Curves and surfaces in geometric modeling: theory and algorithms

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