Cubic Bezier Curve

Click and drag control points to change curve.

For more information, check out the post on my blog: Bezier Curves.
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Cubic bezier curves have 4 control points and total up the values of the 4 functions below to get the final point at time t.
  1. A * (1-t)^3
  2. B * 3t(1-t)^2
  3. C * 3t^2(1-t)
  4. D * t^3
t - "Time", this value goes from 0 to 1 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.

In other words, if you have 4 control points A,B,C and D, and a time t:
CurvePoint = A*(1-t)^3 + B*3t(1-t)^2 + C*3t^2(1-t) + D*t^3.

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