# Source code for cartopy.crs

```# (C) British Crown Copyright 2011 - 2012, Met Office
#
# This file is part of cartopy.
#
# cartopy is free software: you can redistribute it and/or modify it under
# Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# cartopy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with cartopy.  If not, see <http://www.gnu.org/licenses/>.

"""
The crs module defines Coordinate Reference Systems and the transformations
between them.

"""
from abc import ABCMeta, abstractproperty
import math
import warnings

import numpy as np
import shapely.geometry as sgeom
from shapely.geometry.polygon import LinearRing
from shapely.prepared import prep

from cartopy._crs import CRS, Geocentric, Geodetic, Globe, PROJ4_RELEASE
import cartopy.trace

__document_these__ = ['CRS', 'Geocentric', 'Geodetic', 'Globe']

[docs]class RotatedGeodetic(CRS):
"""
Defines a rotated latitude/longitude coordinate system with spherical
topology and geographical distance.

Coordinates are measured in degrees.

"""
def __init__(self, pole_longitude, pole_latitude, globe=None):
"""
Create a RotatedGeodetic CRS.

Args:

* pole_longitude - Pole longitude position, in unrotated degrees.
* pole_latitude - Pole latitude position, in unrotated degrees.

Kwargs:

* globe - An optional :class:`cartopy.crs.Globe`.
Defaults to a "WGS84" datum.

"""
proj4_params = [('proj', 'ob_tran'), ('o_proj', 'latlon'),
('o_lon_p', 0), ('o_lat_p', pole_latitude),
('lon_0', 180 + pole_longitude),
globe = globe or Globe(datum='WGS84')
super(RotatedGeodetic, self).__init__(proj4_params, globe=globe)

[docs]class Projection(CRS):
"""
Defines a projected coordinate system with flat topology and Euclidean
distance.

"""
__metaclass__ = ABCMeta

_method_map = {
'Point': '_project_point',
'LineString': '_project_line_string',
'LinearRing': '_project_linear_ring',
'Polygon': '_project_polygon',
'MultiPoint': '_project_multipoint',
'MultiLineString': '_project_multiline',
'MultiPolygon': '_project_multipolygon',
}

@abstractproperty
def boundary(self):
pass

@abstractproperty
def threshold(self):
pass

@abstractproperty
def x_limits(self):
pass

@abstractproperty
def y_limits(self):
pass

@property
def cw_boundary(self):
try:
boundary = self._cw_boundary
except AttributeError:
boundary = sgeom.LineString(self.boundary)
self._cw_boundary = boundary
return boundary

@property
def ccw_boundary(self):
try:
boundary = self._ccw_boundary
except AttributeError:
boundary = sgeom.LineString(list(self.boundary.coords)[::-1])
self._ccw_boundary = boundary
return boundary

@property
def domain(self):
try:
domain = self._domain
except AttributeError:
domain = self._domain = sgeom.Polygon(self.boundary)
return domain

def _as_mpl_axes(self):
import cartopy.mpl.geoaxes as geoaxes
return geoaxes.GeoAxes, {'map_projection': self}

[docs]    def project_geometry(self, geometry, src_crs=None):
"""
Projects the given geometry into this projection.

:param geometry: The geometry to (re-)project.
:param src_crs: The source CRS, or geodetic CRS if None.
:rtype: Shapely geometry.

If src_crs is None, the source CRS is assumed to be a geodetic
version of the target CRS.

"""
if src_crs is None:
src_crs = self.as_geodetic()
elif not isinstance(src_crs, CRS):
raise TypeError('Source CRS must be an instance of CRS'
' or one of its subclasses, or None.')
geom_type = geometry.geom_type
method_name = self._method_map.get(geom_type)
if not method_name:
raise ValueError('Unsupported geometry '
'type {!r}'.format(geom_type))
return getattr(self, method_name)(geometry, src_crs)

def _project_point(self, point, src_crs):
return sgeom.Point(*self.transform_point(point.x, point.y, src_crs))

def _project_line_string(self, geometry, src_crs):
return cartopy.trace.project_linear(geometry, src_crs, self)

def _project_linear_ring(self, linear_ring, src_crs):
"""
Projects the given LinearRing from the src_crs into this CRS and
returns the resultant LinearRing or MultiLineString.

