Curves and Surfaces in Geometric Modeling

Key Features:

• Achieves a depth of coverage not found in any other book in this
  field
  
• Offers a mathematically rigorous, unifying approach to the algorithmic
  generation and manipulation of curves and surfaces
  
• Presents, in addition to theory, details and examples of implementations,
  demonstrating methods that produce highly continuous curves and surfaces
  
• A compelling book for graduate students, scientists, and advanced
  practitioners across a number of fields
  
• A high-end computer grahics book using a mathimatical approach.
  Offers a wealth of conceptual & practical information for computer
  scientist & engineers
  with a need for the latest geometric & modeling techniques
  
• Attempts to fill the gap between Mathematics an Computer Graphics
  involving Geometric modeling, Computer vision & Motion planning.

Table of contents

1: Introduction
2: Basics of Affine Geometry
3: Introduction to the Algorithmic Geometry of Polynomial Curves
4: Multiaffine Maps and Polar Forms
5: Polynomial Curves as Be'zier Curves
6: B-Spline Curves
7: Polynomial Surfaces
8: Subdivision Algorithms for Polynomial Surfaces
9: Polynomial Spline Surfaces and Subdivision Surfaces
10: Embedding an Affine Space in a Vector Space
11: Tensor Products and Symmetric Tensor Products
12: Appendix 1: Linear Algebra
13: Appendix 2: Complements of Affine Geometry
14: Appendix 3: Topology
15: Appendix 4: Differential Calculus