One Dimensional Cubic Bezier Curve
Click and drag control points to change curve.
For more information, check out the post on my blog: Bezier Curves.
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.
- A * (1-t)^3
- B * 3t(1-t)^2
- C * 3t^2(1-t)
- D * t^3
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.
In this particular case, A, B and C are scalars, which makes the curve into the function:
y = A * (1-x)^3 + B * 3x(1-x)^2 + C * 3x^2(1-x) + D * x^3
y = A*(-x^4/4+x^3-(3 x^2)/2+x) + B*((3 x^4)/4-2 x^3+(3 x^2)/2) + C*(x^3-(3 x^4)/4) + D*(x^4/4) + constant
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.