Geometric Transformations for 3D Modeling

This is the ebook version of the printed book. Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition 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.

  • 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.

 

1101804577
Geometric Transformations for 3D Modeling

This is the ebook version of the printed book. Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition 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.

  • 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.

 

79.95 In Stock
Geometric Transformations for 3D Modeling

Geometric Transformations for 3D Modeling

by Michael E. Mortenson
Geometric Transformations for 3D Modeling

Geometric Transformations for 3D Modeling

by Michael E. Mortenson

Multimedia(2nd ed.)

$79.95 
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Overview

This is the ebook version of the printed book. Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition 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.

  • 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.

 


Product Details

ISBN-13: 9780831133481
Publisher: Industrial Press, Inc.
Publication date: 04/01/2007
Edition description: 2nd ed.
Pages: 380
Product dimensions: 5.00(w) x 7.00(h) x 0.55(d)
Age Range: 18 Years

About the Author

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.

Table of Contents

Geometry
What Is Geometry History Geometric ObjectsSpace Geometry Is… E Pluribus Unum – Transformation and Invariance Theory of Transformations
Functions, Mappings, and Transformations Linear TransformationsGeometric Invariants Isometries Similarities Affinities Projectivities Topological Transformations Vector Spaces
Introduction to Linear Vector Spaces Basis Vectors Eigenvalues and Eigenvectors TensorsRigid-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 TilingPolyhedral 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 SystemsDeformations Answers to Selected ExercisesIndex

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