I can't comprehend what "thinking in angles" means, or what it would be like. I'm a very visual/conceptual/pattern like thinker, but specifically thinking in angles is hard for me to imagine....
What you describe in your post does remind of of things I did when I was younger, though, and even still sometimes (I'm now in my late 20s), I would often put my "line of site", or my visual point of view, at different angles of things. Hard to describe. Like I would put my eyes/line of site at various angles to a door, and would move along with the door as it closed and opened, and would repeat this motion over and over. Or putting my eyes very closely up to a bottle of water, and watching the water move about in the bottle from different angles. Putting my eyes up to small crevices of various items, under chairs, door handles, all sorts of things. Basically just viewing something up close and from different points of view or angles, and really becoming absorbed and lost in this different "point of view".
I can try to elaborate or explain better if that doesn't make sense to anyone.