"""
# 1) Resolve the initial lines into projected segments
# 1abc
# def23ghi
# jkl41
multi_line_string = cartopy.trace.project_linear(linear_ring,
src_crs, self)

# 2) Simplify the segments where appropriate.
if len(multi_line_string) > 1:
# Stitch together segments which are close to continuous.
# This is important when:
# 1) The first source point projects into the map and the
# ring has been cut by the boundary.
# Continuing the example from above this gives:
#   def23ghi
#   jkl41abc
# 2) The cut ends of segments are too close to reliably
# place into an order along the boundary.

# Threshold for whether a point is close enough to be the same
# point as another.
threshold = max(np.abs(self.x_limits + self.y_limits)) * 1e-5

line_strings = list(multi_line_string)
any_modified = False
i = 0
while i < len(line_strings):
modified = False
j = 0
while j < len(line_strings):
if i != j and np.allclose(line_strings[i].coords[0],
line_strings[j].coords[-1],
atol=threshold):
last_coords = list(line_strings[j].coords)
first_coords = list(line_strings[i].coords)[1:]
combo = sgeom.LineString(last_coords + first_coords)
if j < i:
i, j = j, i
del line_strings[j], line_strings[i]
line_strings.append(combo)
modified = True
any_modified = True
break
else:
j += 1
if not modified:
i += 1
if any_modified:
multi_line_string = sgeom.MultiLineString(line_strings)

# 3) Check for a single resulting ring.
if (len(multi_line_string) == 1 and
len(multi_line_string[0].coords) > 3 and
np.allclose(multi_line_string[0].coords[0],
multi_line_string[0].coords[-1])):
result_geometry = LinearRing(multi_line_string[0].coords[:-1])
else:
result_geometry = multi_line_string

return result_geometry

def _project_multipoint(self, geometry, src_crs):
geoms = []
for geom in geometry.geoms:
geoms.append(self._project_point(geom, src_crs))
if geoms:
return sgeom.MultiPoint(geoms)
else:
return sgeom.MultiPoint()

def _project_multiline(self, geometry, src_crs):
geoms = []
for geom in geometry.geoms:
r = self._project_line_string(geom, src_crs)
if r:
geoms.extend(r.geoms)
if geoms:
return sgeom.MultiLineString(geoms)
else:
return []

def _project_multipolygon(self, geometry, src_crs):
geoms = []
for geom in geometry.geoms:
r = self._project_polygon(geom, src_crs)
if r:
geoms.extend(r.geoms)
if geoms:
result = sgeom.MultiPolygon(geoms)
else:
result = sgeom.MultiPolygon()
return result

def _project_polygon(self, polygon, src_crs):
"""
Returns the projected polygon(s) derived from the given polygon.

"""
# Determine orientation of polygon.
# TODO: Consider checking the internal rings have the opposite
# orientation to the external rings?
if src_crs.is_geodetic():
is_ccw = True
else:
is_ccw = polygon.exterior.is_ccw

# Project the polygon exterior/interior rings.
# Each source ring will result in either a ring, or one or more
# lines.
rings = []
multi_lines = []
for src_ring in [polygon.exterior] + list(polygon.interiors):
geometry = self._project_linear_ring(src_ring, src_crs)
if geometry.geom_type == 'LinearRing':
rings.append(geometry)
else:
multi_lines.append(geometry)

# Convert any lines to rings by attaching them to the boundary.
if multi_lines:
rings.extend(self._attach_lines_to_boundary(multi_lines, is_ccw))

# Resolve all the inside vs. outside rings, and convert to the
# final MultiPolygon.
return self._rings_to_multi_polygon(rings, is_ccw)

def _attach_lines_to_boundary(self, multi_line_strings, is_ccw):
"""
Returns a list of LinearRings by attaching the ends of the given lines
to the boundary, paying attention to the traversal directions of the
lines and boundary.

"""
# Accumulate all the boundary and segment end points, along with
# their distance along the boundary.
edge_things = []

# Get the boundary as a LineString of the correct orientation
# so we can compute distances along it.
if is_ccw:
boundary = self.ccw_boundary
else:
boundary = self.cw_boundary

def boundary_distance(xy):
return boundary.project(sgeom.Point(*xy))

# Squash all the LineStrings into a single list.
line_strings = []
for multi_line_string in multi_line_strings:
line_strings.extend(multi_line_string)

# Record the positions of all the segment ends
for i, line_string in enumerate(line_strings):
first_dist = boundary_distance(line_string.coords[0])
thing = _Thing(first_dist, False,
(i, 'first', line_string.coords[0]))
edge_things.append(thing)
last_dist = boundary_distance(line_string.coords[-1])
thing = _Thing(last_dist, False,
(i, 'last', line_string.coords[-1]))
edge_things.append(thing)

# Record the positions of all the boundary vertices
for xy in list(boundary.coords)[:-1]:
point = sgeom.Point(*xy)
dist = boundary.project(point)
thing = _Thing(dist, True, point)
edge_things.append(thing)

