Linear Geometry with Computer Graphics / Edition 1

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Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups.

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Editorial Reviews

A textbook suitable for any of several advanced undergraduate courses for mathematics and computer science students. The emphasis in the first four chapters is on the construction of linear models which satisfy geometric postulate systems. The fifth and final chapter examines computer graphics, treating it as applied geometry. Requires a background in calculus (at least two semesters, preferably three), linear algebra (one semester), and programming experience. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Table of Contents

Part 1 Preliminaries: fields; vector spaces; linear transformations; cosets of a vector space; invariant subspaces. Part 2 Symmetric bilinear forms: symmetric bilinear forms; congruence; orthogonal complements; orthogonal bases; Witt's cancellation theorem; isotropic and anisotropic spaces; functions on inner product spaces. Part 3 Plane geometries: the affine plane; the affine group; postulates for the Euclidean plane; inner product planes; projective planes; conic sections. Part 4 Homogeneous spaces in Rn: topological groups; homogeneous spaces; geometry on homogeneous spaces; the Riemann sphere; the Poincare upper half-plane; differentiable manifolds. Part 5 Topics in computer graphics: a first graphics programme; a computer graphics system overview; geometric mappings in a CG system; the line-drawing algorithm; the wing-edge object representation; the conic sections; Bezier curves and B-splines; hidden surface removal; texture mapping; quadric intermediate surfaces; Koch systems. Appendices: equivalence relations - basics; the Jordan canonical form - proof of Jordan's theorem; GraphLib documentation - types, procedures and functions.

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