Click and drag control points to change curve. Modify weights in boxes below the curve.
For more information, check out the post on my blog: Bezier Curves.
Rational cubic bezier curves have 4 control points, a weight per control point (4 total), and total up the values of the 4 functions below to get the final point at time t.
A * W1 * (1-t)^3
B * W2 * 3t(1-t)^2
C * W3 * 3t^2(1-t)
D * W4 * t^3
They then divide that by the total of these 4 functions.
W1 * (1-t)^3
W2 * 3t(1-t)^2
W3 * 3t^2(1-t)
W4 * t^3
Parameters: t - "time", but in our case we are going to use the x axis value for t. A - The first control point, which is also the value of the function when x = 0. B - The second control point. C - The third control point. D - The fourth control point, which is also the value of the function when x = 1. W1 - The weighting of control point A. W2 - The weighting of control point B. W3 - The weighting of control point C. W4 - The weighting of control point D.
In this particular case, A, B, C and D are scalars, which makes the curve into the function:
y = (A * W1 * (1-x)^3 + B * W2 * 3x(1-x)^2 + C * W3 * 3x^2(1-x) + D * W4 * x^3) / (W1 * (1-x)^3 + W2 * 3x(1-x)^2 + W3 * 3x^2(1-x) + W4 * x^3)
Note that this bezier curve is 1 dimensional because A,B,C,D are 1 dimensional, but you could use these same equations in any dimension. Also,
these control points range from 0 to 1 on the X axis, but you could scale the X axis and/or the Y axis to get a different range of values.