I agree that these techniques has been discussed before on this forum, but probably before MuscleGrothe's time and definitely with not nearly as much detail.

I'm sorry I missed your posts about this, Fett.  I would have given you some credit if I had known about your posts on this subject.  I haven't been here that long, and haven't read the board very often since I joined.  BTW, Thanks for the better elliptical circumference equation.  It should help me out when I get to parts like chest where the aspect ratio is far from 1:1.

You could simplify that to:
sqrt(2*(a²+b²))*pi*ratio

sqrt((a²+b²)/2)*2
=sqrt(a²+b²)*sqrt(1/2)*2
=sqrt(a²+b²)*sqrt(1/2)*sqrt(4)
=sqrt(a²+b²)*sqrt(2)
=sqrt(2*(a²+b²))

So basically the formula Fett gave was the circumference of the circle

r=sqrt(1/2)*sqrt(a^2+b^2)
(circle circumference is 2*r*pi)

A way to look at this is:
1. Draw a circle
2. Draw a perfect square over that circle, with the bottom left corner at the center of the circle, the bottom right corner on the rim of the circle at 0 degrees, and the top left corner at the 90 degree rim point.
3. Draw a line from the bottom left corner of the square to the top right corner.  This line intersects with the circle rim at the 45 degree point.
4. Scale the graphic to the aspect ratio of the ellipse.

After doing that, the 0 degree line should be equal to a, and the 90 degree line equal to b.  That would make the intersection point drawn in step 3 to be of the length sqrt(1/2)*sqrt(a^2+b^2).  So now draw yet another circle over this set of graphics, with that line (from the center to the ellipse intersection point) as the radius.

You can see the similarity in circumference of both the ellipse and the last circle.