Bezier Curve Generator
Instructions
Create and manipulate Bezier curves by adjusting control points. The position, velocity, and acceleration of the curve are displayed in separate plots.
- Drag the red control points to adjust the Bezier curve
- Change the number of control points and click "Update" to regenerate
- Upload a CSV file with x,y coordinates to display data points (format: x,y per line)
- Use "Clear Data Points" to remove all data points
- Blue line: dx/dt (X velocity), Red line: dy/dt (Y velocity)
- Blue line: d²x/dt² (X acceleration), Red line: d²y/dt² (Y acceleration)
Bezier Curve Equation
The Bezier curve is defined by the parametric equations:
$$\mathbf{B}(t) = \sum_{i=0}^{n} \mathbf{P}_i \cdot B_{i,n}(t)$$
$$x(t) = \sum_{i=0}^{n} P_{i,x} \cdot B_{i,n}(t)$$
$$y(t) = \sum_{i=0}^{n} P_{i,y} \cdot B_{i,n}(t)$$
where the Bernstein basis polynomials are:
$$B_{i,n}(t) = \binom{n}{i} t^i (1-t)^{n-i}$$
and the binomial coefficient is:
$$\binom{n}{i} = \frac{n!}{i!(n-i)!}$$
with $t \in [0,1]$ and $n$ = number of control points - 1
Current Control Points
Control points will appear here when you interact with the curve.