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.


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