I've been looking into a solution to this issue for over a day now and haven't managed to find a possible calculation, matrix calculation or similar that can possibly convert between these two systems.
To clarify further I have the following examples, the black circles highlight the corner for the nearest listed x-y coordinates:
Right-hand cartesian system and example object placement with origins:
upside-down y-coordinate system with new object placement origins:
The origin has changed from bottom-left to top-left and the Y-axis is now upside down.
Are there any know approaches that can convert between these two formats? The second example shows the conversion from the first image, what I'm looking to find out is how/if it's possible to calculate the conversion between these systems.
I've made it easier for you by changing your original diagram a little:
Now you should be able to see what the corresponding points are:
Working clockwise from the top left,
$x_1=0, y_1=3400$ maps to $x_2=0, y_2=-200$
$x_1=5200, y_1=3200$ maps to $x_2=5200, y_2=0$
$x_1=5000, y_1=0$ maps to $x_2=5000, y_2=3200$
$x_1=-200, y_1=200$ maps to $x_2=-200, y_2=3000$
It should now be obvious that the relationship between the coordinates is:
$$x_2=x_1$$
$$y_2=3200-y_1$$