Does anyone know if there is a way to traverse a composite bezier path (a path made of multiple bezier curves) with a parameter $t$ such that $0 \le t \le 1$? Basically I want to traverse an entire composite Bézier path with a parameter $t$ instead of a single Bézier curve.
Important: $t$ should correspond relatively to how far along the path I am. This means that I can't just split the entire Bézier path into its Bézier curves and then figure out the index of the Bézier curve that I need to traverse based how big $t$ is because the Bézier curves could be of different lengths.
For example, in the image above you can see that the points are somewhat equally spaced. This is the desired effect. If I were to find the index of the Bézier curve that I want to traverse based on the path parameter $t$, I would get the same number of points for the shorter lines as I do for the longer lines.
Ideally the algorithm should take $O(1)$ time to find a point along the curve (since I'll be using it to traverse many points)