Quad Triangle Fan?

Try for a quad triangle fan instead, subdividing a triangle four ways... I know how this sounds, yeah! 8-P
We make a triangle from two consecutive points, by picking a point on a line segment between these two and pushing a third point out to the right of that, using the delta x and delta y between the two initial random points. The center of the quad triangle fan would be the midpoint between that random point on the first edge and the third point.
I changed to a rectangular map.