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Basic differential geometry
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Thin Shells for Computer
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Introduction
Contents
The continuous
Subsections
Basic differential geometry
Definitions for curves
Parameterizing a curve by arc length
Curvature of curves
Regular surfaces
Tangent plane and surface normal
First fundamental form
Gauss map
Normal curvature
Second fundamental form (shape operator)
Principal curvatures
Mean and Guassian curvatures
Classification of surface points
Expressions for curvature of parametric surfaces
Gauss-Bonnet theorem
One-forms
Closed forms
Stokes theorem
Deformable surface models
Linear elasticity
Stress
Strain
Material (stress-strain) relations
Engineering constants
Copyright © 2005 Adrian Secord. All rights reserved.
