# Copyright Crown and Cartopy Contributors # # This file is part of Cartopy and is released under the BSD 3-clause license. # See LICENSE in the root of the repository for full licensing details. """ The crs module defines Coordinate Reference Systems and the transformations between them. """ from abc import ABCMeta from collections import OrderedDict from functools import lru_cache import io import json import math import warnings import numpy as np import pyproj from pyproj import Transformer from pyproj.exceptions import ProjError import shapely import shapely.geometry as sgeom from shapely.prepared import prep import cartopy.trace try: # https://github.com/pyproj4/pyproj/pull/912 from pyproj.crs import CustomConstructorCRS as _CRS except ImportError: from pyproj import CRS as _CRS __document_these__ = ['CRS', 'Geocentric', 'Geodetic', 'Globe'] WGS84_SEMIMAJOR_AXIS = 6378137.0 WGS84_SEMIMINOR_AXIS = 6356752.3142 # Cache the transformer creation method @lru_cache def _get_transformer_from_crs(src_crs, tgt_crs): return Transformer.from_crs(src_crs, tgt_crs, always_xy=True) def _safe_pj_transform(src_crs, tgt_crs, x, y, z=None, trap=True): transformer = _get_transformer_from_crs(src_crs, tgt_crs) # if a projection is essentially 2d there # should be no harm in setting its z to 0 if z is None: z = np.zeros_like(x) with warnings.catch_warnings(): # pyproj implicitly converts size-1 arrays to scalars, which is # deprecated in numpy 1.25, but *also* handles the future error # see https://github.com/numpy/numpy/pull/10615 # and https://github.com/SciTools/cartopy/pull/2194 warnings.filterwarnings( "ignore", message="Conversion of an array with ndim > 0" ) return transformer.transform(x, y, z, errcheck=trap) class Globe: """ Define an ellipsoid and, optionally, how to relate it to the real world. """ def __init__(self, datum=None, ellipse='WGS84', semimajor_axis=None, semiminor_axis=None, flattening=None, inverse_flattening=None, towgs84=None, nadgrids=None): """ Parameters ---------- datum Proj "datum" definition. Defaults to None. ellipse Proj "ellps" definition. Defaults to 'WGS84'. semimajor_axis Semimajor axis of the spheroid / ellipsoid. Defaults to None. semiminor_axis Semiminor axis of the ellipsoid. Defaults to None. flattening Flattening of the ellipsoid. Defaults to None. inverse_flattening Inverse flattening of the ellipsoid. Defaults to None. towgs84 Passed through to the Proj definition. Defaults to None. nadgrids Passed through to the Proj definition. Defaults to None. """ self.datum = datum self.ellipse = ellipse self.semimajor_axis = semimajor_axis self.semiminor_axis = semiminor_axis self.flattening = flattening self.inverse_flattening = inverse_flattening self.towgs84 = towgs84 self.nadgrids = nadgrids def to_proj4_params(self): """ Create an OrderedDict of key value pairs which represents this globe in terms of proj params. """ proj4_params = ( ['datum', self.datum], ['ellps', self.ellipse], ['a', self.semimajor_axis], ['b', self.semiminor_axis], ['f', self.flattening], ['rf', self.inverse_flattening], ['towgs84', self.towgs84], ['nadgrids', self.nadgrids] ) return OrderedDict((k, v) for k, v in proj4_params if v is not None) class CRS(_CRS): """ Define a Coordinate Reference System using proj. The :class:`cartopy.crs.CRS` class is the very core of cartopy, all coordinate reference systems in cartopy have :class:`~cartopy.crs.CRS` as a parent class. """ #: Whether this projection can handle ellipses. _handles_ellipses = True def __init__(self, proj4_params, globe=None): """ Parameters ---------- proj4_params: iterable of key-value pairs The proj4 parameters required to define the desired CRS. The parameters should not describe the desired elliptic model, instead create an appropriate Globe instance. The ``proj4_params`` parameters will override any parameters that the Globe defines. globe: :class:`~cartopy.crs.Globe` instance, optional If