# Order everything as if walking around the boundary.
# NB. We make line end-points take precedence over boundary points
# to ensure that end-points are still found and followed when they
# coincide.
edge_things.sort(key=lambda thing: (thing.distance, thing.kind))
debug = 0
if debug:
print
print 'Edge things'
for thing in edge_things:
print '   ', thing

to_do = {i: line_string for i, line_string in enumerate(line_strings)}
done = []
while to_do:
i, line_string = to_do.popitem()
if debug:
import sys
sys.stdout.write('+')
sys.stdout.flush()
print
print 'Processing: %s, %s' % (i, line_string)
filter_fn = lambda t: (t.kind or
t.data[0] != i or
t.data[1] != 'last')
edge_things = filter(filter_fn, edge_things)

while True:
# Find the distance of the last point
d_last = boundary_distance(line_string.coords[-1])
if debug:
print '   d_last:', d_last
next_thing = _find_gt(edge_things, d_last)
if debug:
print '   next_thing:', next_thing
if next_thing.kind:
if debug:
boundary_point = next_thing.data
combined_coords = (list(line_string.coords) +
[(boundary_point.x, boundary_point.y)])
line_string = sgeom.LineString(combined_coords)
# XXX
#edge_things.remove(next_thing)
elif next_thing.data[0] == i:
if debug:
print '   close loop'
done.append(line_string)
break
else:
if debug:
j = next_thing.data[0]
line_to_append = line_strings[j]
# XXX pelson: I think this if statement can be removed
if j in to_do:
del to_do[j]
coords_to_append = list(line_to_append.coords)
if next_thing.data[1] == 'last':
coords_to_append = coords_to_append[::-1]
line_string = sgeom.LineString((list(line_string.coords) +
coords_to_append))

# Catch getting stuck in an infinite loop by checking that
else:
raise RuntimeError('Unidentified problem with '
'geometry, linestring being '

# filter out any non-valid linear rings
done = filter(lambda linear_ring: len(linear_ring.coords) > 2, done)

# XXX Is the last point in each ring actually the same as the first?
linear_rings = [LinearRing(line) for line in done]

if debug:
print '   DONE'

return linear_rings

def _rings_to_multi_polygon(self, rings, is_ccw):
exterior_rings = []
interior_rings = []
for ring in rings:
if ring.is_ccw != is_ccw:
interior_rings.append(ring)
else:
exterior_rings.append(ring)

polygon_bits = []

# Turn all the exterior rings into polygon definitions,
# "slurping up" any interior rings they contain.
for exterior_ring in exterior_rings:
polygon = sgeom.Polygon(exterior_ring)
prep_polygon = prep(polygon)
holes = []
for interior_ring in interior_rings[:]:
if prep_polygon.contains(interior_ring):
holes.append(interior_ring)
interior_rings.remove(interior_ring)
polygon_bits.append((exterior_ring.coords,
[ring.coords for ring in holes]))

# Any left over "interior" rings need "inverting" with respect
# to the boundary.
if interior_rings:
boundary_poly = self.domain
x3, y3, x4, y4 = boundary_poly.bounds
bx = (x4 - x3) * 0.1
by = (y4 - y3) * 0.1
x3 -= bx
y3 -= by
x4 += bx
y4 += by
for ring in interior_rings:
polygon = sgeom.Polygon(ring)
if polygon.is_valid:
x1, y1, x2, y2 = polygon.bounds
bx = (x2 - x1) * 0.1
by = (y2 - y1) * 0.1
x1 -= bx
y1 -= by
x2 += bx
y2 += by
box = sgeom.box(min(x1, x3), min(y1, y3),
max(x2, x4), max(y2, y4))

# Invert the polygon
polygon = box.difference(polygon)

# Intersect the inverted polygon with the boundary
polygon = boundary_poly.intersection(polygon)

if not polygon.is_empty:
polygon_bits.append(polygon)

if polygon_bits:
multi_poly = sgeom.MultiPolygon(polygon_bits)
else:
multi_poly = sgeom.MultiPolygon()
return multi_poly

[docs]    def quick_vertices_transform(self, vertices, src_crs):
"""
Where possible, return a vertices array transformed to this CRS from
the given vertices array of shape ``(n, 2)`` and the source CRS.

.. important::

This method may return None to indicate that the vertices cannot
be transformed quickly, and a more complex geometry transformation
is required (see :meth:`cartopy.crs.Projection.project_geometry`).

"""
return_value = None

if self == src_crs:
x = vertices[:, 0]
y = vertices[:, 1]
x_limits = self.x_limits
y_limits = self.y_limits
if (x.min() >= x_limits[0] and x.max() <= x_limits[1]
and y.min() >= y_limits[0] and y.max() <= y_limits[1]):
return_value = vertices

return return_value

class _RectangularProjection(Projection):
"""
The abstract superclass of projections with a rectangular domain which

"""
def __init__(self, proj4_params, half_width, half_height, globe=None):
self._half_width = half_width
self._half_height = half_height
super(_RectangularProjection, self).__init__(proj4_params, globe=globe)

@property
def boundary(self):
# XXX Should this be a LinearRing?
w, h = self._half_width, self._half_height
return sgeom.LineString([(-w, -h), (-w, h), (w, h), (w, -h), (-w, -h)])

@property
def x_limits(self):
return (-self._half_width, self._half_width)

@property
def y_limits(self):
return (-self._half_height, self._half_height)

class _CylindricalProjection(_RectangularProjection):
"""
The abstract class which denotes cylindrical projections where we
want to allow x values to wrap around.

