colour.geometry.ellipse_fitting_Halir1998

colour.geometry.ellipse_fitting_Halir1998(a: ArrayLike) → NDArrayFloat

Return the coefficients of the implicit second-order polynomial/quadratic curve that fits given point array \(a\) using Halir and Flusser (1998) method.

The implicit second-order polynomial is expressed as follows:

\(F\left(x, y\right)\) = ax^2 + bxy + cy^2 + dx + ey + f = 0`

with an ellipse-specific constraint such as \(b^2 -4ac < 0\) and where \(a, b, c, d, e, f\) are coefficients of the ellipse and \(F\left(x, y\right)\) are coordinates of points lying on it.

Parameters:

a (ArrayLike) – Point array \(a\) to be fitted.

Returns:

Coefficients of the implicit second-order polynomial/quadratic curve that fits given point array \(a\).

Return type:

numpy.ndarray

References

[HF98]

Examples

>>> a = np.array([[2, 0], [0, 1], [-2, 0], [0, -1]])
>>> ellipse_fitting_Halir1998(a)  
array([ 0.2425356...,  0.        ,  0.9701425...,  0.        ,  0.        ,
       -0.9701425...])
>>> ellipse_coefficients_canonical_form(ellipse_fitting_Halir1998(a))
array([-0., -0.,  2.,  1.,  0.])