# 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.

Your browser doesn't seem to support the necesary html5 features ):
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
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.

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

Indefinite Integral:
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.