Convexity Preserving Interpolation By Dual Subdivision Schemes

.............................................................................................4 CHAPTER 0: Excursus on the Notion of Convexity..............................5-7 0.1. Geometric Convexity....................................................................5 0.2. Convex Functions........................................................................6 0.3. Some Properties of Convex Functions..........................................7 CHAPTER 1: Introduction..................................................................8-20 1.1. Convexity Preserving Interpolation by Algebraic Curves and Surfaces.........................................................................................8 1.2. Van Damme and Kuijt Subdivision Scheme..............................11 1.3. The Dyn-Levin-Liu Scheme......................................................14 1.4. The Kernel of a Convex Polyhedron..........................................20 CHAPTER 2: The Dual Chaikin Algorithm...............