The quadratic function can be defined as
$z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$
But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$?
I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to e.g. solving a cubic equation in 1D I found nothing unfortunately.
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user32038
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Please use MathJax when formatting your questions. – John Wayland Bales Mar 19 '19 at 16:12
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2Each tuple gives you an equation in six variables. – John Wayland Bales Mar 19 '19 at 16:17
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You can write the equation in determinant form directly from the tuples. – amd Mar 19 '19 at 19:07
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Thanks!! It seems solving the linear equations is not so difficult, and most of my expected problems pop up later (or earlier, e.g. on chosing the 6 points). – user32038 Mar 21 '19 at 06:40
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I solved the problem for myself now. It was easier than expected, thanks for support. – user32038 Mar 29 '19 at 12:58