LinearSphericalInterpolator#

hpx.LinearSphericalInterpolator()#

Piecewise linear interpolation of unstructured data on a unit sphere.

Parameters:
pointsndarray of floats, shape (npoints, 3)

2-D array of the Cartesian coordinates of the sample points, which must be unit vectors. All elements of this array must be finite.

valuesndarray of floats, shape (npoints, …)

Values of the function at the sample points. The length along the first dimension must be the same as the length of points.

Notes

The interpolation method is analogous to SciPy’s LinearNDInterpolator except that the points lie on the surface of a sphere.

The interpolation is done using CGAL [1] by finding the 3D Delaunay triangulation of the sample points [2], finding surface natural neighbor coordinates at the evaluation points [3], and performing linear interpolation [4].

This method is not as fast as we would like because CGAL constructs a miniature 2D Delaunay triangulation in the plane tangent to each evaluation point. The CGAL 2D Triangluations on the Sphere [5] library may be promising but it does not provide a readymade implementation of natural neighbor coordinates.

References

Examples

>>> import numpy as np
>>> from astropy.coordinates import uniform_spherical_random_surface
>>> np.random.seed(1234)  # make the output reproducible
>>> npoints = 100
>>> points = uniform_spherical_random_surface(npoints).to_cartesian().xyz.value.T
>>> points
array([[ 0.30367159,  0.78890962,  0.53423326],
       [-0.65451629, -0.63115799,  0.41623072],
       ...
       [-0.22006045, -0.39686604,  0.89110647]])
>>> values = np.random.uniform(-1, 1, npoints)
values
array([ 0.95807764,  0.76246449,  0.25536384,  0.86097307,  0.44957991,
        ...
       -0.33998522,  0.21335043,  0.64431958,  0.25593013, -0.76415388])
>>> interp = LinearSphericalInterpolator(points, values)
>>> eval_points = uniform_spherical_random_surface(10).to_cartesian().xyz.value.T
>>> interp(eval_points)
array([-0.05681123, -0.14872424, -0.15398783,  0.24820993,  0.6796055 ,
        0.25451712, -0.08408354,  0.20886784,  0.22627028,  0.08563897])