colour.geometry.ellipse_coefficients_canonical_form

colour.geometry.ellipse_coefficients_canonical_form(coefficients: ArrayLike) → NDArrayFloat

Compute canonical form ellipse coefficients from the specified general form ellipse coefficients.

The general form ellipse coefficients are the coefficients of the implicit second-order polynomial/quadratic curve 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 the ellipse coefficients and \(F\left(x, y\right)\) are coordinates of points lying on the ellipse.

Parameters:

coefficients (ArrayLike) – General form ellipse coefficients.

Returns:

Canonical form ellipse coefficients.

Return type:

numpy.ndarray

References

[Wikipedia]

Examples

>>> coefficients = np.array([2.5, -3.0, 2.5, -1.0, -1.0, -3.5])
>>> ellipse_coefficients_canonical_form(coefficients)
array([  0.5,   0.5,   2. ,   1. ,  45. ])