allskymap.py

from __future__ import (absolute_import, division, print_function)

from __future__ importunicode_literals
"""
AllSkyMap is a subclass of Basemap, specialized for handling common plotting
tasks for celestial data.

It is essentially equivalent to using Basemap with full-sphere projections
(e.g., 'hammer' or 'moll') and the `celestial` keyword set to `True`, but
it adds a few new methods:

* label_meridians for, well, labeling meridians with their longitude values;

* geodesic, a replacement for Basemap.drawgreatcircle, that can correctly
 handle geodesics that cross the limb of the map, and providing the user
 easy control over clipping (which affects thick lines at or near the limb);

* tissot, which overrides Basemap.tissot, correctly handling geodesics that
 cross the limb of the map.

Created Jan 2011 by Tom Loredo, based on Jeff Whitaker's code in Basemap's
__init__.py module.
"""

fromnumpyimport*
importmatplotlib.pyplotaspl
frommatplotlib.pyplotimport*
frommpl_toolkits.basemapimportBasemap
importpyproj
frompyprojimportGeod

__all__= ['AllSkyMap']

defangle_symbol(angle, round_to=1.0):
"""
 Return a string representing an angle, rounded and with a degree symbol.

 This is adapted from code in mpl's projections.geo module.
 """
value=np.round(angle/round_to) *round_to
ifpl.rcParams['text.usetex'] andnotpl.rcParams['text.latex.unicode']:
returnr'$%0.0f^\circ$'%value
else:
return'%0.0f\N{DEGREE SIGN}'%value


classAllSkyMap(Basemap):
"""
 AllSkyMap is a subclass of Basemap, specialized for handling common plotting
 tasks for celestial data.

 It is essentially equivalent to using Basemap with full-sphere projections
 (e.g., 'hammer' or 'moll') and the `celestial` keyword set to `True`, but
 it adds a few new methods:

 * label_meridians for, well, labeling meridians with their longitude values;

 * geodesic, a replacement for Basemap.drawgreatcircle, that can correctly
 handle geodesics that cross the limb of the map, and providing the user
 easy control over clipping (which affects thick lines at or near the
 limb);

 * tissot, which overrides Basemap.tissot, correctly handling geodesics that
 cross the limb of the map.
 """

# Longitudes corresponding to east and west edges, reflecting the
# convention that 180 deg is the eastern edge, according to basemap's 
# underlying projections:
east_lon=180.
west_lon=180.+1.e-10

def__init__(self, 
projection='hammer',
lat_0=0., lon_0=0.,
suppress_ticks=True,
boundinglat=None,
fix_aspect=True,
anchor=str('C'),
ax=None):

ifprojection!='hammer'andprojection!='moll':
raiseValueError('Only hammer and moll projections supported!')

# Use Basemap's init, enforcing the values of many parameters that
# aren't used or whose Basemap defaults would not be altered for all-sky
# celestial maps.
Basemap.__init__(self, llcrnrlon=None, llcrnrlat=None,
urcrnrlon=None, urcrnrlat=None,
llcrnrx=None, llcrnry=None,
urcrnrx=None, urcrnry=None,
width=None, height=None,
projection=projection, resolution=None,
area_thresh=None, rsphere=1.,
lat_ts=None,
lat_1=None, lat_2=None,
lat_0=lat_0, lon_0=lon_0,
suppress_ticks=suppress_ticks,
satellite_height=1.,
boundinglat=None,
fix_aspect=True,
anchor=anchor,
celestial=True,
ax=ax)

# Keep a local ref to lon_0 for hemisphere checking.
self._lon_0=self.projparams['lon_0']
self._limb=None

defdrawmapboundary(self,color='k',linewidth=1.0,fill_color=None,\
zorder=None,ax=None):
"""
 draw boundary around map projection region, optionally
 filling interior of region.

 .. tabularcolumns:: |l|L|

 ============== ====================================================
 Keyword Description
 ============== ====================================================
 linewidth line width for boundary (default 1.)
 color color of boundary line (default black)
 fill_color fill the map region background with this
 color (default is no fill or fill with axis
 background color).
 zorder sets the zorder for filling map background
 (default 0).
 ax axes instance to use
 (default None, use default axes instance).
 ============== ====================================================

 returns matplotlib.collections.PatchCollection representing map boundary.
 """
# Just call the base class version, but keep a copy of the limb
# polygon for clipping.
self._limb=Basemap.drawmapboundary(self, color=color,
linewidth=linewidth, fill_color=fill_color, zorder=zorder, ax=ax)
returnself._limb

deflabel_meridians(self, lons, fontsize=10, valign='bottom', vnudge=0,
halign='center', hnudge=0):
"""
 Label meridians with their longitude values in degrees.

 This labels meridians with negative longitude l with the value 360-l;
 for maps in celestial orientation, this means meridians to the right
 of the central meridian are labeled from 360 to 180 (left to right).

