Projective Transformations
Projective Transformations

Author: P. S. Modenov

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 149

ISBN-13: 1483261492

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Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Geometry
Geometry

Author: David A. Brannan

Publisher: Cambridge University Press

Published: 1999-04-13

Total Pages: 516

ISBN-13: 9780521597876

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This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study.

Linear Algebra and Projective Geometry
Linear Algebra and Projective Geometry

Author: Reinhold Baer

Publisher: Courier Corporation

Published: 2012-06-11

Total Pages: 338

ISBN-13: 0486154661

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Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Transformation Groups for Beginners
Transformation Groups for Beginners

Author: Sergeĭ Vasilʹevich Duzhin

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 258

ISBN-13: 0821836439

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Presents a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. This work introduces the notions of a transformation group and of an abstract group. It gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.

Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision

Author: Richard Hartley

Publisher: Cambridge University Press

Published: 2004-03-25

Total Pages: 676

ISBN-13: 1139449141

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A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Computer Graphics Through OpenGL
Computer Graphics Through OpenGL

Author: Sumanta Guha

Publisher: CRC Press

Published: 2014-08-06

Total Pages: 928

ISBN-13: 1482258404

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From geometric primitives to animation to 3D modeling to lighting, shading, and texturing, Computer Graphics Through OpenGL: From Theory to Experiments, Second Edition presents a comprehensive introduction to computer graphics that uses an active learning style to teach key concepts. Equally emphasizing theory and practice, the book provides an und

Great Moments in Mathematics: After 1650
Great Moments in Mathematics: After 1650

Author: Howard Eves

Publisher: American Mathematical Soc.

Published: 2020-07-31

Total Pages: 278

ISBN-13: 0883853116

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What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is a fascinating collection of pivotal points in the historical development of mathematics...The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics. —Herbert Fremont, The Mathematics Teacher Eves is never less than tantalizing and usually inspiring...each 'great moment' has detailed exercises following it, as these have been carefully chosen to illustrate the depth of the ideas in question. —C. W. Kilmister, The London Times, Higher Education Supplement As is usual with Eves' work, the books are well written and entertaining. They give an historical background to many of the best known mathematical results, and, in addition, provide interesting pieces of information about the mathematicians involved. Eves includes relevant exercises at the end of each chapter. These are a good source of different, interesting problems, and when combined with the material in the chapter, could form the basis for a mathematical project...Eves' book provides an interesting, well-written, and enjoyable account. You won't be disappointed. —David Parrott, The Australian Mathematics Teacher