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    Geometry, Perspective Drawing, and Mechanisms

    ISBN-10: 981434382X
    ISBN-13: 9789814343824
    Edition: 2012
    Description: 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  More...
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    List Price: $82.00
    Copyright Year: 2012
    Publisher: World Scientific Publishing Co Pte Ltd
    Publication Date: 11/22/2011
    Binding: Hardcover
    Pages: 340
    Size: 6.25" wide x 9.00" long x 1.00" tall
    Weight: 1.386
    Language: English

    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.

    Combinatorial Figures
    Drawing figures
    Modeling figures
    The circuits of a figure
    Combinatorial Geometries
    The definition of a combinatorial geometry
    Lines and planes of a combinatorial geometry
    Two families of combinatorial geometries
    Sketches of planar geometries and figures
    Models of some combinatorial cubes
    Subgeometries of a combinatorial geometry
    Isomorphic combinatorial geometries
    Planar Geometries and Projective Planes
    The intersection of coplanar lines
    Projective planes
    Subgeometries of a projective plane
    An extended Euclidean plane
    Pencil and roller constructions
    Coordinatizing an extended Euclidean plane
    Sylvester's Theorem and the Fano plane
    Non-Planar Geometries and Projective Spaces
    Projective spaces
    Subgeometries of a projective space
    Desargues' Theorem and projective spaces
    Extended Euclidean space
    Coordinatizing extended Euclidean space
    Perpendicular lines and planes
    Pythagoras' Theorem, length and angle
    The existence of a tetrahedron
    Perspective Drawings
    The definition and basic properties of a perspective drawing
    Perspective drawings in a combinatorial geometry
    Practical perspective drawing methods
    Vanishing points
    Perspective drawings of a box
    Perspective rendition from an ideal viewpoint
    Binocular Vision and Single Image Stereograms
    Binocular vision
    Binocular vision and random-dot stereograms
    Single-image stereograms
    Scene Analysis
    Perspective drawings of intersections of planes
    Scenes and other planar figures
    The existence of boxes
    Completing a partial scene
    Two problems
    Distortion and Anamorphic Art
    Viewing perspective drawings
    Anamorphic art
    Distortion in 3-point perspective drawings
    Distortion in 2-point perspective drawings
    Distortion in 1-point perspective drawings
    Distortion in affine projections
    Planar Bar-And-Joint Mechanisms
    Bar-and-joint models
    Four-bar linkages
    Rocking and rotation in 4-bar linkages
    Coupler curves
    Parallelogram and kite linkages
    Cognate linkages
    Approximate and exact linear motion
    Non-Planar Hinged-Panel-Mechanisms
    Hinged-panel models
    Four-panel cycles
    Panel cycles of at least five panels
    Polyhedral models
    Graphs, Models and Geometries
    The definition of a graph
    Connected graphs and acyclic graphs
    The rigidity of a one-story building
    Hinge graphs and developments
    Graphs that are also geometries
    Spherical Polyhedra
    The definition of a polyhedron
    Planar graphs and three-connected graphs
    The definition of a spherical polyhedron
    Vertices, edges, and faces of a spherical polyhedron
    The existence of spherical polyhedra
    D�rer's melancholy octahedron
    Scene Analysis and Spherical Polyhedra
    Perspective drawings of a spherical polyhedron
    Some applications of the theorem
    Perspective drawings of a wider class of unions of polygonal regions
    . Matroids
    The definition of a matroid
    Geometries, graphs, and matroids
    Bases of a matroid
    The rank function of a matroid
    Isomorphism and representable matroids
    Projective and affine geometry
    Dual matroids
    Restrictions and contractions of a matroid
    Minors of a matroid
    Paving matroids

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