Good morning,
Is there a simple way of fitting an ellipse equation to a simplier (like polynomial) method, minimizing the error? Or must we take several points and do the fit?
Cheers,
Kepler
This can still be a linear regression [least squares] fit. The linear applies to the coefficients, not the data, in this case the 'x' and 'y' data. First we note that an ellipse can be written as as the general conic
\(\displaystyle a\, x^2\, + b\, x\, +\, c\, y^2\, +d\, y\, +\, e\, =\, 0\)
with certain restrictions on the coefficients. You can fit that 'straight up', i.e. let
\(\displaystyle \epsilon_i\, =\, a\, x_i^2\, + b\, x_i\, +\, c\, y_i^2\, +d\, y_i\, +\, e\)
and minimize
E(a, b, c, d, e) = \(\displaystyle \Sigma_{i=1}^{i=n}\, \epsilon_i^2\)
with respect to a, b, c, d, and e and see if that is an ellipse or do a fitting procedure with the constraints.
