Coordinate systems for windows generally have the origin (0,0) positioned at the upper left corner of the window with X positive to the right and Y positive downwards. This is the "window coordinates" system. Generalized coordinates are implemented using scaling, rotation and translation operations such that any Cartesian coordinates can be used within a window. The Graphics Ports system uses a transform object to achieve this.
So, the six elements ( p , q , r , s , u , and v ) of the 3 x 3 matrix contain all the transformation information. These elements are stored in a list (of type transform) in the graphics-state slot transform .
Functions are provided in Graphics Ports which apply translation, scaling and rotation to a transform, combine transforms by pre- or post-multiplication, invert a transform, perform some operations while ignoring an established transform, and so on. The macros with-graphics-rotation, with-graphics-scale and with-graphics-translation pre-multiply a supplied transform while a body of code is executed.
Drawing functions such as draw-line and draw-ellipse modify pixels, but you cannot assume that they have exactly the same effect on all platforms. Some platforms might put pixels below and to the right of integer coordinates (x y) while others may center the pixel at (x y) .
This applies to all the drawing functions which are documented in GRAPHICS-PORTS Reference Entries - see the entries for functions with names beginning
CAPI User Guide and Reference Manual (Macintosh version) - 3 Aug 2017