vector2xy#

StereographicProjection.vector2xy(v: Vector3d) Tuple[ndarray, ndarray][source]#

Return stereographic coordinates (X, Y) of 3D unit vectors.

Parameters:
v

If it is not a unit vector, it will be made into one.

Returns:
x

Stereographic coordinate X of shape same shape as the input vector shape. Only the vectors with z coordinate positive (pole = -1) or negative (pole = 1) are returned.

y

Stereographic coordinate Y of shape same shape as the input vector shape. Only the vectors with \(z\) coordinate positive (pole = -1) or negative (pole = 1) are returned.

Notes

The stereographic coordinates \((X, Y)\) are calculated from the unit vectors’ cartesian coordinates \((x, y, z)\) as

\[(X, Y) = \left(\frac{-px}{z - p}, \frac{-py}{z - p}\right),\]

where \(p\) is either 1 (north pole as projection point) or -1 (south pole as projection point).

Examples using StereographicProjection.vector2xy#