Geometry, Perspective Drawing, and Mechanisms

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Author: Don Row,Talmage James Reid

Publisher: World Scientific

ISBN: 981434382X

Category: Mathematics

Page: 328

View: 4407

The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter. The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.

Multiple View Geometry in Computer Vision

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Author: Richard Hartley,Andrew Zisserman

Publisher: Cambridge University Press

ISBN: 1139449141

Category: Computers

Page: N.A

View: 9707

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.

Distinguished Figures in Descriptive Geometry and Its Applications for Mechanism Science

From the Middle Ages to the 17th Century

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Author: Michela Cigola

Publisher: Springer

ISBN: 3319201972

Category: Technology & Engineering

Page: 248

View: 5334

This book consists of chapters that focus specifically on single figures that worked on Descriptive Geometry and also in Mechanisms Sciences and contain biographical notes, a survey of their work and their achievements, together with a modern interpretation of their legacy. Since Vitruvius in ancient times, and with Brunelleschi in the Renaissance, the two disciplines began to share a common direction which, over the centuries, took shape through less well-known figures until the more recent times in which Gaspard Monge worked. Over the years, a gap has been created between Descriptive Geometry and Mechanism Science, which now appear to belong to different worlds. In reality, however, there is a very close relationship between the two disciplines, with a link based on extremely solid foundations. Without the theoretical foundations of Geometry it would not be possible to draw and design mechanical parts such as gears, while in Kinematics it would be less easy to design and predict the reciprocal movements of parts in a complex mechanical assembly.

Picturing Space, Displacing Bodies

Anamorphosis in Early Modern Theories of Perspective

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Author: Lyle Massey

Publisher: Penn State Press

ISBN: 0271029803

Category: Art

Page: 175

View: 4788

In Picturing Space, Displacing Bodies, Lyle Massey argues that we can only learn how and why certain kinds of spatial representation prevailed over others by carefully considering how Renaissance artists and theorists interpreted perspective. Combining detailed historical studies with broad theoretical and philosophical investigations, this book challenges basic assumptions about the way early modern artists and theorists represented their relationship to the visible world and how they understood these representations. By analyzing technical feats such as anamorphosis (the perspectival distortion of an object to make it viewable only from a certain angle), drawing machines, and printed diagrams, each chapter highlights the moments when perspective theorists failed to unite a singular, ideal viewpoint with the artist&’s or viewer&’s viewpoint or were unsuccessful at conjoining fictive and lived space.Showing how these &“failures&” were subsequently incorporated rather than rejected by perspective theorists, the book presents an important reassessment of the standard view of Renaissance perspective. While many scholars have maintained that perspective rationalized the relationships among optics, space, and painting, Picturing Space, Displacing Bodies asserts instead that Renaissance and early modern theorists often revealed a disjunction between geometrical ideals and practical applications. In some cases, they not only identified but also exploited these discrepancies. This discussion of perspective shows that the painter&’s geometry did not always conform to the explicitly rational, Cartesian formula that so many have assumed, nor did it historically unfold according to a standard account of scientific development.

The Geometry of an Art

The History of the Mathematical Theory of Perspective from Alberti to Monge

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Author: Kirsti Andersen

Publisher: Springer Science & Business Media

ISBN: 9780387489469

Category: Mathematics

Page: 814

View: 5820

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.

Elementary Geometry for College Students

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Author: Daniel C. Alexander,Geralyn M. Koeberlein

Publisher: Cengage Learning

ISBN: 1285965906

Category: Mathematics

Page: 624

View: 9557

Building on the success of its first five editions, the Sixth Edition of the market-leading text explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, the text includes intuitive, inductive, and deductive experiences in its explorations. Goals of the authors for the students include a comprehensive development of the vocabulary of geometry, an intuitive and inductive approach to development of principles, and the strengthening of deductive skills that leads to both verification of geometric theories and the solution of geometry-based real world applications. Updates in this edition include the addition of 150 new problems, new applications, new Discover! activities and examples and additional material on select topics such as parabolas and a Three-Dimensional Coordinate System. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Geometric and Engineering Drawing

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Author: Ken Morling

Publisher: Routledge

ISBN: 0415536197

Category: Technology & Engineering

Page: 360

View: 4366

For all students and lecturers of basic engineering and technical drawing The new edition of this successful text describes all the geometric instructions and engineering drawing information, likely to be needed by anyone preparing or interpreting drawings or designs. There are also plenty of exercises to practise these principles.

