Transforming logical points to device points:GDI uses the following equations to transform logical points to device points, and device points to logical points:
Transforming logical points to device points:
Dx = (Lx – xWO) ´ xVE/xWE + xVO
Dy = (Ly – yWO) ´ yVE/yWE + yVO
Transforming device points to logical points:
Lx = (Dx – xVO) ´ xWE/xVE + xWO
Ly = (Dy – yVO) ´ yWE/yVE + yWO
The following list describes the variables used in these transformation equations:
| Variable | Description | |
| xWO | Window origin x-coordinate | |
| yWO | Window origin y-coordinate | |
| xWE | Window extent x-coordinate | |
| yWE | Window extent y-coordinate | |
| xVO | Viewport origin x-coordinate | |
| yVO | Viewport origin y-coordinate | |
| xVE | Viewport extent x-coordinate | |
| yVE | Viewport extent y-coordinate | |
| Lx | Logical-coordinate system x-coordinate | |
| Ly | Logical-coordinate system y-coordinate | |
| Dx | Device x-coordinate | |
| Dy | Device y-coordinate |
The following four ratios are scaling factors:
xVE/xWE
yVE/yWE
xWE/xVE
yWE/yVE
They are used to determine the necessary stretching or compressing of logical units. The subtraction and addition of viewport and window origins is referred to as the translational component of the equation.