I'm working with cubic bezier curve fitting algorithms for a given discrete curve.
But I'm having some problems with the input data. The discrete curve representation used as input may vary, in a way that sometimes I recieve too many points in regions of high curvature, or a uniform distance between points, or either no pre-defined pattern.
Thus, I'm planning to use a good curve re-parameterization scheme so that the algorithm that I'm developing could run despite the nature of the curve, receiving always a discrete curve with a well-known pattern.
My question is: What is the possibilities for discrete curve (re)-parameterization for discrete curves that I should consider use in this task? My input is an ordered vector of points $v \in \mathbb{R}^2$, representing the curve.
I have worked with chord-length parameterization, and it is a good option. But sometimes I have noticed that regions of high curvature lost some information (points discarded).
A interesting constraint for me is that I need one parameterization scheme that could preserve the original curve information as much as possible.
Thanks in advance!
There is no one scheme that is universally better than all others (as far as I know).
The chord-length scheme is the most commonly used.
Another common choice is the centripetal scheme, which is described here.
For a solution that is optimal in some sense, you should not pre-assign parameter values, you should treat them as unknowns that are to be computed as part of the interpolation process. This makes the problem much more complex, but it allows you to interpolate a larger number of data points. Specifically, you can interpolate 6 points with a cubic Bezier curves. For details, see here, and other papers by the same authors..