CD-ROM PDF

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**Overview**

Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition of *Geometric Transformations for 3D Modeling* is a comprehensive introduction to the theory and application of transformations.

Presenting the more abstract foundation material in the first three chapters, *Geometric Transformations in 3D Modeling* reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics.

**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.

**Requirements: ** The CD-ROM is compatible with most Microsoft Windows operating systems from *Windows 98* to *Windows 8 and 8 Pro*. The product requires Adobe Reader or Adobe Acrobat. The CD-ROM should operate with corresponding Windows-compatible hardware, including desktops, notebooks, laptops, netbooks and tablet computers. Internet access is required for product activation. PLEASE NOTE: The CD-ROM version is not compatible with Windows 8 RT, smart phones and tablets including the iPhone, iPad, Android devices and/or ebook readers such as Kindle, Nook or the Sony Wi-Fi E-Reader. For such applications, check out the ebook version.

**Michael E. Mortenson**, a graduate of the UCLA School of Engineering, writes and does independent research in 3D geometric modeling and computer-aided design. He is a former research scientist with a major aerospace corporation and the author of several highly successful textbooks.

**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