Re: [Matplotlib-users] query abuot plotting polygons using a basemap projection
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)
Re: [Matplotlib-users] query abuot plotting polygons using a basemap projection
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
def Mollweide(theta, phi):
def combinations(iterable, r):
''' Python 2.6 itertools function'''
# combinations('ABCD', 2) -- AB AC AD BC BD CD
# combinations(range(4), 3) -- 012 013 023 123
pool = tuple(iterable)
n = len(pool)
if r n:
return
indices = range(r)
yield tuple(pool[i] for i in indices)
while True:
for i in reversed(range(r)):
if indices[i] != i + n - r:
break
else:
return
indices[i] += 1
for j in range(i+1, r):
indices[j] = indices[j-1] + 1
yield tuple(pool[i] for i in indices)
def boundary_crossed(pts):
crossed = False
for c in combinations(pts, 2):
if abs(c[0]-c[1])180:
crossed = True
break
return crossed
# 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()
# draw lat/lon grid lines every 30 degrees.
m.drawmeridians(np.arange(0,360,30), dashes=[10,0])
m.drawparallels(np.arange(-90,90,30), dashes=[10,0])
ax = plt.gca() # get current axes instance
for i in range(theta.shape[0]):
pts = np.vstack((theta[i], phi[i])).T
if boundary_crossed(pts[:,1]):
continue# skip polys that cross the map boundary
polypts = [m(pt[1], pt[0]) for pt in pts]
poly = Polygon(polypts, facecolor=b, edgecolor=None,
alpha=0.5)
ax.add_patch(poly)
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Re: [Matplotlib-users] query abuot plotting polygons using a basemap projection
Thank you Jeff. I'll try out this solution. Gary. Jeff Whitaker wrote: snip 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 snip -- Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference ___ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users
