Solid Shape Book

Series Foreword
Preface
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
Bibliography
IndeX