Multiple displays

A window snaps within its own display

Press ⌃⌥→ and the window fills the right half of the display it is already on, not the one your pointer happens to be over.

This is deliberate, and it is the behaviour most people expect once they have both. Using the cursor’s display instead means a shortcut can fling a window to another screen because the mouse drifted, which is a surprising way to lose a window.

When a window straddles two displays, Orthant picks the one covering more of it.

Mixed resolutions and scaling

A Retina display and an external monitor at a different scale can be mixed freely. Orthant works in one coordinate space throughout and converts exactly once, natively, so a window moved between displays of different densities keeps the size you asked for.

The overlay works the other way round

⌃⌥O puts a grid on all of them at once, each sized to its own screen. The window lands on the display you draw on, so drawing on a different screen from the one the window is currently on is how you move it there.

That is the opposite of the shortcut rule above, and deliberately so. A shortcut is aimed with one keypress and should not depend on where the pointer drifted; a drawn selection is aimed at a specific place on a specific screen, and honouring that is the whole point of drawing it.