"""

[docs]class PlateCarree(_CylindricalProjection):
def __init__(self, central_longitude=0.0, globe=None):
proj4_params = [('proj', 'eqc'), ('lon_0', central_longitude)]
if globe is None:
globe = Globe(semimajor_axis=math.degrees(1))
x_max = math.radians(globe.semimajor_axis or 6378137.0) * 180
y_max = math.radians(globe.semimajor_axis or 6378137.0) * 90
# Set the threshold around 0.5 if the x max is 180.
self._threshold = x_max / 360.
super(PlateCarree, self).__init__(proj4_params, x_max, y_max,
globe=globe)

@property
def threshold(self):
return self._threshold

def _bbox_and_offset(self, other_plate_carree):
"""
Returns a pair of (xmin, xmax) pairs and an offset which can be used
for identification of whether data in ``other_plate_carree`` needs
to be transformed to wrap appropriately.

>>> import cartopy.crs as ccrs
>>> src = ccrs.PlateCarree(central_longitude=10)
>>> bboxes, offset = ccrs.PlateCarree()._bbox_and_offset(src)
>>> print bboxes
[[-180.0, -170.0], [-170.0, 180.0]]
>>> print offset
10.0

The returned values are longitudes in ``other_plate_carree``'s
coordinate system.

.. important::

The two CRSs must be identical in every way, other than their
central longitudes. No checking of this is done.

"""
self_lon_0 = self.proj4_params['lon_0']
other_lon_0 = other_plate_carree.proj4_params['lon_0']

lon_0_offset = other_lon_0 - self_lon_0

lon_lower_bound_0 = self.x_limits[0]
lon_lower_bound_1 = (other_plate_carree.x_limits[0] + lon_0_offset)

if lon_lower_bound_1 < self.x_limits[0]:
lon_lower_bound_1 += np.diff(self.x_limits)[0]

lon_lower_bound_0, lon_lower_bound_1 = sorted(
[lon_lower_bound_0, lon_lower_bound_1])

bbox = [[lon_lower_bound_0, lon_lower_bound_1],
[lon_lower_bound_1, lon_lower_bound_0]]

bbox[1][1] += np.diff(self.x_limits)[0]

return bbox, lon_0_offset

def quick_vertices_transform(self, vertices, src_crs):
return_value = super(PlateCarree,
self).quick_vertices_transform(vertices, src_crs)

# Optimise the PlateCarree -> PlateCarree case where no
# wrapping or interpolation needs to take place.
if return_value is None and isinstance(src_crs, PlateCarree):
self_params = self.proj4_params.copy()
src_params = src_crs.proj4_params.copy()
self_params.pop('lon_0'), src_params.pop('lon_0')

xs, ys = vertices[:, 0], vertices[:, 1]

potential = (self_params == src_params and
self.y_limits[0] <= ys.min() and
self.y_limits[1] >= ys.max())

if potential:
mod = np.diff(src_crs.x_limits)[0]
bboxes, proj_offset = self._bbox_and_offset(src_crs)
x_lim = xs.min(), xs.max()
y_lim = ys.min(), ys.max()
for poly in bboxes:
# Arbitrarily choose the number of moduli to look
# above and below the -180->180 range. If data is beyond
# this range, we're not going to transform it quickly.
for i in [-1, 0, 1, 2]:
offset = mod * i - proj_offset
if ((poly[0] + offset) <= x_lim[0]
and (poly[1] + offset) >= x_lim[1]):
return_value = vertices + [[-offset, 0]]
break
if return_value is not None:
break

return return_value

[docs]class TransverseMercator(Projection):
"""
A Transverse Mercator projection.

"""
def __init__(self, central_longitude=0.0, central_latitude=0.0,
false_easting=0.0, false_northing=0.0,
scale_factor=1.0, globe=None):
"""
Kwargs:

* central_longitude - The true longitude of the central meridian in
degrees. Defaults to 0.
* central_latitude - The true latitude of the planar origin in
degrees. Defaults to 0.
* false_easting - X offset from the planar origin in metres.
Defaults to 0.
* false_northing - Y offset from the planar origin in metres.
Defaults to 0.
* scale_factor - Scale factor at the central meridian. Defaults
to 1.
* globe - An instance of :class:`cartopy.crs.Globe`. If omitted, a
default globe is created.

