# One Dimensional Quadratic 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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Quadratic bezier curves have 3 control points and total up the values of the 3 functions below to get the final point at time t.
1. A * (1-t)^2
2. B * 2t(1-t)
3. C * t^2
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, 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)^2 + B * 2x(1-x) + C * x^2

Indefinite Integral:
y = A*(x^3/3-x^2+x) + B*(x^2-(2x^3)/3) + C*(x^3/3) + constant

Note that this bezier curve is 1 dimensional because A,B,C 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.