🚀 go-pugleaf

For those without the Red Book (page 64):
 
PostScript's coordinate transformations are based on the idea
of a transformation matrix.  In a 2-dimensional system, 6
numbers can describe all linear transformations of a
2-dimensional vector. Given a matrix [a b c d tx ty] and a
coordinate pair (x y), a transformed point (newx newy) can be
calculated with:
 
newx = a*x + c*y + tx
newy = b*x + d*y + ty
 
For normal operations, you can think of (x y) as user-space
coordinates, and (newx newy) as the device coordinates.
 
Numerous operators work on matrices; some operate on the
currentmatrix which transforms user coordinates into device
coordinates.
 
Examples of the former are matrix (creates an indentity
matrix), concatmatrix (three arguments, multiplies two matrices
together, putting the result in the third, returns the third),
and invertmatrix.
 
Examples of the latter are scale, translate, rotate, and
concat.
 
The concat operator concatenates its argument with the
currentmatrix (ie. the currentmatrix is changed to the argument
times the old currentmatrix).  This is more efficient than
using separate translate, rotate, and scale operations.  It
also allows skewing, for which there is no builtin operator.
 
Here's a definition of translate:
 
/translate {
  /ty exch def			% get y-translation
  /tx exch def			% get x-translation
  /tmp-matrix matrix def	% create identity matrix
  tmp-matrix 4 tx put
  tmp-matrix 5 ty put
  tmp-matrix concat
} def
 
Here's a definition of scale:
 
/scale {
  /sy exch def			% get y-scale
  /sx exch def			% get x-scale
  /tmp-matrix matrix def	% create identity matrix
  tmp-matrix 0 sx put
  tmp-matrix 2 sy put
  tmp-matrix concat
} def
 
Here's rotate:
 
/rotate {
  /angle exch def
  /tmp-cos angle cos def	% get cosine and sine of angle
  /tmp-sin angle sin def
  /tmp-matrix matrix def	% create identity matrix
  tmp-matrix 0 tmp-cos put
  tmp-matrix 1 tmp-sin put
  tmp-matrix 2 tmp-sin neg put
  tmp-matrix 3 tmp-cos put
  tmp-matrix concat
} def
 
Ken (shiva@well.sf.ca.us)