Need a way to detect wall collison approximate without actually colliding?

somewhat like a radial radar to detect any nearest wall, and then push maybe AABB, sweeptest or raycasts, and the filter for the nearest contact point.

I tried some solutions like brute forcing through every single triangle in unity, or implementing GJK, so i understand some concept... but the solution isnt exactly cheap on the runtime, and i have reference from PSP titles that the concept can be achieved with less and higher precision.

Any ideas? i may need the right mathemathical algorythm or terms to even begin seeing whats the solution....

http://www.gamedev.net/topic/678418-procedural-wall-angle-detection-intersection-point/

You can edit your original post to clarify what you want. Don't re-post essentially the same question, rewritten.