 `vnudge` and `hnudge` specify amounts in degress to nudge the labels
 from their default placements, vertically and horizontally. This
 values obey the map orientation, so to nudge to the right, use a
 negative `hnudge` value.
 """
# Run through (lon, lat) pairs, with lat=0 in each pair.
lats=len(lons)*[0.]
forlon,latinzip(lons, lats):
x, y=self(lon+hnudge, lat+vnudge)
iflon<0:
lon_lbl=360+lon
else:
lon_lbl=lon
pl.text(x, y, angle_symbol(lon_lbl), fontsize=fontsize,
verticalalignment=valign,
horizontalalignment=halign)

defeast_hem(self, lon):
"""
 Return True if lon is in the eastern hemisphere of the map wrt lon_0.
 """
if (lon-self._lon_0) %360.<=self.east_lon:
returnTrue
else:
returnFalse

defgeodesic(self, lon1, lat1, lon2, lat2, del_s=.01, clip=True, **kwargs):
"""
 Plot a geodesic curve from (lon1, lat1) to (lon2, lat2), with
 points separated by arc length del_s. Return a list of Line2D
 instances for the curves comprising the geodesic. If the geodesic does
 not cross the map limb, there will be only a single curve; if it
 crosses the limb, there will be two curves.
 """

# TODO: Perhaps return a single Line2D instance when there is only a
# single segment, and a list of segments only when there are two segs?

# TODO: Check the units of del_s.

# This is based on Basemap.drawgreatcircle (which draws an *arc* of a
# great circle), but addresses a limitation of that method, supporting
# geodesics that cross the map boundary by breaking them into two
# segments, one in the eastern hemisphere and the other in the western.
gc=pyproj.Geod(a=self.rmajor,b=self.rminor)
az12,az21,dist=gc.inv(lon1,lat1,lon2,lat2)
npoints=int((dist+0.5**del_s)/del_s)
# Calculate lon & lat for points on the arc.
lonlats=gc.npts(lon1,lat1,lon2,lat2,npoints)
lons= [lon1]; lats= [lat1]
forlon, latinlonlats:
lons.append(lon)
lats.append(lat)
lons.append(lon2); lats.append(lat2)
# Break the arc into segments as needed, when there is a longitudinal
# hemisphere crossing.
segs= []
seg_lons, seg_lats= [lon1], [lat1]
cur_hem=self.east_hem(lon1)
forlon, latinzip(lons[1:], lats[1:]):
ifself.east_hem(lon) ==cur_hem:
seg_lons.append(lon)
seg_lats.append(lat)
else:
# We should interpolate a new pt at the boundary, but in
# the mean time just rely on the step size being small.
segs.append( (seg_lons, seg_lats) )
seg_lons, seg_lats= [lon], [lat]
cur_hem=notcur_hem
segs.append( (seg_lons, seg_lats) )
# Plot each segment; return a list of the mpl lines.
lines= []
forlons, latsinsegs:
x, y=self(lons, lats)
ifclipandself._limb:
line=plot(x, y, clip_path=self._limb, **kwargs)[0]
else:
line=plot(x, y, **kwargs)[0]
lines.append(line)
# If there are multiple segments and no color args, reconcile the
# colors, which mpl will have autoset to different values.
# *** Does this screw up mpl's color set sequence for later lines?
if'c'notinkwargsor'color'inkwargs:
iflen(lines) >1:
c1=lines[0].get_color()
forlineinlines[1:]:
line.set_color(c1)
returnlines

deftissot(self,lon_0,lat_0,radius_deg,npts,ax=None,**kwargs):
"""
 Draw a polygon centered at ``lon_0,lat_0``. The polygon
 approximates a circle on the surface of the earth with radius
 ``radius_deg`` degrees latitude along longitude ``lon_0``,
 made up of ``npts`` vertices.

 The polygon represents a Tissot's indicatrix
 (http://en.wikipedia.org/wiki/Tissot's_Indicatrix),
 which when drawn on a map shows the distortion inherent in the map
 projection. Tissots can be used to display azimuthally symmetric
 directional uncertainties ("error circles").

 Extra keyword ``ax`` can be used to override the default axis instance.

 Other \**kwargs passed on to matplotlib.patches.Polygon.

 returns a list of matplotlib.patches.Polygon objects, with two polygons
 when the tissot crosses the limb, and just one polygon otherwise.
 """

