Let r
be the radius of the circle sweeping out the torus and R
the radius of the center circle. Assuming r is less
than R-r, the interval from the minimum to the supremum
curvature of the curve
is [0, 1/r). We map this to the interval
from 1 to infinity using f(x) = 1/(1-rx).
The tubes are created by sweeping an ellipse in the normal
plane of the Frenet fram and varying its aspect-ratio with
f of the curvature. The ellipse does not rotate
within its frame and the major axis is aligned with the
binormal vector.