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()
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