Gives the reader a full understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relationships between transformations. Describes how geometric objects, or things represented as such, when subjected to mathematical operations called geometric transformations, may change position, orientation, or shape even though the properties that characterize their geometric identity and integrity remain unchanged or invariant.
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The book initially examines the history and content of geometry before discussing the theory of transformations and vector spaces. It then examines the synthetic and analytic modes of expressing transformations before beginning analytical studies. Affine transformations are then covered including rigid-body transformations, homogeneous coordinates, transformation matrices, reflections, and dilations (including isotropic varieties and shear.) Projective transformations are then examined with discussions of parallel, central and map projections, and display transformations. It then covers the fascinating world of nonlinear transformations and symmetry including tilings, polyhedral symmetry, and symmetry groups. The reader will come to discover how geometric transformations control not only position and orientation, but also the shape of geometric objects, to understand the role of invariants, to discover the effects of composite transformations, to discover how the set of rigid body transformations of Euclidean geometry is related to other transformations, and to appreciate the historical development of geometric concepts from the point of view of transformations that leave various sets of properties invariant.
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Most Helpful Customer Reviews
3 of 3 people found the following review helpful:
5.0 out of 5 stars
the best book on this subject for "the rest of us"...,
By exphys2000 "exphys2000" (New York United States) - See all my reviews
This review is from: Geometric Transformations (Hardcover)
This book does a *great* job describing geometric transformations, their meaning and use. All the gaps left by Computer Graphics classes are filled in, and (most amazing of all) it's an interesting read as well. Mathematicians may find this too practical, but it's perfect for CS and engineering people. When you finish this book, you'll now exactly *why* it's been OK to use those 4x4 homogeneous matrices in graphics and robotics!!
2 of 2 people found the following review helpful:
5.0 out of 5 stars
Second edition will soon be available in hardcopy and electronic form.,
By Sunny (Washington) - See all my reviews
This review is from: Geometric Transformations (Hardcover)
The 2nd edition of this highly acclaimed textbook will soon be available in hardcopy and electronic form.
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