# TODO: Just return the polygon (not a list) when there is only one
# polygon? Or stick with the list for consistency?

# This is based on Basemap.tissot, but addresses a limitation of that
# method by handling tissots that cross the limb of the map by finding
# separate polygons in the eastern and western hemispheres comprising
# the tissot.
ax=kwargs.pop('ax', None) orself._check_ax()
g=pyproj.Geod(a=self.rmajor,b=self.rminor)
az12,az21,dist=g.inv(lon_0,lat_0,lon_0,lat_0+radius_deg)
start_hem=self.east_hem(lon_0)
segs1= [self(lon_0,lat_0+radius_deg)]
over, segs2= [], []
delaz=360./npts
az=az12
last_lon=lon_0
# Note adjacent and opposite edge longitudes, in case the tissot
# runs over the edge.
ifstart_hem: # eastern case
adj_lon=self.east_lon
opp_lon=self.west_lon
else:
adj_lon=self.west_lon
opp_lon=self.east_lon
forninrange(npts):
az=az+delaz
# skip segments along equator (Geod can't handle equatorial arcs)
ifnp.allclose(0.,lat_0) and (np.allclose(90.,az) ornp.allclose(270.,az)):
continue
else:
lon, lat, az21=g.fwd(lon_0, lat_0, az, dist)
# If in the starting hemisphere, add to 1st polygon seg list.
ifself.east_hem(lon) ==start_hem:
x, y=self(lon, lat)
# Add segment if it is in the map projection region.
ifx<1.e20andy<1.e20:
segs1.append( (x, y) )
last_lon=lon
# Otherwise, we cross hemispheres.
else:
# Trace the edge of each hemisphere.
x, y=self(adj_lon, lat)
ifx<1.e20andy<1.e20:
segs1.append( (x, y) )
# We presume if adj projection is okay, opposite is.
segs2.append( self(opp_lon, lat) )
# Also store the overlap in the opposite hemisphere.
x, y=self(lon, lat)
ifx<1.e20andy<1.e20:
over.append( (x, y) )
last_lon=lon
poly1=Polygon(segs1, **kwargs)
ax.add_patch(poly1)
ifsegs2:
over.reverse()
segs2.extend(over)
poly2=Polygon(segs2, **kwargs)
ax.add_patch(poly2)
return [poly1, poly2]
else:
return [poly1]


if__name__=='__main__':

# Note that Hammer & Mollweide projections enforce a 2:1 aspect ratio.
# Use figure size good for a 2:1 plot.
fig=figure(figsize=(12,6))

# Set up the projection and draw a grid.
map=AllSkyMap(projection='hammer')
# Save the bounding limb to use as a clip path later.
limb=map.drawmapboundary(fill_color='white')
map.drawparallels(np.arange(-75,76,15), linewidth=0.5, dashes=[1,2],
labels=[1,0,0,0], fontsize=9)
map.drawmeridians(np.arange(-150,151,30), linewidth=0.5, dashes=[1,2])

# Label a subset of meridians.
lons=np.arange(-150,151,30)
map.label_meridians(lons, fontsize=9, vnudge=1,
halign='left', hnudge=-1) # hnudge<0 shifts to right

# x, y limits are [0, 4*rt2], [0, 2*rt2].
rt2=sqrt(2)

# Draw a slanted green line crossing the map limb.
line=plot([rt2,0], [rt2,2*rt2], 'g-')

# Draw a slanted magenta line crossing the map limb but clipped.
line=plot([rt2+.1,0+.1], [rt2,2*rt2], 'm-', clip_path=limb)

# Draw some geodesics.
# First a transparent thick blue geodesic crossing the limb but not clipped,
# overlayed by a thinner red geodesic that is clipped (by default), to
# illustrate the effect of clipping.
lines=map.geodesic(120, 30, 240, 60, clip=False, c='b', lw=7, alpha=.5)
lines=map.geodesic(240, 60, 120, 30, c='r', lw=3, alpha=.5)

# Next two large limb-crossing geodesics with the same path, but rendered
# in opposite directions, one transparent blue, the other transparent
# yellow. They should be right on top of each other, giving a greenish
# brown hue.
lines=map.geodesic(240, -60, 120, 30, c='b', lw=2, alpha=.5)
lines=map.geodesic(120, 30, 240, -60, c='y', lw=2, alpha=.5)

# What happens if a geodesic is given coordinates spanning more than
# a single rotation? Not sure what to expect, but it shoots off the
# map (clipped here). Perhaps we should ensure lons are in [0, 360].
#lines = map.geodesic(120, 20, 240+360, 50, del_s=.2, c='g')

# Two tissots fully within the limb.
poly=map.tissot(60, -15, 10, 100)
poly=map.tissot(280, 60, 10, 100)
#poly = map.tissot(90, -85, 10, 100)

# Limb-spanning tissots in each quadrant.
# lower left:
poly=map.tissot(170, -60, 15, 100)
# upper left:
poly=map.tissot(175, 70, 15, 100)
# upper right (note negative longitude):
poly=map.tissot(-175, 30, 15, 100, color='r', alpha=.6)
# lower right:
poly=map.tissot(185, -40, 10, 100)

# Plot the tissot centers as "+" symbols. Note the top left symbol
# would cross the limb without the clip_path argument; this might be
# desired to enhance visibility.
lons= [170, 175, -175, 185]
lats= [-60, 70, 30, -40]
x, y=map(lons, lats)
map.scatter(x, y, s=40, marker='+', linewidths=1, edgecolors='g',
facecolors='none', clip_path=limb, zorder=10) # hi zorder -> top

title('AllSkyMap demo: Clipped lines, markers, geodesics, tissots')
show()