©zier Curve?
  13. Chapter 7. Convexity and a Multidimensional Version of the Variation Diminishing Property of Bernstein Polynomials
  14. Chapter 8. Gröbner Basis Methods for Multivariate Splines
  15. Chapter 9. On Finite Element Interpolation Problems
  16. Chapter 10. The Design of Curves and Surfaces by Subdivision Algorithms
  17. Chapter 11. A Data Dependent Parametrization for Spline Approximation
  18. Chapter 12. On the Evaluation of Box Splines
  19. Chapter 13. Smooth Piecewise Quadric Surfaces
  20. CHapter 14. Inserting New Knots Into Beta-Spline Curves
  21. Chapter 15. Recursive Subdivision and Iteration in Intersections and Related Problems
  22. Chapter 16. Rational Curves and Surfaces
  23. Chapter 17. Algebraic Aspects of Geometric Continuity
  24. Chapter 18. Shape Preserving Representations
  25. Chapter 19. Geometric Continuity
  26. Chapter 20. Curvature Continuous Triangular Interpolants
  27. Chapter 21. Box-Spline Surfaces
  28. Chapter 22. Parallelization of the Subdivision Algorithm for Intersection of BĂ©zier Curves on the FPS T20
  29. Chapter 23. Composite Quadrilateral Finite Elements of Class C
  30. Chapter 24. Interpolation Systems and the Finite Element Method
  31. Chapter 25. Uniform Bivariate Hermite Interpolation
  32. Chapter 26. A Survey of Applications of an Affine Invariant Norm
  33. Chapter 27. An Algorithm for Smooth Interpolation to Scattered Data in R
  34. Chapter 28. Some Remarks on Three B-Spline Constructions
  35. Chapter 29. Modified B-Spline Approximation for Quasi-Interpolation or Filtering
  36. Chapter 30. Design Tools for Shaping Spline Models
  37. Chapter 31. A Process Oriented Design Method for Three-dimensional CAD Systems
  38. Chapter 32. Open Questions in the Application of Multivariate B-splines
  39. Chapter 33. On Global GC2 Convexity Preserving Interpolation of Planar Curves by Piecewise BĂ©zier Polynomials
  40. Chapter 34. Best Interpolation with Free Nodes by Closed Curves
  41. Chapter 35. Segmentation Operators on Coons' Patches
  42. Chapter 36. neral Subdivision Theorem for BĂ©zier Triangles
  43. Chapter 37. Cardinal Interpolation with Translates of Shifted Bivariate Box-Splines
  44. Chapter 38. Approximation of Surfaces Constrained by a Differential Equation Using Simplex Splines
  45. Chapter 39. A Construction for VC1 Continuity of Rational BĂ©zier Patches
  46. References