def points(self,npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# must ask for at least 2 points.
if npoints <= 1:
raise ValueError,'npoints must be greater than 1'
elif npoints == 2:
return [math.degrees(self.lon1),math.degrees(self.lon2)],[math.degrees(self.lat1),math.degrees(self.lat2)]
# can't do it if endpoints are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError,'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.gcarclen
delta = 1.0/(npoints-1)
f = delta*NX.arange(npoints) # f=0 is point 1, f=1 is point 2.
incdist = self.distance/(npoints-1)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
# perfect sphere, use great circle formula
if self.f == 0.:
A = NX.sin((1-f)*d)/math.sin(d)
B = NX.sin(f*d)/math.sin(d)
x = A*math.cos(lat1)*math.cos(lon1)+B*math.cos(lat2)*math.cos(lon2)
y = A*math.cos(lat1)*math.sin(lon1)+B*math.cos(lat2)*math.sin(lon2)
z = A*math.sin(lat1) +B*math.sin(lat2)
lats=NX.arctan2(z,NX.sqrt(x**2+y**2))
lons=NX.arctan2(y,x)
lons = map(math.degrees,lons.tolist())
lats = map(math.degrees,lats.tolist())
# use ellipsoid formulas
else:
latpt = self.lat1
lonpt = self.lon1
azimuth = self.azimuth12
lons = [math.degrees(lonpt)]
lats = [math.degrees(latpt)]
for n in range(npoints-2):
latptnew,lonptnew,alpha21=vinc_pt(self.f,self.a,latpt,lonpt,azimuth,incdist)
d,azimuth,a21=vinc_dist(self.f,self.a,latptnew,lonptnew,lat2,lon2)
lats.append(math.degrees(latptnew))
lons.append(math.degrees(lonptnew))
latpt = latptnew; lonpt = lonptnew
lons.append(math.degrees(self.lon2))
lats.append(math.degrees(self.lat2))
return lons,lats
def points(self, npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# must ask for at least 2 points.
if npoints <= 1:
raise ValueError, 'npoints must be greater than 1'
elif npoints == 2:
return [math.degrees(self.lon1),
math.degrees(self.lon2)
], [math.degrees(self.lat1),
math.degrees(self.lat2)]
# can't do it if endpoints are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError, 'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.gcarclen
delta = 1.0 / (npoints - 1)
f = delta * NX.arange(npoints) # f=0 is point 1, f=1 is point 2.
incdist = self.distance / (npoints - 1)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
# perfect sphere, use great circle formula
if self.f == 0.:
A = NX.sin((1 - f) * d) / math.sin(d)
B = NX.sin(f * d) / math.sin(d)
x = A * math.cos(lat1) * math.cos(lon1) + B * math.cos(
lat2) * math.cos(lon2)
y = A * math.cos(lat1) * math.sin(lon1) + B * math.cos(
lat2) * math.sin(lon2)
z = A * math.sin(lat1) + B * math.sin(lat2)
lats = NX.arctan2(z, NX.sqrt(x**2 + y**2))
lons = NX.arctan2(y, x)
lons = map(math.degrees, lons.tolist())
lats = map(math.degrees, lats.tolist())
# use ellipsoid formulas
else:
latpt = self.lat1
lonpt = self.lon1
azimuth = self.azimuth12
lons = [math.degrees(lonpt)]
lats = [math.degrees(latpt)]
for n in range(npoints - 2):
latptnew, lonptnew, alpha21 = vinc_pt(self.f, self.a, latpt,
lonpt, azimuth, incdist)
d, azimuth, a21 = vinc_dist(self.f, self.a, latptnew, lonptnew,
lat2, lon2)
lats.append(math.degrees(latptnew))
lons.append(math.degrees(lonptnew))
latpt = latptnew
lonpt = lonptnew
lons.append(math.degrees(self.lon2))
lats.append(math.degrees(self.lat2))
return lons, lats
def draw_networkx_edges(G, pos,
edgelist=None,
width=1.0,
edge_color='k',
style='solid',
alpha=1.0,
edge_cmap=None,
edge_vmin=None,
edge_vmax=None,
ax=None,
arrows=True,
**kwds):
"""Draw the edges of the graph G
This draws only the edges of the graph G.
pos is a dictionary keyed by vertex with a two-tuple
of x-y positions as the value.
See networkx_v099.layout for functions that compute node positions.
edgelist is an optional list of the edges in G to be drawn.
If provided, only the edges in edgelist will be drawn.
edgecolor can be a list of matplotlib color letters such as 'k' or
'b' that lists the color of each edge; the list must be ordered in
the same way as the edge list. Alternatively, this list can contain
numbers and those number are mapped to a color scale using the color
map edge_cmap.
