Pub. Date:
MIT Press
Solid Shape

Solid Shape

by Jan J. Koenderink


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Solid Shape gives engineers and applied scientists access to the extensive mathematical literature on three dimensional shapes. Drawing on the author's deep and personal understanding of three-dimensional space, it adopts an intuitive visual approach designed to develop heuristic tools of real use in applied contexts. Increasing activity in such areas as computer aided design and robotics calls for sophisticated methods to characterize solid objects. A wealth of mathematical research exists that can greatly facilitate this work yet engineers have continued to "reinvent the wheel" as they grapple with problems in three dimensional geometry. Solid Shape bridges the gap that now exists between technical and modern geometry and shape theory or computer vision, offering engineers a new way to develop the intuitive feel for behavior of a system under varying situations without learning the mathematicians' formal proofs. Reliance on descriptive geometry rather than analysis and on representations most easily implemented on microcomputers reinforces this emphasis on transforming the theoretical to the practical. Chapters cover shape and space, Euclidean space, curved submanifolds, curves, local patches, global patches, applications in ecological optics, morphogenesis, shape in flux, and flux models. A final chapter on literature research and an appendix on how to draw and use diagrams invite readers to follow their own pursuits in threedimensional shape.

Solid Shape is included in the Artificial Intelligence series, edited by Patrick Winston, Michael Brady, and Daniel Bobrow

Product Details

ISBN-13: 9780262111393
Publisher: MIT Press
Publication date: 03/21/1990
Series: Artificial Intelligence Series
Edition description: New Edition
Pages: 720
Product dimensions: 6.30(w) x 9.20(h) x 2.05(d)
Age Range: 18 Years

About the Author

Jan Koenderink was Professor of Physics at Utrecht University for many years. He is currently a Research Fellow at Delft University of Technology and Visiting Professor at MIT and École National Supérieure Paris. He is the author of Solid Shape (MIT Press, 1990).

Table of Contents

Series Foreword
I Prologue
1 Introduction
1.1 About this book
1.2 The necessary background
1.3 Where the emphasis is
1.4 What not to eXpect
2 Shape and Space
2.1 An operational view of space
2.2 Basic entities and methods
2.3 How to define constraints
2.4 Constraint defined operationally
2.5 Mechanical operationalizations
2.6 Optical operationalizations
2.7 Shape tolerances
2.8 Shape models and their use
2.9 Models for curves
2.10 Models for surfaces
2.11 Volumometric models
II Space
3 Euclidean Space
3.1 Geometries
3.2 ConveX sets
3.3 Coordinates systems
3.4 The myopic view
3.5 Frame fields
4 Curved Submanifolds
4.1 General considerations
4.2 Codimension
4.3 Curvature, eXtrinsic and intrinsic
4.4 The method of "Moving Frames"
4.5 Calculus on the manifold
4.6 Transversality
4.7 Order of contact
4.8 The topologically distinct surfaces
4.9 Singularities of vector fields
III Smooth Entities
5 Curves
5.1 Why study curves?
5.2 Curves as orbits
5.3 The edge of regression
5.4 The polar developments
5.5 Curves in central projection
5.6 Computer implementation
6 Local Patches
6.1 Strips
6.2 Local surface patches
6.3 Intrinsic curvature
6.4 EXtrinsic curvature
6.5 The asymptotic spherical image
6.6 The osculating cubic
6.7 Special patches
6.8 The local shape indeX
6.9 Assorted singular points
6.10 The Fundamental Theorem
IV Static Shape
7 Global Patches
7.1 Local & Global
7.2 Curve congruences
7.3 Patches
7.4 EXamples
7.5 Global GaussBonnet
8 Application to Ecological Optics
8.1 Ranging data
8.2 Thecontour
8.3 Furrow, dimple & bell revisited
8.4 The illuminance
8.5 FeliX Klein's Conjecture
V Dynamic Shape
9 Morphogenesis
9.1 Evolutionary processes
9.2 Scale space
9.3 Theory of measurement
9.4 Densities and Level Sets
9.5 Singularities
9.6 Canonical projection
9.7 Morphological scripts
9.8 "Shape Language"
10 Shape in FluX
10.1 Applicability
10.2 Special results
10.3 Deformation of a curve
10.4 Deformation of a surface
10.5 Infinitesimal bending
10.6 Final remark
VI Epilogue
11 Shape Models
11.1 AXes
11.2 Cratings & polyhedral approXimations
11.3 Ovoid assemblies
11.4 Nets
11.5 Functions with "knobs"
11.6 Plies of sugar cubes
12 How to Draw and Use Diagrams
12.1 What to avoid
AppendiX A. Your Way Into the Literature
A.1 Some helpful literature
A.2 Pedestrian's guide to the past
A.3 Special subjects
AppendiX B. Glossary

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