"""
proj4_params = [('proj', 'tmerc'), ('lon_0', central_longitude),
('lat_0', central_latitude), ('k', scale_factor),
('x_0', false_easting), ('y_0', false_northing),
('units', 'm')]
super(TransverseMercator, self).__init__(proj4_params, globe=globe)

@property
def threshold(self):
return 1e4

@property
def boundary(self):
x0, x1 = self.x_limits
y0, y1 = self.y_limits
return sgeom.LineString([(x0, y0), (x0, y1),
(x1, y1), (x1, y0),
(x0, y0)])

@property
def x_limits(self):
return (-2e7, 2e7)

@property
def y_limits(self):
return (-1e7, 1e7)

[docs]class OSGB(TransverseMercator):
def __init__(self):
super(OSGB, self).__init__(central_longitude=-2, central_latitude=49,
scale_factor=0.9996012717,
false_easting=400000,
false_northing=-100000,
globe=Globe(datum='OSGB36', ellipse='airy'))

@property
def boundary(self):
w = self.x_limits[1] - self.x_limits[0]
h = self.y_limits[1] - self.y_limits[0]
return sgeom.LineString([(0, 0), (0, h), (w, h), (w, 0), (0, 0)])

@property
def x_limits(self):
return (0, 7e5)

@property
def y_limits(self):
return (0, 13e5)

[docs]class OSNI(TransverseMercator):
def __init__(self):
globe = Globe(semimajor_axis=6377340.189,
semiminor_axis=6356034.447938534)
super(OSNI, self).__init__(central_longitude=-8,
central_latitude=53.5,
scale_factor=1.000035,
false_easting=200000,
false_northing=250000,
globe=globe)

@property
def boundary(self):
w = self.x_limits[1] - self.x_limits[0]
h = self.y_limits[1] - self.y_limits[0]
return sgeom.LineString([(0, 0), (0, h), (w, h), (w, 0), (0, 0)])

@property
def x_limits(self):
return (18814.9667, 386062.3293)

@property
def y_limits(self):
return (11764.8481, 464720.9559)

[docs]class EuroPP(Projection):
"""
UTM Zone 32 projection for EuroPP domain.

Ellipsoid is International 1924, Datum is ED50.

"""
def __init__(self):
proj4_params = [('proj', 'tmerc'),
('lat_0', 50), ('lon_0', 9),
('k', 0.9996),
('x_0', 1750000), ('y_0', 1500000),
('zone', 32),
('units', 'm')]
globe = Globe(ellipse='intl', towgs84='-87,-98,-121')
super(EuroPP, self).__init__(proj4_params, globe=globe)

@property
def boundary(self):
w, h = 3.19e6, 3.8e6
return sgeom.LineString([(0, 0), (0, h), (w, h),
(w, 0), (0, 0)])

@property
def x_limits(self):
return (0, 3.19e6)

@property
def y_limits(self):
return (0, 3.8e6)

@property
def threshold(self):
return 1e4

[docs]class Mercator(Projection):
"""
A Mercator projection.

"""

def __init__(self, central_longitude=0.0,
min_latitude=-80.0, max_latitude=84.0,
globe=None):
"""
Kwargs:

* central_longitude - the central longitude. Defaults to 0.
* min_latitude - the maximum southerly extent of the projection.
Defaults to -80 degrees.
* max_latitude - the maximum northerly extent of the projection.
Defaults to 84 degrees.
* globe - A :class:`cartopy.crs.Globe`.
If omitted, a default globe is created.

"""
proj4_params = [('proj', 'merc'),
('lon_0', central_longitude),
('k', 1),
('units', 'm')]
super(Mercator, self).__init__(proj4_params, globe=globe)

# Calculate limits.
limits = self.transform_points(Geodetic(),
np.array([-180., 180.]),
np.array([min_latitude, max_latitude]))
self._xlimits = tuple(limits[..., 0])
self._ylimits = tuple(limits[..., 1])
self._threshold = np.diff(self.x_limits)[0] / 720

def __eq__(self, other):
res = super(Mercator, self).__eq__(other)
if hasattr(other, "_ylimits") and hasattr(other, "_xlimits"):
res = res and self._ylimits == other._ylimits and \
self._xlimits == other._xlimits
return res

def __ne__(self, other):
return not self == other

def __hash__(self):
return hash((self.proj4_init, self._xlimits, self._ylimits))

@property
def threshold(self):
return self._threshold

@property
def boundary(self):
x0, x1 = self.x_limits
y0, y1 = self.y_limits
return sgeom.LineString([(x0, y0), (x0, y1),
(x1, y1), (x1, y0),
(x0, y0)])

@property
def x_limits(self):
return self._xlimits

@property
def y_limits(self):
return self._ylimits

[docs]class LambertCylindrical(_RectangularProjection):
def __init__(self, central_longitude=0.0):
proj4_params = [('proj', 'cea'), ('lon_0', central_longitude)]
globe = Globe(semimajor_axis=math.degrees(1))
super(LambertCylindrical, self).__init__(proj4_params, 180,
math.degrees(1), globe=globe)

@property
def threshold(self):
return 0.5

[docs]class LambertConformal(Projection):
"""
A Lambert Conformal conic projection.

"""

def __init__(self, central_longitude=-96.0, central_latitude=39.0,
false_easting=0.0, false_northing=0.0,
secant_latitudes=(33, 45), globe=None, cutoff=-30):
"""
Kwargs:

* central_longitude - The central longitude. Defaults to 0.
* central_latitude - The central latitude. Defaults to 0.
* false_easting - X offset from planar origin in metres.
