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.
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.
- A * (1-t)^2
- B * 2t(1-t)
- C * t^2
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
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.