Zane Selvans wrote:

Is there a method built into Numpy/SciPy or friends that will generate

a set of N points evenly (regularly - not randomly) sampling the

entire surface of a sphere? I imagine people doing GCMs and other

geoscience in spherical coordinates have to do this pretty frequently,

so I'm sure someone's written it in Python somewhere. My searches

aren't turning anything up immediately though.

Thanks,

Zane

Zane: This one has puzzled mathematicians for centuries - there is no evenly spaced set of points on a sphere. The golden section spiral (or fibonacci) points are easy to code (see code below), but don't form the vertices of polygons. For modelling, where you need the points to be vertices of polygons, hexagonal icosahedral grid are typically used (see http://kiwi.atmos.colostate.edu/BUGS/geodesic/), but they are tricky to compute (I don't have any python code handy).

Regards,

-Jeff

import numpy as np

from mpl_toolkits.basemap import Basemap

import matplotlib.pyplot as plt

import sys

# from http://www.xsi-blog.com/archives/115

def fibonacci(N):

inc = np.pi * (3 - np.sqrt(5))

off = 2. / N

r2d = 180./np.pi

k = np.arange(0,N)

y = k*off - 1. + 0.5*off

r = np.sqrt(1 - y*y)

phi = k * inc

x = np.cos(phi)*r

z = np.sin(phi)*r

theta = np.arctan2(np.sqrt(x**2+y**2),z)

phi = np.arctan2(y,x)

lats = 90.-r2d*theta

lons = r2d*phi

return lats, lons

npts = int(sys.argv[1])

lats, lons = fibonacci(npts)

map = Basemap(projection ='ortho',lat_0=0,lon_0=-90)

map.drawcoastlines()

map.fillcontinents(color='coral')

map.drawmapboundary(fill_color='aqua')

x,y = map(lons, lats)

map.scatter(x,y,10,marker='o',zorder=10)

plt.show()