Take your curve that represents the top of the slat. From the start of the first slat, draw a circle with a 1.5" radius, with the center on the start of the curve. The slat starts at the end of the curve, and ends where the circle intersects the curve.
Now, where the circle intersects the curve (slat end), draw another circle with a radius of 0.5". Where it intersects the curve, defines the gap.
From that point, repeat from the beginning, and you'll have evenly spaced slats.
I'd draw lines between the intersecting lines and circles, then offset them for the bottom of the slats.
Gerry - http://www.thecncwoodworker.com