For directed graphs, "arrows" (actually just thicker stubs) are drawn
at the head end. Arrows can be turned off with keyword arrows=False.
See draw_networkx_v099 for the list of other optional parameters.
"""
if ax is None:
ax=matplotlib.pylab.gca()
if edgelist is None:
edgelist=G.edges()
if not edgelist or len(edgelist)==0: # no edges!
return None
# set edge positions
edge_pos=asarray([(pos[e[0]],pos[e[1]]) for e in edgelist])
if not cb.iterable(width):
lw = (width,)
else:
lw = width
if not cb.is_string_like(edge_color) \
and cb.iterable(edge_color) \
and len(edge_color)==len(edge_pos):
if matplotlib.numerix.alltrue([cb.is_string_like(c)
for c in edge_color]):
# (should check ALL elements)
# list of color letters such as ['k','r','k',...]
edge_colors = tuple([colorConverter.to_rgba(c,alpha)
for c in edge_color])
elif matplotlib.numerix.alltrue([not cb.is_string_like(c)
for c in edge_color]):
# numbers (which are going to be mapped with a colormap)
edge_colors = None
else:
raise ValueError('edge_color must consist of either color names or numbers')
else:
if len(edge_color)==1:
edge_colors = ( colorConverter.to_rgba(edge_color, alpha), )
else:
raise ValueError('edge_color must be a single color or list of exactly m colors where m is the number or edges')
edge_collection = LineCollection(edge_pos,
colors = edge_colors,
linewidths = lw,
antialiaseds = (1,),
linestyle = style,
transOffset = ax.transData,
)
edge_collection.set_alpha(alpha)
# need 0.87.7 or greater for edge colormaps
mpl_version=matplotlib.__version__
if mpl_version.endswith('svn'):
mpl_version=matplotlib.__version__[0:-3]
if mpl_version.endswith('pre'):
mpl_version=matplotlib.__version__[0:-3]
if map(int,mpl_version.split('.'))>=[0,87,7]:
if edge_colors is None:
if edge_cmap is not None: assert(isinstance(edge_cmap, Colormap))
edge_collection.set_array(asarray(edge_color))
edge_collection.set_cmap(edge_cmap)
if edge_vmin is not None or edge_vmax is not None:
edge_collection.set_clim(edge_vmin, edge_vmax)
else:
edge_collection.autoscale()
matplotlib.pylab.sci(edge_collection)
# else:
# sys.stderr.write(\
# """matplotlib version >= 0.87.7 required for colormapped edges.
# (version %s detected)."""%matplotlib.__version__)
# raise UserWarning(\
# """matplotlib version >= 0.87.7 required for colormapped edges.
# (version %s detected)."""%matplotlib.__version__)
arrow_collection=None
if G.directed and arrows:
# a directed graph hack
# draw thick line segments at head end of edge
# waiting for someone else to implement arrows that will work
arrow_colors = ( colorConverter.to_rgba('k', alpha), )
a_pos=[]
p=1.0-0.25 # make head segment 25 percent of edge length
for src,dst in edge_pos:
x1,y1=src
x2,y2=dst
dx=x2-x1 # x offset
dy=y2-y1 # y offset
d=sqrt(float(dx**2+dy**2)) # length of edge
if d==0: # source and target at same position
continue
if dx==0: # vertical edge
xa=x2
ya=dy*p+y1
if dy==0: # horizontal edge
ya=y2
xa=dx*p+x1
else:
theta=arctan2(dy,dx)
xa=p*d*cos(theta)+x1
ya=p*d*sin(theta)+y1
a_pos.append(((xa,ya),(x2,y2)))
arrow_collection = LineCollection(a_pos,
colors = arrow_colors,
linewidths = [4*ww for ww in lw],
antialiaseds = (1,),
transOffset = ax.transData,
)
# update view
minx = amin(ravel(edge_pos[:,:,0]))
maxx = amax(ravel(edge_pos[:,:,0]))
miny = amin(ravel(edge_pos[:,:,1]))
maxy = amax(ravel(edge_pos[:,:,1]))
w = maxx-minx
h = maxy-miny
padx, pady = 0.05*w, 0.05*h
corners = (minx-padx, miny-pady), (maxx+padx, maxy+pady)
ax.update_datalim( corners)
ax.autoscale_view()
edge_collection.set_zorder(1) # edges go behind nodes
ax.add_collection(edge_collection)
if arrow_collection:
arrow_collection.set_zorder(1) # edges go behind nodes
ax.add_collection(arrow_collection)
return edge_collection