How to Draw Perspective

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Author: Mark Bergin

Publisher: N.A

ISBN: 9781908973450

Category: Drawing

Page: 32

View: 4526

This comprehensive drawing handbook covers all aspects of perspective drawing, including essential concepts such as horizon line and vanishing point. With its clear step-by-step labelled drawings, this is an essential book for any budding artist who would like to master the art of drawing perspective.

Introduction to Graph Theory

H3 Mathematics

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Author: Khee Meng Koh,F. M. Dong,Eng Guan Tay

Publisher: World Scientific

ISBN: 9812705252

Category: Mathematics

Page: 228

View: 7514

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Machine Interpretation of Line Drawings

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Author: Kōkichi Sugihara

Publisher: Mit Press

ISBN: N.A

Category: Computer vision

Page: 233

View: 782

This book solves a long-standing problem in computer vision, the interpretation of line drawings and, in doing so answers many of the concerns raised by this problem, particularly with regard to errors in the placement of lines and vertices in the images. Sugihara presents a computational mechanism that functionally mimics human perception in being able to generate three-dimensional descriptions of objects from two-dimensional line drawings. The objects considered are polyhedrons or solid objects bounded by planar faces, and the line drawings are single-view pictures of these objects. Sugihara's mechanism has several potential applications. It can facilitate man-machine communication by extracting object structures automatically from pictures drawn by a designer, which can be particularly useful in the computer-aided design of geometric objects, such as mechanical parts and buildings. It can also be used in the intermediate stage of computer vision systems used to obtain and analyze images in the outside world. The computational mechanism itself is not accompanied by a large database but is composed of several simple procedures based on linear algebra and combinatorial theory. Contents:Introduction. Candidates for Spatial Interpretation. Discrimination between Correct and Incorrect Pictures. Correctness of HiddenPart-Drawn Pictures. Algebraic Structures of Line Drawings. Combinatorial Structures of Line Drawings. Overcoming Superstrictness. Algorithmic Aspects of Generic Reconstructibility. Specification of Unique Shapes. Recovery of Shape from Surface Information. Polyhedrons and Rigidity. Kokichi Sugihara is Professor in the Department of Mathematical Engineering and instrumentation Physics, Faculty of Engineering, the University of Tokyo, Tokyo, Japan. Machine interpretation of Line Drawingsis included in The MIT Press Series in Artificial Intelligence, edited by Patrick Henry Winston and Michael Brady.

Drawing on the Air

The Kinetic Sculpture of Tim Prentice

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Author: Tim Prentice

Publisher: Easton Studio Press, LLC

ISBN: 193521294X

Category: Art

Page: 144

View: 2087

In the New York Times Michael Kimmelman called them "sleek, whimsical contraptions in a modernist mode"; the Basler Zeitung termed them "net-like structures . . . like hedgehogs or serpents." The kinetic sculptures of Tim Prentice create a novel geometry of air and light. Concentrating on movement rather than object, Prentice harnesses natural elements into his art machines-delicate structures that walk the tightrope between order and chaos, control and serendipity, understated technique and extravagant wonder. Prentice purposely circumscribes the artist's prerogatives, distilling the power of wind and sun into an ever-changing dance of light and shadow. These understated, subtle inventions provide endless distraction, delighting the child in all of us. Drawing on Air offers a many-sided vision of the kinetic sculptor and his works. An essay by Nicholas Fox Weber introduces the artist and his work, while a chapter on "Mechanics" explains some of the physical principles underlying Prentice's whimsical sculptures. Photographs of works-in-progress, principal public commissions as well as occasional pieces created for casual amusement are punctuated by the artist's mordant, sometimes mischievous comments. "Prentice's sculptures . . .are about fluid movement and change, reminding us that everything is in flux. . . . Wonders of engineering, they create evanescent drawings in thin air." -Michael Amy, Art in America "What is grand in these sculptures is the sense of immensity created by their movements, a sense resonant with our most pleasurable apprehensions of land, sea, and sky." -Elaine Bleakney, Sculpture "These refined sculptures are never ponderous, plump or boring but constantly and slowly transforming themselves as though imbued by perpetuum mobile." -Karen Gerig, Basler Zeitung Experiencing Tim Prentice's work is like taking a ride on a roller coaster" -Catalog of the Connecticut Biennial

Viewpoints

Mathematical Perspective and Fractal Geometry in Art

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Author: Marc Frantz,Annalisa Crannell

Publisher: Princeton University Press

ISBN: 9781400839056

Category: Mathematics

Page: 248

View: 6453

An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

Modern Robotics

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Author: Kevin M. Lynch,Frank C. Park

Publisher: Cambridge University Press

ISBN: 1107156300

Category: Computers

Page: 544

View: 2021

A modern and unified treatment of the mechanics, planning, and control of robots, suitable for a first course in robotics.