Defaults to 0.
* false_northing - Y offset from planar origin in metres.
Defaults to 0.
* secant_latitudes - The two latitudes of secant intersection.
Defaults to (33, 45).
* globe - A :class:`cartopy.crs.Globe`.
If omitted, a default globe is created.
* cutoff - Latitude of map cutoff.
The map extends to infinity opposite the central pole
so we must cut off the map drawing before then.
A value of 0 will draw half the globe. Defaults to -30.

"""
proj4_params = [('proj', 'lcc'),
('lon_0', central_longitude),
('lat_0', central_latitude),
('x_0', false_easting),
('y_0', false_northing)]
if secant_latitudes is not None:
proj4_params.append(('lat_1', secant_latitudes[0]))
proj4_params.append(('lat_2', secant_latitudes[1]))
super(LambertConformal, self).__init__(proj4_params, globe=globe)

# are we north or south polar?
if abs(secant_latitudes[0]) > abs(secant_latitudes[1]):
poliest_sec = secant_latitudes[0]
else:
poliest_sec = secant_latitudes[1]
plat = 90 if poliest_sec > 0 else -90

# bounds
self.cutoff = cutoff
n = 91
lons = [0]
lats = [plat]
lons.extend(np.linspace(central_longitude - 180 + 0.001,
central_longitude + 180 - 0.001, n))
lats.extend(np.array([cutoff] * n))
lons.append(0)
lats.append(plat)

points = self.transform_points(PlateCarree(),
np.array(lons), np.array(lats))

self._boundary = sgeom.LineString(points)
bounds = self._boundary.bounds
self._x_limits = bounds[0], bounds[2]
self._y_limits = bounds[1], bounds[3]

def __eq__(self, other):
res = super(LambertConformal, self).__eq__(other)
if hasattr(other, "cutoff"):
res = res and self.cutoff == other.cutoff
return res

def __ne__(self, other):
return not self == other

def __hash__(self):
return hash((self.proj4_init, self.cutoff))

@property
def boundary(self):
return self._boundary

@property
def threshold(self):
return 1e5

@property
def x_limits(self):
return self._x_limits

@property
def y_limits(self):
return self._y_limits

[docs]class Miller(_RectangularProjection):
def __init__(self, central_longitude=0.0):
proj4_params = [('proj', 'mill'), ('lon_0', central_longitude)]
globe = Globe(semimajor_axis=math.degrees(1))
# XXX How can we derive the vertical limit of 131.98?
super(Miller, self).__init__(proj4_params, 180, 131.98, globe=globe)

@property
def threshold(self):
return 0.5

[docs]class RotatedPole(_CylindricalProjection):
def __init__(self, pole_longitude=0.0, pole_latitude=90.0, globe=None):
proj4_params = [('proj', 'ob_tran'), ('o_proj', 'latlon'),
('o_lon_p', 0), ('o_lat_p', pole_latitude),
('lon_0', 180 + pole_longitude),
super(RotatedPole, self).__init__(proj4_params, 180, 90, globe=globe)

@property
def threshold(self):
return 0.5

[docs]class Gnomonic(Projection):
def __init__(self, central_latitude=0.0, globe=None):
proj4_params = [('proj', 'gnom'), ('lat_0', central_latitude)]
super(Gnomonic, self).__init__(proj4_params, globe=globe)
self._max = 5e7

@property
def boundary(self):
return sgeom.Point(0, 0).buffer(self._max).exterior

@property
def threshold(self):
return 1e5

@property
def x_limits(self):
return (-self._max, self._max)

@property
def y_limits(self):
return (-self._max, self._max)

[docs]class Stereographic(Projection):
def __init__(self, central_latitude=0.0, central_longitude=0.0,
false_easting=0.0, false_northing=0.0,
true_scale_latitude=None, globe=None):
proj4_params = [('proj', 'stere'), ('lat_0', central_latitude),
('lon_0', central_longitude),
('x_0', false_easting), ('y_0', false_northing)]
if true_scale_latitude:
proj4_params.append(('lat_ts', true_scale_latitude))
super(Stereographic, self).__init__(proj4_params, globe=globe)

# TODO: Factor this out, particularly if there are other places using
# it (currently: Stereographic & Geostationary). (#340)
def ellipse(semimajor=2, semiminor=1, easting=0, northing=0, n=200):
t = np.linspace(0, 2 * np.pi, n)
coords = np.vstack([semimajor * np.cos(t), semiminor * np.sin(t)])
coords += ([easting], [northing])
return coords

# TODO: Let the globe return the semimajor axis always.
a = np.float(self.globe.semimajor_axis or 6378137.0)
b = np.float(self.globe.semiminor_axis or 6356752.3142)

# Note: The magic number has been picked to maintain consistent
# behaviour with a wgs84 globe. There is no guarantee that the scaling
# should even be linear.
x_axis_offset = 5e7 / 6378137.
