My aim is to study the sensitivity of the operation that results these points. In order to do that, the reasonable idea was to have a tengible description of this curve. Thus my question here is about some ideas that may help me to describe a curve other than its formula( y=f(x)).
In fact what I have tried is:
- As you see the shape of the curve starts to be straight then rounded,, then straight again. So my firts idea was to define the initial point, then find the curvature numerically at the centred points,and lastly approximate a slope for the last straight part of the curve(eventhough it hs some fluctuations we can assueme it smooth enough).
- I try the idea of Bezier curves. Having the sample points I try to find the controls points of the bezier curve that best fit my curve. Thihs method is much helpful, however, to get a cubic BEzier curve we just need 4 sample points to get the two central control points. And as the number of the sample points increase(in my case I have about 200) this will be no more applicable, since either I have to define my curve by several patches and thus several cubic bezier curves, or I have to find just 4 control points from the huge data I have(In fact I wrote a matlab code to this but the fitting was worth!!).
So does any one help me by suggesting ideas that I can use to describe a curve other than interpolation and fitting ??
Edit: To be more precise: my aim is to do sensitivity analysis, so it would be great for me if I can tell that this graph is determined by X, Y ,... where X , Y and ... are parameters. For example: according to my second try my curve was determined by the four control points of the bezier curve that fit my curve. Or for example the slopes of the two lines discribing the begining and the neding part of my curve + the center and radius of the circle that best firt the central part of my curve.