All window tiling apps I've seen are designed to make windows snap to preset screen areas, such as "the left half of the screen" or even "this size of rectangle specified with a grid." Is there one that would let me do, say, this:
Window tiling app that snaps to other windows’ edges rather than predefined screen areas
applicationssoftware-recommendationwindow-manager
Related Solutions
SizeUp is exactly what you need:
SizeUp allows you to quickly position a window to fill exactly half the screen (splitscreen), a quarter of the screen (quadrant), full screen, or centered via the menu bar or configurable system-wide shortcuts (hotkeys). Similar to "tiled windows" functionality available on other operating systems.
Try out Stay. It lets you save window configurations (position and size) in profiles. Unfortunately, these profiles only deal (multi) display arrangements.
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Best Answer
Update in 2018:
Rejoice, this is now an OS feature!
Try dragging your window slowly against another one, you'll encounter some resistance. You can use this to line them up quite easily.
I can't remember for sure when they added this, but I believe it was in OS X v10.12 Sierra.