A circle of radius 1.

ellipse e constructs an ellipse with eccentricity e by scaling the unit circle in the X direction. The eccentricity must be within the interval [0,1).

An ellipse is represented by an affine transformation acting on the unit circle.

Compute the center of an ellipse.

Compute the angle to the major axis of an ellipse, measured counterclockwise from the positive x axis in radians. The result will be in the range [0, tau/2).

Compute the vectors (va, vb) from the center of the ellipse to the edge of the ellipse along the major and minor axes. These vectors can lie in any quadrant, depending on how the ellipse has been transformed.

Compute the scaling factors of an ellipse, i.e. (a,b) where a and b are half the lengths of the major and minor axes respectively.

Compute the coefficients of the quadratic form

A x^2 + B x y + C y^2 + D x + E y + F = 0

for an ellipse. Returns A through F (in that order) as a tuple.