omitted, the default Globe instance will be created. See :class:`~cartopy.crs.Globe` for details. """ self.input = (proj4_params, globe) # for compatibility with pyproj.CRS and rasterio.crs.CRS try: proj4_params = proj4_params.to_wkt() except AttributeError: pass # handle PROJ JSON if ( isinstance(proj4_params, dict) and "proj" not in proj4_params and "init" not in proj4_params ): proj4_params = json.dumps(proj4_params) if globe is not None and isinstance(proj4_params, str): raise ValueError("Cannot have 'globe' with string params.") if globe is None and not isinstance(proj4_params, str): if self._handles_ellipses: globe = Globe() else: globe = Globe(semimajor_axis=WGS84_SEMIMAJOR_AXIS, ellipse=None) if globe is not None and not self._handles_ellipses: a = globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS b = globe.semiminor_axis or a if a != b or globe.ellipse is not None: warnings.warn(f'The {self.__class__.__name__!r} projection ' 'does not handle elliptical globes.') self.globe = globe if isinstance(proj4_params, str): self._proj4_params = {} self.proj4_init = proj4_params else: self._proj4_params = self.globe.to_proj4_params() self._proj4_params.update(proj4_params) init_items = [] for k, v in self._proj4_params.items(): if v is not None: if isinstance(v, float): init_items.append(f'+{k}={v:.16}') elif isinstance(v, np.float32): init_items.append(f'+{k}={v:.8}') else: init_items.append(f'+{k}={v}') else: init_items.append(f'+{k}') self.proj4_init = ' '.join(init_items) + ' +no_defs' super().__init__(self.proj4_init) def __eq__(self, other): if isinstance(other, CRS) and self.proj4_init == other.proj4_init: # Fast path Cartopy's CRS return True # For everything else, we let pyproj handle the comparison return super().__eq__(other) def __hash__(self): """Hash the CRS based on its proj4_init string.""" return hash(self.proj4_init) def __reduce__(self): """ Implement the __reduce__ method used when pickling or performing deepcopy. """ if type(self) is CRS: # State can be reproduced by the proj4_params and globe inputs. return self.__class__, self.input else: # Produces a stateless instance of this class (e.g. an empty tuple). # The state will then be added via __getstate__ and __setstate__. # We are forced to this approach because a CRS does not store # the constructor keyword arguments in its state. return self.__class__, (), self.__getstate__() def __getstate__(self): """Return the full state of this instance for reconstruction in ``__setstate__``. """ state = self.__dict__.copy() # remove pyproj specific attrs state.pop('srs', None) state.pop('_local', None) # Remove the proj4 instance and the proj4_init string, which can # be re-created (in __setstate__) from the other arguments. state.pop('proj4', None) state.pop('proj4_init', None) state['proj4_params'] = self.proj4_params return state def __setstate__(self, state): """ Take the dictionary created by ``__getstate__`` and passes it through to this implementation's __init__ method. """ # Strip out the key state items for a CRS instance. CRS_state = {key: state.pop(key) for key in ['proj4_params', 'globe']} # Put everything else directly into the dict of the instance. self.__dict__.update(state) # Call the init of this class to ensure that the projection is # properly initialised with proj4. CRS.__init__(self, **CRS_state) def _as_mpl_transform(self, axes=None): """ Cast this CRS instance into a :class:`matplotlib.axes.Axes` using the Matplotlib ``_as_mpl_transform`` interface. """ # lazy import mpl.geoaxes (and therefore matplotlib) as mpl # is only an optional dependency import cartopy.mpl.geoaxes as geoaxes if not isinstance(axes, geoaxes.GeoAxes): raise ValueError( 'Axes should be an instance of GeoAxes, got %s' % type(axes) ) return ( geoaxes.InterProjectionTransform(self, axes.projection) + axes.transData ) @property def proj4_params(self): return dict(self._proj4_params) def as_geocentric(self): """ Return a new Geocentric CRS with the same ellipse/datum as this CRS. """ return CRS( { "$schema": ( "https://proj.org/schemas/v0.2/projjson.schema.json" ), "type": "GeodeticCRS", "name": "unknown", "datum": self.datum.to_json_dict(), "coordinate_system": { "subtype": "Cartesian", "axis": [ { "name": "Geocentric X", "abbreviation": "X", "direction": "geocentricX", "unit": "metre" }, { "name": "Geocentric Y", "abbreviation": "Y", "direction": "geocentricY", "unit": "metre" }, { "name": "Geocentric Z", "abbreviation": "Z", "direction": "geocentricZ", "unit": "metre" } ] } } ) def as_geodetic(self): """ Return a new Geodetic CRS with the same ellipse/datum as this CRS. """ return CRS(self.geodetic_crs.srs) def is_geodetic(self): return self.is_geographic def transform_point(self, x, y, src_crs, trap=True): """ transform_point(x, y, src_crs) Transform the given float64 coordinate pair, in the given source coordinate system (``src_crs``), to this coordinate system. Parameters ---------- x the x coordinate, in ``src_crs`` coordinates, to transform y the y coordinate, in ``src_crs`` coordinates, to transform src_crs instance of :class:`CRS` that represents the coordinate system of ``x`` and ``y``. trap Whether proj errors for "latitude or longitude exceeded limits" and "tolerance condition error" should be trapped. Returns ------- (x, y) in this coordinate system """ result = self.transform_points( src_crs, np.array([x]), np.array([y]), trap=trap, ).reshape((1, 3)) return result[0, 0], result[0, 1] def transform_points(self, src_crs, x, y, z=None, trap=False): """ transform_points(src_crs, x, y[, z]) Transform the given coordinates, in the given source coordinate system (``src_crs``), to this coordinate system. Parameters ---------- src_crs instance of :class:`CRS` that represents the coordinate system of ``x``, ``y`` and ``z``. x the x coordinates (array), in ``src_crs`` coordinates, to transform. May be 1 or 2 dimensional. y the y coordinates (array), in ``src_crs`` coordinates, to transform. Its shape must match that of x. z: optional the z coordinates (array), in ``src_crs`` coordinates, to transform. Defaults to None. If supplied, its shape must match that of x. trap Whether proj errors for "latitude or longitude exceeded limits" and "tolerance condition error" should be trapped. Returns ------- Array of shape ``x.shape + (3, )`` in this coordinate system. """ result_shape = tuple(x.shape[i] for i in range(x.ndim)) + (3, ) if z is None: if x.ndim > 2 or y.ndim > 2: raise ValueError('x and y arrays must be 1 or 2 dimensional') elif x.ndim != 1 or y.ndim != 1: x, y = x.flatten(), y.flatten() if x.shape[0] != y.shape[0]: raise ValueError('x and y arrays must have the same length') else: if x.ndim > 2 or y.ndim > 2 or z.ndim > 2: raise ValueError('x, y and z arrays must be 1 or 2 ' 'dimensional') elif x.ndim != 1 or y.ndim != 1 or z.ndim != 1: x, y, z = x.flatten(), y.flatten(), z.flatten() if not x.shape[0] == y.shape[0] == z.shape[0]: raise ValueError('x, y, and z arrays must have the same ' 'length') npts = x.shape[0] result = np.empty([npts, 3], dtype=np.double) if npts: if self == src_crs and ( isinstance(src_crs, _CylindricalProjection) or self.is_geodetic()): # convert from [0,360] to [-180,180] x = np.array(x, copy=True) to_180 = (x > 180) | (x < -180) x[to_180] = (((x[to_180] + 180) % 360) - 180) try: result[:, 0], result[:, 1], result[:, 2] = \ _safe_pj_transform(src_crs, self, x, y, z, trap=trap) except ProjError as err: msg = str(err).lower() if ( "latitude" in msg or "longitude" in msg or "outside of projection domain" in msg or "tolerance condition error" in msg ): result[:] = np.nan else: raise if not trap: result[np.isinf(result)] = np.nan if len(result_shape) > 2: return result.reshape(result_shape) return result def transform_vectors(self, src_proj, x, y, u, v): """ transform_vectors(src_proj, x, y, u, v) Transform the given vector components, with