ddg.datastructures.nets.net_generators.jacobi_elliptic_curve module

ddg.datastructures.nets.net_generators.jacobi_elliptic_curve.jacobi_elliptic_curve(k)

Returns the elliptic curve [cn, sn, dn] for a parameter k.

More precisely, returns the collection of curves obtained by first taking the curve

u -> [cn(u, k), sn(u, k), dn(u, k)]

and adding the reflection of this about the plane z = 0. In the case where k = 1, we also have to reflect about the planes x = 0 and x + z = 0.

This curve (collection) is the intersection of the two cylinders

x^2 + y^2 = 1,
k^2 * y^2 + z^2 = 1

Homogenizing in the last component, to [cn, sn, dn, 1], gives the intersection curve of any two quadrics in the pencil

u1 * diag([1, 1, 0, -1]) + u2 * diag([0, k, 1, -1])

in homogeneous coordinates.

Parameters:

kfloat

Parameter in the interval [0, 1]. It is best to avoid values close (about 1e-9) but not equal to 1 because the scipy.ellipj functions do not work well for those values.

Returns:

NetCollection