y_axis_offset = 5e7 / 6356752.3142
self._x_limits = (-a * x_axis_offset + false_easting,
a * x_axis_offset + false_easting)
self._y_limits = (-b * y_axis_offset + false_northing,
b * y_axis_offset + false_northing)
if self._x_limits[1] == self._y_limits[1]:
point = sgeom.Point(false_easting, false_northing)
self._boundary = point.buffer(self._x_limits[1]).exterior
else:
coords = ellipse(self._x_limits[1], self._y_limits[1],
false_easting, false_northing, 90)
coords = tuple(tuple(pair) for pair in coords.T)
self._boundary = sgeom.polygon.LinearRing(coords)
self._threshold = np.diff(self._x_limits)[0] * 1e-3

@property
def boundary(self):
return self._boundary

@property
def threshold(self):
return self._threshold

@property
def x_limits(self):
return self._x_limits

@property
def y_limits(self):
return self._y_limits

[docs]class NorthPolarStereo(Stereographic):
def __init__(self, central_longitude=0.0, globe=None):
super(NorthPolarStereo, self).__init__(
central_latitude=90,
central_longitude=central_longitude, globe=globe)

[docs]class SouthPolarStereo(Stereographic):
def __init__(self, central_longitude=0.0, globe=None):
super(SouthPolarStereo, self).__init__(
central_latitude=-90,
central_longitude=central_longitude, globe=globe)

[docs]class Orthographic(Projection):
def __init__(self, central_longitude=0.0, central_latitude=0.0,
globe=None):
proj4_params = [('proj', 'ortho'), ('lon_0', central_longitude),
('lat_0', central_latitude)]
super(Orthographic, self).__init__(proj4_params, globe=globe)
self._max = 6.4e6

@property
def boundary(self):
return sgeom.Point(0, 0).buffer(self._max).exterior

@property
def threshold(self):
return 1e5

@property
def x_limits(self):
return (-self._max, self._max)

@property
def y_limits(self):
return (-self._max, self._max)

class _WarpedRectangularProjection(Projection):
def __init__(self, proj4_params, central_longitude, globe=None):
super(_WarpedRectangularProjection, self).__init__(proj4_params,
globe=globe)

# Obtain boundary points
points = []
n = 91
geodetic_crs = self.as_geodetic()
for lat in np.linspace(-90, 90, n):
points.append(
self.transform_point(180 + central_longitude,
lat, geodetic_crs)
)
for lat in np.linspace(90, -90, n):
points.append(
self.transform_point(-180 + central_longitude,
lat, geodetic_crs)
)
points.append(
self.transform_point(180 + central_longitude, -90, geodetic_crs))

self._boundary = sgeom.LineString(points[::-1])

x = [p[0] for p in points]
y = [p[1] for p in points]
self._x_limits = min(x), max(x)
self._y_limits = min(y), max(y)

@property
def boundary(self):
return self._boundary

@property
def x_limits(self):
return self._x_limits

@property
def y_limits(self):
return self._y_limits

[docs]class Mollweide(_WarpedRectangularProjection):
def __init__(self, central_longitude=0, globe=None):
proj4_params = [('proj', 'moll'), ('lon_0', central_longitude)]
super(Mollweide, self).__init__(proj4_params, central_longitude,
globe=globe)

@property
def threshold(self):
return 1e5

[docs]class Robinson(_WarpedRectangularProjection):
def __init__(self, central_longitude=0, globe=None):
# Warn when using Robinson with proj4 4.8 due to discontinuity at
# 40 deg N introduced by incomplete fix to issue #113 (see
# https://trac.osgeo.org/proj/ticket/113).
import re
match = re.search(r"\d\.\d", PROJ4_RELEASE)
if match is not None:
proj4_version = float(match.group())
if 4.8 <= proj4_version < 4.9:
warnings.warn('The Robinson projection in the v4.8.x series '
'of Proj.4 contains a discontinuity at '
'40 deg latitude. Use this projection with '
'caution.')
else:
warnings.warn('Cannot determine Proj.4 version. The Robinson '
'projection may be unreliable and should be used '
'with caution.')

proj4_params = [('proj', 'robin'), ('lon_0', central_longitude)]
super(Robinson, self).__init__(proj4_params, central_longitude,
globe=globe)

@property
def threshold(self):
return 1e4

def transform_point(self, x, y, src_crs):
"""
Capture and handle any input NaNs, else invoke parent function,
:meth:`_WarpedRectangularProjection.transform_point`.

Needed because input NaNs can trigger a fatal error in the underlying
implementation of the Robinson projection.

.. note::

Although the original can in fact translate (nan, lat) into
(nan, y-value), this patched version doesn't support that.

"""
if np.isnan(x) or np.isnan(y):
result = (np.nan, np.nan)
else:
result = super(Robinson, self).transform_point(x, y, src_crs)
return result

def transform_points(self, src_crs, x, y, z=None):
"""
Capture and handle NaNs in input points -- else as parent function,
:meth:`_WarpedRectangularProjection.transform_points`.

