Geometric Transformations

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9780831130572: Geometric Transformations

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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Mortenson, Michael E
Published by Industrial Press, Inc. (1995)
ISBN 10: 0831130571 ISBN 13: 9780831130572
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Mortenson, Michael E
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