Playing around with GJK algorithm and managed to get visualization to the debug UI.

The 2 simplex case is without any conditions, 3 simplex with 4 and 4 simplex has 4 as well; where one condition is shared between the cases. All in SIMD so it's checking 4 pairwise collisions, but table lookup is sadly not SIMD.

Black line segment from middle: Search direction
Gray dot: Origin.
Black dot: Newly added point.
Red, green and blue dots: Previously added points.