 # query abuot plotting polygons using a basemap projection

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.

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-c)>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):
pts = np.vstack((theta[i], phi[i])).T
if boundary_crossed(pts[:,1]):
continue # skip polys that cross the map boundary

polypts = [m(pt, pt) for pt in pts]
poly = Polygon(polypts, facecolor="b", edgecolor="None",
alpha=0.5) 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-c)>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):
pts = np.vstack((theta[i], phi[i])).T
if boundary_crossed(pts[:,1]):
continue # skip polys that cross the map boundary

polypts = [m(pt, pt) for pt in pts]
poly = Polygon(polypts, facecolor="b", edgecolor="None",
alpha=0.5)

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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>

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:

subdiv.py (2.93 KB)

···

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