Distribute points on a surface for CMM touches

I’m looking for suggestions on after I have picked a surface how can I distribute at least 3 points evenly distributed over the surface, I have to use a min of 3, may go up to 10 or more. I want to just pick n number of surfaces and produce the DMIS code needed for my CMM to measure each surface with a number of points to determine profile tolerance.



I’ve tried offsetting the edge curve and then dividing the curve into n segments but the offset doesn’t create a closed curve due to the edges.