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I have the equation of two 5th degree polynomials which they don't intersect with each other. Each curve is made of 100 points and these two curves look similar but there are small differences. I am looking for a transformation matrix/mathematical relation between these two curves to describe the mathematical relation between these two curves.

The equation of each line is defined in the following format and all of the parameters are known.

 f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y 
                + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2 
                + p13*x*y^3 + p04*y^4 + p50*x^5 + p41*x^4*y + p32*x^3*y^2 
                + p23*x^2*y^3 + p14*x*y^4 + p05*y^5

I am looking for a transformation matrix between these two curves to map one curve based on another one. I would appreciate if you could help me with a MATLAB code or any mathematical solution to solve this problem.

enter image description here

Floern
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Adrex
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    You may have better luck at http://math.stackexchange.com/ or http://mathoverflow.net/ asking this question. This isn't particularly programming related. – rjp Jun 19 '14 at 20:17
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    Welcome to Stackoverflow! without having info about these curves or some data, like the polynomial coefficients, how can we help you exactly? please edit the question and add everything you have (plot or links to images, data, etc) – bla Jun 19 '14 at 20:31

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