Using MoI to investigate the arcLoop shows the affect of the parameters.
For "aspect" of 1:
Radial and Transverse = 0 results in a circle plotted as a curve. It is not a regular simple nurbs circle. (The loop becomes an ellipse for aspect !=1)
Radial != 0 alone causes a lens of the intersection of two equal circles.
Transverse !=0 alone causes a lens of the intersection of two equal circles, At 90 degrees.
The loop is that of two intersectiing circles. The rounded corners are just the natural rounding from limited numpoints plotting a curve with lots of points, which rounds the corners automatically, rather than a simple nurbs circle.

Both radial and transverse != 1 causes a diamond quad lens, with all 4 sides being circular arcs of many plotted points, with automatic corner rounding.
The loop approximates the intersection of 4 equal big circles.
For "aspect" != 1, the arcs are each a segment of an ellipse.

"Flat" tends to make a line flat area, for large enough flat value, on the right side.

radiusFil scales the loop. It does not "fillet" any corners.

radius also scales the loop.

- Brian