coordinates in the given source coordinate system (``src_proj``), to this coordinate system. The vector components must be given relative to the source projection's coordinate reference system (grid eastward and grid northward). Parameters ---------- src_proj The :class:`CRS.Projection` that represents the coordinate system the vectors are defined in. x The x coordinates of the vectors in the source projection. y The y coordinates of the vectors in the source projection. u The grid-eastward components of the vectors. v The grid-northward components of the vectors. Note ---- x, y, u and v may be 1 or 2 dimensional, but must all have matching shapes. Returns ------- ut, vt: The transformed vector components. Note ---- The algorithm used to transform vectors is an approximation rather than an exact transform, but the accuracy should be good enough for visualization purposes. """ if not (x.shape == y.shape == u.shape == v.shape): raise ValueError('x, y, u and v arrays must be the same shape') if x.ndim not in (1, 2): raise ValueError('x, y, u and v must be 1 or 2 dimensional') # Transform the coordinates to the target projection. proj_xyz = self.transform_points(src_proj, x, y) target_x, target_y = proj_xyz[..., 0], proj_xyz[..., 1] # Rotate the input vectors to the projection. # # 1: Find the magnitude and direction of the input vectors. vector_magnitudes = np.hypot(u, v) vector_angles = np.arctan2(v, u) # 2: Find a point in the direction of the original vector that is # a small distance away from the base point of the vector (near # the poles the point may have to be in the opposite direction # to be valid). factor = 360000. delta = (src_proj.x_limits[1] - src_proj.x_limits[0]) / factor x_perturbations = delta * np.cos(vector_angles) y_perturbations = delta * np.sin(vector_angles) # 3: Handle points that are invalid. These come from picking a new # point that is outside the domain of the CRS. The first step is # to apply the native transform to the input coordinates to make # sure they are in the appropriate range. Then detect all the # coordinates where the perturbation takes the point out of the # valid x-domain and fix them. After that do the same for points # that are outside the valid y-domain, which may reintroduce some # points outside of the valid x-domain proj_xyz = src_proj.transform_points(src_proj, x, y) source_x, source_y = proj_xyz[..., 0], proj_xyz[..., 1] # Detect all the coordinates where the perturbation takes the point # outside of the valid x-domain, and reverse the direction of the # perturbation to fix this. eps = 1e-9 invalid_x = np.logical_or( source_x + x_perturbations < src_proj.x_limits[0] - eps, source_x + x_perturbations > src_proj.x_limits[1] + eps) if invalid_x.any(): x_perturbations[invalid_x] *= -1 y_perturbations[invalid_x] *= -1 # Do the same for coordinates where the perturbation takes the point # outside of the valid y-domain. This may reintroduce some points # that will be outside the x-domain when the perturbation is # applied. invalid_y = np.logical_or( source_y + y_perturbations < src_proj.y_limits[0] - eps, source_y + y_perturbations > src_proj.y_limits[1] + eps) if invalid_y.any(): x_perturbations[invalid_y] *= -1 y_perturbations[invalid_y] *= -1 # Keep track of the points where the perturbation direction was # reversed. reversed_vectors = np.logical_xor(invalid_x, invalid_y) # See if there were any points where we cannot reverse the direction # of the perturbation to get the perturbed point within the valid # domain of the projection, and issue a warning if there are. problem_points = np.logical_or( source_x + x_perturbations < src_proj.x_limits[0] - eps, source_x + x_perturbations > src_proj.x_limits[1] + eps) if problem_points.any(): warnings.warn('Some vectors at source domain corners ' 'may not have been transformed correctly') # 4: Transform this set of points to the projection coordinates and # find the