- Problem 2
Write down the formula for each of these distance-preserving maps.
- the map that rotates radians, and then
- the map that reflects about the line
- the map that reflects about and translates over
Some of these are nonlinear,
because they involve a nontrivial translation.
- The line makes an angle of
with the -axis.
Thus and .
- Problem 4
In practice the matrix for the distance-preserving linear transformation
and the translation are often combined into one.
Check that these two computations yield the same
first two components.
(These are homogeneous coordinates;
see the Topic on Projective Geometry).
The first two components of each are and .