Gathering data for correlation coefficient.
Red curve is produced via programming to produce a true cycloid curve.
Yellow curve is produced via Bezier curves to exactly follow the red curve.
However, Bezier curves are controlled by 2 'control points' (CP), as indicated by the blue dots above the curves.
Determining where these 2 points are is a trial-and-error experiment, so we are gathering data from several different generating circles, in order to see if there is a relationship between the radius of the circle, and where the 2 control points should be.
This particular curve is produced by a circle with radius 60px as it rolls without sliding along the baseline.
Thus far we have 12 sets of data, which we will be performing various statistical formulae on to determine if a relationship exists.
One of the variables we are looking at is the angle between the center point on the baseline and a control point, as indicated by the green lines. This involves some simple trigonometry.
Another variable is the radius from the Midpoint to the Control Points (green lines).