Focusing now on the ellipse, we consider the curve produced by a point on an ellipse rolling, without slipping, along a straight line.
We are calling this curve an
The formula used to determine baseline length is from Perimeter of Ellipse.
Placing an ellipse at 0, 1/4, 1/2, 3/4, 4/4 points, we rotate each ellipse 90°, to simulate rolling.
Using the red dot as a reference point, we can determine the path it makes as the ellipse rolls along the baseline.
The yellow curve is an approximation using a Bezier curve, with Control Points CP1 and CP2.