Hi Jeff,
I finally had a chance to try this. I can't get it to work but I think
I'm close - for some reason, the way I'm creating the geos polygons
seems to always intersect the boundary polygon. It's hard to think of a
good minimal example for this so I've attached an example that
illustrates the problem - it tries to plot an icosahedron on the
Mollweide plot.
Gary R.
Jeff Whitaker wrote:
Gary Ruben wrote:
I'm plotting a coverage map of a sphere using the Mollweide plot in
basemap. The attachment is an example that is produced by sending an
array of polygons (one polygon per row described as four corners, one
per column) described using polar (theta) and azimuthal (phi) angles to
the following function. As a kludge, I discard any polygons that cross
the map boundary, but this produces artefacts and it would be better to
subdivide these and keep the parts. I was wondering whether there's a
function I missed that allows me to add polygons and performs the split
across the map boundary.
Gary R.
Gary: You might be able to use the _geoslib module to compute the
intersections of those polygons with the map boundary. I do a similar
thing with the coastline polygons in the _readboundarydata function.
The _boundarypolyll and _boundarypolyxy instance variables have the
vertices of the map projection region polygons in lat/lon and projection
coords. You could do somethig like this:
from mpl_toolkits.basemap import _geoslib
poly = _geoslib.Polygon(b) # a geos Polygon instance
describing your polygon)
b = self._boundarypolyxy.boundary
bx = b[:,0]; by= b[:,1]
boundarypoly = _geoslib.Polygon(b) # a geos Polygon instance
describing the map region
if poly.intersects(boundarypoly):
geoms = poly.intersection(boundarypoly)
polygons = [] # polygon intersections to plot.
for psub in geoms:
b = psub.boundary # boundary of an intersection
polygons.append(zip(b[:,0],b[:,1]))
-Jeff
from mpl_toolkits.basemap import Basemap, _geoslib
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
import numpy as np
from numpy import pi
icosahedron = \
[[0.53,0.,-0.53,0.53,-0.53,0.,0.53,-0.53,0.,0.53,0.,
-0.53,0.85,0.53,0.85,0.85,0.85,0.53,-0.85,-0.53,-0.85,
-0.85,-0.85,-0.53,0.,0.85,0.,0.,0.,-0.85,0.,0.,0.85,
0.,-0.85,0.,0.,0.53,0.85,0.,0.85,0.53,0.53,0.,0.85,
0.53,0.85,0.,-0.53,0.,-0.85,-0.53,-0.85,0.,-0.53,
-0.85,0.,-0.53,0.,-0.85],
[0.,0.85,0.,0.,0.,-0.85,0.,0.,0.85,0.,-0.85,0.,0.53,
0.,-0.53,0.53,-0.53,0.,-0.53,0.,0.53,-0.53,0.53,0.,
0.85,0.53,0.85,0.85,0.85,0.53,-0.85,-0.85,-0.53,-0.85,
-0.53,-0.85,0.85,0.,0.53,0.85,0.53,0.,0.,-0.85,-0.53,
0.,-0.53,-0.85,0.,0.85,0.53,0.,0.53,0.85,0.,-0.53,
-0.85,0.,-0.85,-0.53],
[0.85,0.53,0.85,0.85,0.85,0.53,-0.85,-0.85,-0.53,-0.85,
-0.53,-0.85,0.,0.85,0.,0.,0.,-0.85,0.,0.85,0.,0.,0.,
-0.85,0.53,0.,-0.53,0.53,-0.53,0.,0.53,-0.53,0.,0.53,
0.,-0.53,0.53,0.85,0.,-0.53,0.,-0.85,0.85,0.53,0.,
-0.85,0.,-0.53,0.85,0.53,0.,-0.85,0.,-0.53,0.85,0.,
0.53,-0.85,-0.53,0.]]
icosahedron1 = \
[[0.53, 0. ,-0.53, 0.53,-0.53, 0. ],
[0. , 0.85, 0. ,0. , 0. ,-0.85],
[0.85, 0.53, 0.85 ,0.85, 0.85, 0.53]]
def pointsOnSphere():
x,y,z = np.array(icosahedron)/0.851
return 180/pi*np.arcsin(z), 180/pi*np.arctan2(y,x)
if __name__=='__main__':
if 0:
from enthought.mayavi import mlab
x,y,z = icosahedron
sphere = mlab.triangular_mesh(x, y, z, \
np.arange(len(x)).reshape(-1,3), representation = 'wireframe')
mlab.show()
raise SystemExit
# Make Mollweide plot
m = Basemap(projection='moll', lon_0=0, resolution='c')
# draw the edge of the map projection region (the projection limb)
m.drawmapboundary()
theta, phi = pointsOnSphere()
theta.shape = phi.shape = (-1,3)
print theta.shape[0], 'polys'
ax = plt.gca() # get current axes instance
# create a geos Polygon instance describing the map region
boundarypoly = _geoslib.Polygon(m._boundarypolyxy.boundary)
for i in range(theta.shape[0]):
pts = np.vstack((phi[i], theta[i])).T
polypts = np.array([m(*pt) for pt in pts]) # to projection coords
poly = _geoslib.Polygon(polypts) # geos polygon for testing
if poly.intersects(boundarypoly):
for psub in poly.intersection(boundarypoly):
b = psub.boundary # boundary of an intersection
polypts = zip(b[:,0],b[:,1])
c = (1,) + tuple(np.random.random(2)) # warm colour
poly = Polygon(polypts, facecolor=c, edgecolor=c)
ax.add_patch(poly)
else:
c = tuple(np.random.random(2)) + (1,) # cool colour
poly = Polygon(polypts, facecolor=c, edgecolor=c)
ax.add_patch(poly)
plt.show()------------------------------------------------------------------------------
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