Needed because input NaNs can trigger a fatal error in the underlying
implementation of the Robinson projection.

.. note::

Although the original can in fact translate (nan, lat) into
(nan, y-value), this patched version doesn't support that.
Instead, we invalidate any of the points that contain a NaN.

"""
input_point_nans = np.isnan(x) | np.isnan(y)
if z is not None:
input_point_nans |= np.isnan(z)
handle_nans = np.any(input_point_nans)
if handle_nans:
# Remove NaN points from input data to avoid the error.
x[input_point_nans] = 0.0
y[input_point_nans] = 0.0
if z is not None:
z[input_point_nans] = 0.0
result = super(Robinson, self).transform_points(src_crs, x, y, z)
if handle_nans:
# Result always has shape (N, 3).
# Blank out each (whole) point where we had a NaN in the input.
result[input_point_nans] = np.nan
return result

[docs]class InterruptedGoodeHomolosine(Projection):
def __init__(self, central_longitude=0, globe=None):
proj4_params = [('proj', 'igh'), ('lon_0', central_longitude)]
super(InterruptedGoodeHomolosine, self).__init__(proj4_params,
globe=globe)

# Obtain boundary points
points = []
n = 31
geodetic_crs = self.as_geodetic()

# Right boundary
for lat in np.linspace(-90, 90, n):
points.append(self.transform_point(180 + central_longitude,
lat, geodetic_crs))

# Top boundary
interrupted_lons = (-40.0,)
delta = 0.001
for lon in interrupted_lons:
for lat in np.linspace(90, 0, n):
points.append(self.transform_point(lon + delta +
central_longitude,
lat, geodetic_crs))
for lat in np.linspace(0, 90, n):
points.append(self.transform_point(lon - delta +
central_longitude,
lat, geodetic_crs))

# Left boundary
for lat in np.linspace(90, -90, n):
points.append(self.transform_point(-180 + central_longitude,
lat, geodetic_crs))

# Bottom boundary
interrupted_lons = (-100.0, -20.0, 80.0)
delta = 0.001
for lon in interrupted_lons:
for lat in np.linspace(-90, 0, n):
points.append(self.transform_point(lon - delta +
central_longitude,
lat, geodetic_crs))
for lat in np.linspace(0, -90, n):
points.append(self.transform_point(lon + delta +
central_longitude,
lat, geodetic_crs))

# Close loop
points.append(self.transform_point(180 + central_longitude, -90,
geodetic_crs))

self._boundary = sgeom.LineString(points[::-1])

x = [p[0] for p in points]
y = [p[1] for p in points]
self._x_limits = min(x), max(x)
self._y_limits = min(y), max(y)

@property
def boundary(self):
return self._boundary

@property
def threshold(self):
return 2e4

@property
def x_limits(self):
return self._x_limits

@property
def y_limits(self):
return self._y_limits

[docs]class Geostationary(Projection):
def __init__(self, central_longitude=0.0, satellite_height=35785831,
false_easting=0, false_northing=0, globe=None):
proj4_params = [('proj', 'geos'), ('lon_0', central_longitude),
('lat_0', 0), ('h', satellite_height),
('x_0', false_easting), ('y_0', false_northing),
('units', 'm')]
super(Geostationary, self).__init__(proj4_params, globe=globe)

# TODO: Factor this out, particularly if there are other places using
# it (currently: Stereographic & Geostationary). (#340)
def ellipse(semimajor=2, semiminor=1, easting=0, northing=0, n=200):
t = np.linspace(0, 2 * np.pi, n)
coords = np.vstack([semimajor * np.cos(t), semiminor * np.sin(t)])
coords += ([easting], [northing])
return coords

# TODO: Let the globe return the semimajor axis always.
a = np.float(self.globe.semimajor_axis or 6378137.0)
b = np.float(self.globe.semiminor_axis or 6378137.0)
h = np.float(satellite_height)
max_x = h * math.atan(a / (a + h))
max_y = h * math.atan(b / (b + h))

coords = ellipse(max_x, max_y,
false_easting, false_northing, 60)
coords = tuple(tuple(pair) for pair in coords.T)
self._boundary = sgeom.polygon.LinearRing(coords)
self._xlim = self._boundary.bounds[::2]
self._ylim = self._boundary.bounds[1::2]
self._threshold = np.diff(self._xlim)[0] * 0.02

@property
def boundary(self):
return self._boundary

@property
def threshold(self):
return self._threshold

@property
def x_limits(self):
return self._xlim

@property
def y_limits(self):
return self._ylim

class _Thing(object):
def __init__(self, distance, kind, data):
self.distance = distance
self.kind = kind
self.data = data

def __repr__(self):
return '_Thing(%r, %r, %s)' % (self.distance, self.kind, self.data)

def _find_gt(a, x):
for v in a:
# TODO: Fix the problem of co-incident boundary & line points
#if v.distance >= x:
if v.distance > x:
return v
return a[0]
```