Guess this is a little late to help the OP
(took a bit of review and head scratching)
but, fwiw, to add to ...
A non-rational degree 2 bezier describes a precise
parabolic curve. A Sketcher Conic Arc entity with
rho = 0.5 is that curve.
(It might be worthwhile to review the definition
of 'rho'. It is the ratio of distances ...
chord to a parallel line tangent to the curve
divided by chord to tangent vector intersection.)
System tolerance b-spline approximations of
parabolic curves with monotone rate (maximum
curvature at one end) can be created using
the equations
x = t, y = t^2 or x = t, y = t^(1/2)
The equations
r = t^(1/2), theta = 360 * turns * t, z = t
will create a helical curve tracing the form
of a parabolic revolute.
The attached (WF2) might help connect the dots.
-Jeff Howard (wf2)
Sure it's true. I saw it on the internet.