Attempted to speed things up by moving the transformation from [0,1]^2
-> [-1,1]^2 into the actual sampling code rather than requiring a pre-
and post- transform every sample.  It is significantly faster (~8fps
rather than ~5) and removes at least one of the ugly lhs and rhs steps.
The zooming part is still not quite working right, so I'll need to get
that sorted next.