angle between the base point and the perturbed point # in the projection coordinates (reversing the direction at any # points where the original was reversed in step 3). proj_xyz = self.transform_points(src_proj, source_x + x_perturbations, source_y + y_perturbations) target_x_perturbed = proj_xyz[..., 0] target_y_perturbed = proj_xyz[..., 1] projected_angles = np.arctan2(target_y_perturbed - target_y, target_x_perturbed - target_x) if reversed_vectors.any(): projected_angles[reversed_vectors] += np.pi # 5: Form the projected vector components, preserving the magnitude # of the original vectors. projected_u = vector_magnitudes * np.cos(projected_angles) projected_v = vector_magnitudes * np.sin(projected_angles) return projected_u, projected_v class Geodetic(CRS): """ Define a latitude/longitude coordinate system with spherical topology, geographical distance and coordinates are measured in degrees. """ def __init__(self, globe=None): """ Parameters ---------- globe: A :class:`cartopy.crs.Globe`, optional Defaults to a "WGS84" datum. """ proj4_params = [('proj', 'lonlat')] globe = globe or Globe(datum='WGS84') super().__init__(proj4_params, globe) # XXX Implement fwd such as Basemap's Geod. # Would be used in the tissot example. # Could come from https://geographiclib.sourceforge.io class Geocentric(CRS): """ Define a Geocentric coordinate system, where x, y, z are Cartesian coordinates from the center of the Earth. """ def __init__(self, globe=None): """ Parameters ---------- globe: A :class:`cartopy.crs.Globe`, optional Defaults to a "WGS84" datum. """ proj4_params = [('proj', 'geocent')] globe = globe or Globe(datum='WGS84') super().__init__(proj4_params, globe) class RotatedGeodetic(CRS): """ Define a rotated latitude/longitude coordinate system with spherical topology and geographical distance. Coordinates are measured in degrees. The class uses proj to perform an ob_tran operation, using the pole_longitude to set a lon_0 then performing two rotations based on pole_latitude and central_rotated_longitude. This is equivalent to setting the new pole to a location defined by the pole_latitude and pole_longitude values in the GeogCRS defined by globe, then rotating this new CRS about it's pole using the central_rotated_longitude value. """ def __init__(self, pole_longitude, pole_latitude, central_rotated_longitude=0.0, globe=None): """ Parameters ---------- pole_longitude Pole longitude position, in unrotated degrees. pole_latitude Pole latitude position, in unrotated degrees. central_rotated_longitude: optional Longitude rotation about the new pole, in degrees. Defaults to 0. globe: optional A :class:`cartopy.crs.Globe`. Defaults to a "WGS84" datum. """ globe = globe or Globe(datum='WGS84') proj4_params = [('proj', 'ob_tran'), ('o_proj', 'latlon'), ('o_lon_p', central_rotated_longitude), ('o_lat_p', pole_latitude), ('lon_0', 180 + pole_longitude), ('to_meter', math.radians(1) * ( globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS))] super().__init__(proj4_params, globe=globe) class Projection(CRS, metaclass=ABCMeta): """ Define a projected coordinate system with flat topology and Euclidean distance. """ _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', 'GeometryCollection': '_project_geometry_collection' } # Whether or not this projection can handle wrapped coordinates _wrappable = False def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) self.bounds = None if self.area_of_use: # Convert lat/lon bounds to projected bounds. # Geographic area of the entire dataset referenced to WGS 84 # NB. We can't use a polygon transform at this stage because # that relies on the existence of the map boundary... the very # thing we're trying to work out! ;-) x0 = self.area_of_use.west x1 = self.area_of_use.east y0 = self.area_of_use.south y1 = self.area_of_use.north lons = np.array([x0, x0, x1, x1]) lats = np.array([y0, y1, y1, y0]) points = self.transform_points( PlateCarree().as_geodetic(), lons, lats ) x = points[:, 0] y = points[:, 1] self.bounds = (x.min(), x.max(), y.min(), y.max()) x0, x1, y0, y1 = self.bounds self.threshold = min(x1 - x0, y1 - y0) / 100. elif self.is_geographic: # If the projection is geographic without an area of use, assume # the bounds are the full globe. self.bounds = (-180, 180, -90, 90) @property def boundary(self): if self.bounds is None: raise NotImplementedError x0, x1, y0, y1 = self.bounds return sgeom.LineString([(x0, y0), (x0, y1), (x1, y1), (x1, y0), (x0, y0)]) @property def x_limits(self): if self.bounds is None: raise NotImplementedError x0, x1, y0, y1 = self.bounds return (x0, x1) @property def y_limits(self): if self.bounds is None: raise NotImplementedError x0, x1, y0, y1 = self.bounds return (y0, y1) @property def threshold(self): return getattr(self, '_threshold', 0.5) @threshold.setter def threshold(self, t): self._threshold = t @property def cw_boundary(self): try: boundary = self._cw_boundary except AttributeError: boundary = sgeom.LinearRing(self.boundary) self._cw_boundary = boundary return boundary @property def ccw_boundary(self): try: boundary = self._ccw_boundary except AttributeError: boundary = sgeom.LinearRing(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 is_geodetic(self): return False def _determine_longitude_bounds(self, central_longitude): # In new proj, using exact limits will wrap-around, so subtract a # small epsilon: epsilon = 1e-10 minlon = -180 + central_longitude maxlon = 180 + central_longitude if central_longitude > 0: maxlon -= epsilon elif central_longitude < 0: minlon += epsilon return minlon, maxlon def _repr_html_(self): from html import escape try: # As matplotlib is not a core cartopy dependency, don't error # if it's not available. import matplotlib.pyplot as plt except ImportError: # We can't return an SVG of the CRS, so let Jupyter fall back to # a default repr by returning None. return None # Produce a visual repr of the Projection instance. fig, ax = plt.subplots(figsize=(5, 3), subplot_kw={'projection': self}) ax.set_global() ax.coastlines('auto') ax.gridlines() buf = io.StringIO() fig.savefig(buf, format='svg', bbox_inches='tight') plt.close(fig) # "Rewind" the buffer to the start and return it as an svg string. buf.seek(0) svg = buf.read() return f'{svg}
{escape(object.__repr__(self))}
' def _as_mpl_axes(self): import cartopy.mpl.geoaxes as geoaxes return geoaxes.GeoAxes, {'projection': self} def project_geometry(self, geometry, src_crs=None): """ Project the given geometry into this projection. Parameters ---------- geometry The geometry to (re-)project. src_crs: optional The source CRS. Defaults to None. If src_crs is None, the source CRS is assumed to be a geodetic version of the target CRS. Returns ------- geometry The projected result (a shapely geometry). """ 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(f'Unsupported geometry type {geom_type!r}') 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): """ Project the given LinearRing from the src_crs into this CRS and returns a GeometryCollection containing zero or more LinearRings and a single MultiLineString. """ debug = False # 1) Resolve the initial lines into projected segments # 1abc # def23ghi # jkl41 multi_line_string = cartopy.trace.project_linear(linear_ring, src_crs, self) # 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 # 2) Simplify the segments where appropriate. if len(multi_line_string.geoms) > 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. line_strings = list(multi_line_string.geoms) any_modified = False i = 0 if debug: first_coord = np.array([ls.coords[0] for ls in line_strings]) last_coord = np.array([ls.coords[-1] for ls in line_strings]) print('Distance matrix:') np.set_printoptions(precision=2) x = first_coord[:, np.newaxis, :] y = last_coord[np.newaxis, :, :] print(np.abs(x - y).max(axis=-1)) 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): if debug: print(f'Joining together {i} and {j}.') 