Geometric Transformations For 3d Modeling

Contents :

Preface
Chapter 1: Geometry
What Is Geometry
History
Geometric Objects
Space
Geometry Is..
E Pluribus Unum - Transformation and Invariance
Chapter 2: Theory of Transformations
Functions, Mappings, and Transformations
Linear Transformations
Geometric Invariants
Isometries
Similarities
Affinities
Projectivities
Topological Transformations
Chapter 3: Vector Spaces
Introduction to Linear Vector Spaces
Basis Vectors
Eigenvalues and Eigenvectors
Tensors
Chapter 4: Rigid-Body Motion
Translation
Rotation
Composite Motion
Kinematics
Chapter 5: Reflection and Symmetry
Central Inversion
Reflections in the Plane
Reflections in Space
Summary of Reflection Matrices
Symmetry Basics
Symmetry Groups
Ornamental Groups
Polygonal Symmetry and Tiling
Polyhedral Symmetry
Chapter 6: More Linear Transformations
Isotropic Dilation
Anisotropic Dilation
Shear
Projective Geometry
Parallel Projection
Central Projection
Map Projections
Display Projection
Chapter 7: Nonlinear Transformations
Linear and Nonlinear Equations
Inversion in a Circle
Curvilinear Coordinate Systems
Deformations
Answers to Selected Exercises
Index