coords.Coords.project_on_sphere

Coords.project_on_sphere(radius=1.0, center=(0.0, 0.0, 0.0))

Project a Coords on a sphere.

Creates a central projection of a Coords on a sphere.

Parameters

radius: float, optional

The radius of the sphere, default 1.

center: float array_like (3,), optional

The center of the sphere. The default is the origin of the global axes.

Returns

Coords

A Coords with the input points projected from the center of the sphere onto its surface.

Notes

Projection is undefined for points coinciding with the center of the sphere (division by zero). Such points will result in NaN values.

This is a central projection from the center of the sphere. For a parallel projection on a spherical surface, see the last example below.

Examples

>>> X = Coords([[x,x,1.] for x in range(1,4)])
>>> X
Coords([[1., 1., 1.],
        [2., 2., 1.],
        [3., 3., 1.]])
>>> X.project_on_sphere()
Coords([[0.5774, 0.5774, 0.5774],
        [0.6667, 0.6667, 0.3333],
        [0.6882, 0.6882, 0.2294]])

Parallel projection (along the Z-axis) on a sphere with radius 1.5, and center at the origin:

>>> C = Coords([[0.0, 0.0],[1.0, 0.0],[1.0, 1.0],[0.0, 1.0]])
>>> dist = np.sqrt(C.x**2 + C.y**2)
>>> C.z = np.sqrt(1.5**2 - dist**2)
>>> print(C)
[[0.    0.    1.5  ]
 [1.    0.    1.118]
 [1.    1.    0.5   ]
 [0.    1.    1.118]]