Thank you for the replies. The data being processed are:
data={{-0.0893812, -0.0140775}, {-0.0904977, -0.0146514}, {-0.0914695, -0.0154373}, {-0.0924943, -0.0161461}, {-0.0934767,-0.0169158},{-0.0943115, -0.0178996}, {-0.0951481, -0.0188803}, {-0.0958544, -0.0200493}, {-0.0965879, -0.0211791}, {-0.0974918, -0.0220623}, {-0.0984529, -0.0228627}, {-0.0992755, -0.0238636}, {-0.100107, -0.0248522}, {-0.100968, -0.0257978}, {-0.101778, -0.0268171}, {-0.102616, -0.0277946}, {-0.103483, -0.0287318}, {-0.104312, -0.0297239}, {-0.105068, -0.0308208}, {-0.105771, -0.0319949}, {-0.106386, -0.0332957}, {-0.106925, -0.0347073}, {-0.107456, -0.0361294}, {-0.108057, -0.0374492},{-0.108753, -0.0386353}, {-0.109534, -0.0396923}, {-0.110253, -0.040859}, {-0.110614, -0.0422182}}
S M Blinder: thanks for the material, I will study them carefully.
Henrik: Thank you for the suggestion, FindFormula is a very rough approximation of the data for my purposes. Try
ifun = Interpolation[data]
Plot[ifun[x], {x, -0.089381226, -0.110613757}, Epilog -> Point[data]]
You'll see the level of accuracy required. Only if I could see the output function that represents the final curve you see here.
Daniel: Thanks for your reply. You are looking at the data considered. The goal is to find the functional form that accurately interpolates these data set. This is actually a part of a geometry that will be deformed in a finite element code. I'm doing this to get a proper parameterization of the geometry to be able to perform a shape optimization, just to give you an idea of my purposes here. B-splines and Bezier Functions are all that comes up in the literature. I don't really care so much about the backend stuff that produces the interpolated function, as I will only use this function to parameterize the geometry.
Thanks,