General conic curve fit with constrained coefficients

Hello,

I would like to fit a set of xy points to a general conic equation of the form:

ax^2 + bxy + cy^2 +dx + ey + f = 0

where I need to constrain the coefficient "c" to zero. So I would like to fit:

ax^2 + bxy +dx + ey + f = 0

to determine the values of the coefficients.

I have tried:

https://www.mathworks.com/matlabcentral/fileexchange/22683-ellipse-fit-taubin-method

but I cannot determine how to contrain the coefficient. It gives me a good fit, but the coefficient "c" is non-zero. The fit is not good if I plot it with the "c" coefficient set to zero.

[Matt J]

It would be recommendable to attach a single.mat file containing your x,y data, so we can play with it.

Answer 1

[Matt J]

Here's a basic analytical fit, using the tools in this File Exchange package:

[xy,T]=conicFit.homogNorm([x(:),y(:)].');

x=xy(1,:).'; y=xy(2,:).';

q = conicFit.mostnull([x.^2, x.*y, x, y, x.^0]);

C=[q(1), q(2), q(3);
    0      0   q(4);
    0      0   q(5)];

C= T.'*(C/2+C.'/2)*T;

[a, b, d, e, f] = deal(C(1), 2*C(4), 2*C(7), 2*C(8), C(9));

[Scott Larwood]

Thank you, that solved my problem.

Answer 2

[Shadaab Siddiqie]

From my understanding you want to create conic curve with constrained coefficients. Here is a similar question which might help you.