differt.geometry.fibonacci_lattice

differt.geometry.fibonacci_lattice#

fibonacci_lattice(n, dtype=None, *, frustum=None)[source]#

Return a lattice of vertices on the unit sphere.

This function uses the Fibonacci lattice method [8] to generate an almost uniformly distributed set of points on the unit sphere.

If frustum is passed, points are distributed in the region defined by the frustum’s limits.

Parameters:

  • n (int) – The size of the lattice.

  • dtype (str | type[Any] | dtype | SupportsDType | None) – The float dtype of the vertices.

  • frustum (Float[ArrayLike, '2 2'] | Float[ArrayLike, '2 3'] | None) –

    The spatial region where to sample points.

    The frustum in an array of min. and max. values for azimuthal and elevation angles, see viewing_frustum for example.

    It is allowed to pass a frustum with distance values, but it will be ignored as the distance of from sampled points to origin is always 1.

Return type:

Float[Array, '{n} 3']

Returns:

The array of vertices.

Raises:

ValueError – If the provided dtype is not a floating dtype, or if n is not strictly positive.

Examples

The following example shows how to generate and plot a fibonacci lattice.

>>> from differt.geometry import (
...     fibonacci_lattice,
... )
>>> from differt.plotting import draw_markers
>>>
>>> xyz = fibonacci_lattice(100)
>>> fig = draw_markers(xyz, marker={"color": xyz[:, 0]}, backend="plotly")
>>> fig
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