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From: Zane Selvans <zane@id...>  20090415 06:51:42

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 A. Selvans Amateur Earthling http://zaneselvans.org +1 303 815 6866 
From: Jeff Whitaker <jswhit@fa...>  20090415 11:14:24

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.xsiblog.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() 
From: Andrew Straw <strawman@as...>  20090415 15:48:36
Attachments:
subdivided_icosahedron.png
subdivided_icosahedron.py

Jeff Whitaker wrote: > 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). I'm attaching some code I wrote to subdivide and icosahedron for tiling a sphere with hexagons (and the occasional pentagon). Andrew 