🚀 go-pugleaf

pandit@ssd.intel.com writes:
>Can some one explain exactly what each element of a six-element
>transformation matrix does?  I was under the impression it worked as follows:
>
>x y [a b c d e f] transform --> x' y'
>
>where x' = ax + b + cy and y' = dy + e + fx.

No--you've got the right idea, but the coefficients are in the wrong place.
Given your transformation matrix [a b c d e f], and your input coordinates
x and y, the transformation gives output coordinates x' y' as:
	x' = ax + cy + e
	y' = bx + dy + f
In terms of matrix multiplication, the user coordinates are shorthand for
the vector [ x y 1 ] and the 6-element CTM is shorthand for the 3x3 matrix
| a b 0 |
| c d 0 |
| e f 1 |
"Transformation" is a multiplication of the vector by the matrix (in that
order!) giving the new vector  [ x' y' 1 ] .

As long as the subject has come up, a digression/caution: Realize that
operators which modify the CTM (scale, translate, rotate, which are special
cases of concat) do so by pre-multiplying the new transformation with the
existing CTM.  The default CTM for a device invariably incorporates nonzero
translations (e,f above), scaling (a,b,c,d will be other than 0 or 1), and
sometimes reflections and/or rotations.

The CTM doesn't enter into what you sketched, since you used an explicit
matrix with the transform operator...but if you omit the matrix you'll see
the effects of the CTM.
-- 
Dick Dunn    rcd@raven.eklektix.com   -or-   raven!rcd    Boulder, Colorado
   ...Never offend with style when you can offend with substance.