1 Introduction
2 Mathematical Background
2.1 Definition. Bijective Functions and Isomorphisms
2.2 Definition. Metric or Distance Function
2.3 Definition. Open Ball
2.4 Definition. Open Set vs. Closed Set
2.5 Definition. Boundary, Interior, Regular Sets
2.6 Definition. Topology and Topological Space
2.7 Definition. Neighborhood
2.8 Definition. Neighborhood Topology
2.9 Definition. Disks and Half-disks 82 and S1
2.10 Definition. 2-Manifold in R3
2.11 Definition. 2-Manifold with Border in R3
2.12 Definition. 1-Manifold in R3
2.13 Definition. 1-Manifold with Border in R3
2.14 Examples of Non-manifold Topologies
2.15 Definition. Connected Set in R3
3 B-Reps
3.1 Solid (BODY) in R3
3.2 LUMP in R3
3.3 SHELL
3.4 FACE
3.5 LOOP
3.6 EDGE
3.7 VERTEX
3.8 Example. Pre-Columbian Shape
3.9 Examples Non-Manifold
3.10 Example. Manifold Preservation in Parametric CAD
3.10.1 Questions on Boundary - Representation
3.11 Example. Repair of Extrusion of Non-manifold Sections
3.11.1 Extrusion of Non-Manifold Cross Section
3.11.2 Manifold Repair
3.12 Exam Example. Repair of Non-manifold Pyramid
3.12.1 Context
3.12.2 B-Rep example
3.12.3 Solution
3.13 22D Elements
4 Triangular B-Reps
4.1 Definition. Convex Set
4.2 Definition. Convex Hull
4.3 Definition. k - simplices
4.3.1 Low Dimension Simplices
4.3.2 Inventory of i-Faces in a k-Simplex
4.3.3 Example. Simplicial Complex
4.4 Boundary Representation for Triangle-Based Meshes
5 CSG Modeling
5.1 Constructive Solid Geometry tree
5.2 Primitives operands
5.3 Unary Operations
5.4 Binary operators
5.4.1 Regularized Set Operations
5.5 Example CSG
5.5.1 Primitive operands
5.5.2 Unary operations
5.5.3 Binary operations
5.5.4 CSG Tree structure
5.6 Observations
6 Enumerations
6.1 Scalar Fields
6.2 Uniform Cell
6.2.1 Fixed Grids
6.2.2 Medical Imaging
6.3 Non-Uniform Cell Decompositions. Quadtrees
6.3.1 Example Quadtree 3 Levels
6.3.2 Example Quadtree 4 Levels
6.3.3 Observations on Quadtrees
6.3.4 Quadtree Boolean Operations
6.3.5 Theoretical Discussion
6.3.6 Octrees.
7 Acknowledgments
