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33382
Geometric Transformations for 3D Modeling
Published: 2007
Format: Print Book
Pages: 380
Status: In Stock
ISBN: 9780831133382
Price: $58.95 (SAVE $5.00) |
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Features
- Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations.
- Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged.
- Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand.
- Contains revised and improved figures, with many in color to highlight important features.
- Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.
Table of Contents
Geometry
- What Is Geometry
- History
- Geometric Objects
- Space
- Geometry Is…
- E Pluribus Unum – Transformation and Invariance
Theory of Transformations
- Functions, Mappings, and Transformations
- Linear Transformations
- Geometric Invariants
- Isometries
- Similarities
- Affinities
- Projectivities
- Topological Transformations
Vector Spaces
- Introduction to Linear Vector Spaces
- Basis Vectors
- Eigenvalues and Eigenvectors
- Tensors
Rigid-Body Motion
- Translation
- Rotation
- Composite Motion
- Kinematics
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
More Linear Transformations
- Isotropic Dilation
- Anisotropic Dilation
- Shear
- Projective Geometry
- Parallel Projection
- Central Projection
- Map Projections
- Display Projection
Nonlinear Transformations
- Linear and Nonlinear Equations
- Inversion in a Circle
- Curvilinear Coordinate Systems
- Deformations
- Answers to Selected Exercises
Index |
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