[cairo] API Shakeup: cairo_current_matrix

[Bill Spitzak]

This is equivalent to describing the matrix and transforms by it this way:

  |X|   | xx xy x0 |   |x|
  |Y| = | yx yy y0 | x |y|
  |1|   |  0  0  1 |   |1|

where X,Y is the device position and x,y is the user position.

In this syntax a transformation such as rotation is done by 
pre-multiplication:

  [new_current_matrix] = [rotation_matrix] x [current_matrix]

Note that some Postscript and OpenGL documentation trasposes the matrix, 
describe the vectors as rows instead of columns, and transform by 
post-multiply. This is mathematically the same, however it appears the 
above syntax is much more popular nowadays. (And to further confuse 
things OpenGL does transformations completely opposite the way 
PostScript does, by post-multiply in the above syntax. Translate 
followed by rotate in OpenGL rotates about the real origin, not the 
translated point. I find this very confusing and like the PostScript 
method much better!)

I suspect you have xy and yx swapped in either your description of the 
structure or in your functions. If you meant to order them in the same 
way PostScript does it  is xx,yx,xy,yy,x0,y0, ie. by column in the above 
diagram.

Carl Worth wrote:

> 	/*
> 	x_device = x_user * matrix.xx + y_user * matrix.xy + matrix.x0;
> 	y_device = x_user * matrix.yx + y_user * matrix.yy + matrix.y0;
> 	*/
> 
> 	typedef struct _cairo_matrix {
> 	    double xx;
> 	    double xy;
> 	    double yx;
> 	    double yy;
> 	    double x0;
> 	    double y0;
> 	};