1.1 Parametric versus Implicit Form
1.2 Motivation
1.3 Scope and Overview
2. Manifolds
2.1 Definition
2.2 Local Charts
2.3 Atlases and Structures
2.4 Calculus on Manifolds
2.5 Immersions and Embeddings
2.6 Submanifolds
2.7 Realizations of a Manifold
2.8 Manifolds with Boundary
2.9 Orientability
2.10 Classification of Manifolds
2.11 A Suitable Model
4.1 Types of Space Decompositions
4.2 Properties of Space Decompositions
4.3 Algebraic Structure of Space Decompositions
4.4 Spatial Data Structures
5. Shape and Space
5.1 Tubular Neighborhoods
5.2 Medial Axes
5.3 Morse Theory
5.4 Surfaces in Space
5.5 Universal Representation
5.6 Summary
6. Implicit Objects
6.1 Definition of an Implict Object
6.2 Mathematical Elements
6.3 Geometrical Characterization
6.4 Differentiable Attributes
6.5 Computational Attributes
7. Manipulating Implicit Objects
7.1 The Implicit Function as a Metric
7.2 Properties of the Implicit Function
7.3 Operations on the Range of F
7.4 Mappings of the Embedding Space
7.5 Operations on the Domain of F
8. Combining Implicit Objects
8.1 Compound Objects
8.2 Boolean Operations
8.3 Blending Operation
8.4 Global and Local Blends
