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.

W1:
W2:
W3:
W4:

This rational trigonometric spline has 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. t ranges from 0 to pi/2 instead of the usual 0 to 1.

A * W1 * (0.5*cos(x)*(cos(x)+1.0))

B * W2 * (0.5*sin(x)*(sin(x)-1.0))

C * W3 * (0.5*cos(x)*(cos(x)-1.0))

D * W4 * (0.5*sin(x)*(sin(x)+1.0))

It then divides that by the total of these 4 functions.

W1 * (0.5*cos(x)*(cos(x)+1.0))

W2 * (0.5*sin(x)*(sin(x)-1.0))

W3 * (0.5*cos(x)*(cos(x)-1.0))

W4 * (0.5*sin(x)*(sin(x)+1.0))

Parameters: t - "Time", this value goes from 0 to pi/2 to generate each point on the curve A - The first control point, also the starting point of the curve. B - The second control point. C - The third control point. D - The fourth control point, also the ending point of the curve. 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 other words, if you have 4 control points A,B,C and D, 4 weights W1,W2,W3,W4 and a time t:
CurvePoint = (A*W1*(0.5*cos(t)*(cos(t)+1.0)) + B*W2*(0.5*sin(t)*(sin(t)-1.0)) + C*W2*(0.5*cos(t)*(cos(t)-1.0)) + D*W3*(0.5*sin(t)*(sin(t)+1.0)))/(W1*(0.5*cos(t)*(cos(t)+1.0)) + W2*(0.5*sin(t)*(sin(t)-1.0)) + W2*(0.5*cos(t)*(cos(t)-1.0)) + W3*(0.5*sin(t)*(sin(t)+1.0)))

Note that this spline is 2 dimensional because A,B,C,D are 2 dimensional, but you could use these same equations in any dimenion!