## 3.2.1 General Concepts

Before giving specific transformations, it will be helpful to define them in general to avoid confusion in later parts when intuitive notions might fall apart. Suppose that a rigid robot, , is defined as a subset of or . A rigid-body transformation is a function, , that maps every point of into with two requirements: 1) The distance between any pair of points of must be preserved, and 2) the orientation of must be preserved (no mirror images'').

Using standard function notation, for some refers to the point in that is occupied'' by . Let

 (3.21)

which is the image of and indicates all points in occupied by the transformed robot.

Subsections
Steven M LaValle 2012-04-20