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.
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
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.
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