Diagrid on Triangular Surfaces

I was wondering if anyone can give me some advice for creating a diagrid on a faceted object comprised of triangular surfaces.  I am able to create a diagrid on both curved and rectilinear surfaces, but as soon as I make a triangular surface it creates a square grid of points that stretch beyond my
surface.  I was also able to then create a grid of points that was limited
by the triangular surface but I can't connect lines between the
points in order to create the diagird. 

Any advice on how I can create a diagrid where I can control the spacing of the grid and place it on a triangulated surface?

Thanks