
Orientations and
Rotations
Computations in Crystallographic Textures
Preliminaries
Rotations as Displacements
Composition of Rotations
Improper Rotations
Matrix Representation
Formal Approach to Orthogonal
Transformations
Parameterizations
Half–turns
Cayley Transformation and Rodrigues
Parameters
Axis and Angle Parameters
Euler Angles
Cayley–Klein Parameters
Quaternions
Rotation Vector
Rotation Matrix in
Non–Cartesian Coordinate
Systems
Miller Indices
Computational Properties of
Parameterizations
Geometry of the Rotation Space
SO(3) as a Riemannian Manifold
Exponential Mapping
SO(3) as a Lie Group
Integration on SO(3)
More on Small Orientation Changes
Vector of Infinitesimal Rotation
Rotation Rate Field and Continuity
Equation
Short Excursion into Mechanics
Some Statistical Issues
Mean Orientation
Distributions on the Rotation Manifold
Generation of Orientations
Comparing Smooth Orientation Functions
Symmetry
Finite Point Groups
Crystallographic Point Groups
Asymmetric Domains
Asymmetric Domains in Rodrigues Space
Misorientation Angle and Axis Distributions
Misorientation Angle Distributions
Distributions of Rotation Axes
Crystalline Interfaces and Symmetry
Symmetrically Equivalent Boundaries
Boundary Distributions
Crystallographic Textures
Texture Components in
Cubic–Orthorhombic Case
Rational Orientation Relationships
Coincident Sublattices
Diffraction Geometry
Elementary Relations
Orientations of Individual Crystallites
Orientation Distributions from Pole
Figures
Effective Elastic Properties of Polycrystals
Definitions and Simplest Principles
Perturbation Methods
Related Issues