We are dealing here with parameterized curves. These are curves that define a curve point in 2d or 3d for each parameter from a real interval.
The standard interval for curve parameters contains the real numbers from 0 to 1 (0 indicates the start point, 1 the end point).
I do the same here. I also use this interval for the ellipse segments, which are sometimes parameterized (by others) with the angle.