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 rings that have been created by the projection stage. rings = [] line_strings = [] for line in multi_line_string.geoms: if len(line.coords) > 3 and np.allclose(line.coords[0], line.coords[-1], atol=threshold): result_geometry = sgeom.LinearRing(line.coords[:-1]) rings.append(result_geometry) else: line_strings.append(line) # If we found any rings, then we should re-create the multi-line str. if rings: multi_line_string = sgeom.MultiLineString(line_strings) return sgeom.GeometryCollection([*rings, multi_line_string]) def _project_multipoint(self, geometry, src_crs): geoms = [] for geom in geometry.geoms: geoms.append(self._project_point(geom, src_crs)) return sgeom.MultiPoint(geoms) 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) return sgeom.MultiLineString(geoms) 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) return sgeom.MultiPolygon(geoms) def _project_geometry_collection(self, geometry, src_crs): return sgeom.GeometryCollection( [self.project_geometry(geom, src_crs) for geom in geometry.geoms]) def _project_polygon(self, polygon, src_crs): """ Return 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): geom_collection = self._project_linear_ring(src_ring, src_crs) *p_rings, p_mline = geom_collection.geoms if p_rings: rings.extend(p_rings) if len(p_mline.geoms) > 0: multi_lines.append(p_mline) # 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): """ Return 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. """ debug = False debug_plot_edges = False # 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.geoms) # 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 = _BoundaryPoint(first_dist, False, (i, 'first', line_string.coords[0])) edge_things.append(thing) last_dist = boundary_distance(line_string.coords[-1]) thing = _BoundaryPoint(last_dist, False, (i, 'last', line_string.coords[-1])) edge_things.append(thing) # Record the positions of all the boundary vertices for xy in boundary.coords[:-1]: point = sgeom.Point(*xy) dist = boundary.project(point) thing = _BoundaryPoint(dist, True, point) edge_things.append(thing) if debug_plot_edges: import matplotlib.pyplot as plt current_fig = plt.gcf() fig = plt.figure() # Reset the current figure so we don't upset anything. plt.figure(current_fig.number) ax = fig.add_subplot(1, 1, 1) # 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)) remaining_ls = dict(enumerate(line_strings)) prev_thing = None for edge_thing in edge_things[:]: if (prev_thing is not None and not edge_thing.kind and not prev_thing.kind and edge_thing.data[0] == prev_thing.data[0]): j = edge_thing.data[0] # Insert a edge boundary point in between this geometry. mid_dist = (edge_thing.distance + prev_thing.distance) * 0.5 mid_point = boundary.interpolate(mid_dist) new_thing = _BoundaryPoint(mid_dist, True, mid_point) if debug: print(f'Artificially insert boundary: {new_thing}') ind = edge_things.index(edge_thing) edge_things.insert(ind, new_thing) prev_thing = None else: prev_thing = edge_thing if debug: print() print('Edge things') for thing in edge_things: print(' ', thing) if debug_plot_edges: for thing in edge_things: if isinstance(thing.data, sgeom.Point): ax.plot(*thing.data.xy, marker='o') else: ax.plot(*thing.data[2], marker='o') ls = line_strings[thing.data[0]] coords = np.array(ls.coords) ax.plot(coords[:, 0], coords[:, 1]) ax.text(coords[0, 0], coords[0, 1], thing.data[0]) ax.text(coords[-1, 0], coords[-1, 1], f'{thing.data[0]}.') def filter_last(t): return t.kind or t.data[1] == 'first' edge_things = list(filter(filter_last, edge_things)) processed_ls = [] while remaining_ls: # Rename line_string to current_ls i, current_ls = remaining_ls.popitem() if debug: import sys sys.stdout.write('+') sys.stdout.flush() print() print(f'Processing: {i}, {current_ls}') added_linestring = set() while True: # Find out how far around this linestring's last # point is on the boundary. We will use this to find # the next point on the boundary. d_last = boundary_distance(current_ls.coords[-1]) if debug: print(f' d_last: {d_last!r}') next_thing = _find_first_ge(edge_things, d_last) # Remove this boundary point from the edge. edge_things.remove(next_thing) if debug: print(' next_thing:', next_thing) if next_thing.kind: # We've just got a boundary point, add it, and keep going. if debug: print(' adding boundary point') boundary_point = next_thing.data combined_coords = (list(current_ls.coords) + [(boundary_point.x, boundary_point.y)]) current_ls = sgeom.LineString(combined_coords) elif next_thing.data[0] == i: # We've gone all the way around and are now back at the # first boundary thing. if debug: print(' close loop') processed_ls.append(current_ls) if debug_plot_edges: coords = np.array(current_ls.coords) ax.plot(coords[:, 0], coords[:, 1], color='black', linestyle='--') break else: if debug: print(' adding line') j = next_thing.data[0] line_to_append = line_strings[j] if j in remaining_ls: remaining_ls.pop(j) coords_to_append = list(line_to_append.coords) # Build up the linestring. current_ls = sgeom.LineString(list(current_ls.coords) + coords_to_append) # Catch getting stuck in an infinite loop by checking that # linestring only added once. if j not in added_linestring: added_linestring.add(j) else: if debug_plot_edges: plt.show() raise RuntimeError('Unidentified problem with ' 'geometry, linestring being ' 're-added. Please raise an issue.') # filter out any non-valid linear rings def makes_valid_ring(line_string): if len(line_string.coords) == 3: # When sgeom.LinearRing is passed a LineString of length 3, # if the first and last coordinate are equal, a LinearRing # with 3 coordinates will be created. This object will cause # a segfault when evaluated. coords = list(line_string.coords) return coords[0] != coords[-1] and line_string.is_valid else: return len(line_string.coords) > 3 and line_string.is_valid linear_rings = [ sgeom.LinearRing(line_string) for line_string in processed_ls if makes_valid_ring(line_string)] 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) elif polygon.crosses(interior_ring): # Likely that we have an invalid geometry such as # that from #509 or #537. 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 interior_polys = [] for ring in interior_rings: polygon = shapely.make_valid(sgeom.Polygon(ring)) if not polygon.is_empty: if isinstance(polygon, sgeom.Polygon): interior_polys.append(polygon) elif isinstance(polygon, sgeom.MultiPolygon): interior_polys.extend(polygon.geoms) elif isinstance(polygon, sgeom.GeometryCollection): for geom in polygon.geoms: if isinstance(geom, sgeom.Polygon): interior_polys.append(geom) elif isinstance(geom, sgeom.MultiPolygon): interior_polys.extend(geom.geoms) else: # make_valid may produce some linestrings. Ignore these continue x1, y1, x2, y2 = polygon.bounds bx = (x2 - x1) * 0.1 by = (y2 - y1) * 0.1 x1 -= bx y1 -= by x2 += bx y2 += by x3 = min(x1, x3) x4 = max(x2, x4) y3 = min(y1, y3) y4 = max(y2, y4) box = sgeom.box(x3, y3, x4, y4, ccw=is_ccw) # Invert the polygons multi_poly = shapely.make_valid(sgeom.MultiPolygon(interior_polys)) polygon = box.difference(multi_poly) # Intersect the inverted polygon with the boundary polygon = boundary_poly.intersection(polygon) if not polygon.is_empty: if isinstance(polygon, sgeom.MultiPolygon): polygon_bits.extend(polygon.geoms) else: polygon_bits.append(polygon) return sgeom.MultiPolygon(polygon_bits) 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. Note ---- 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`). """ if vertices.size == 0: return vertices if self == src_crs: x = vertices[:, 0] y = vertices[:, 1] # Extend the limits a tiny amount to allow for precision mistakes epsilon = 1.e-10 x_limits = (self.x_limits[0] - epsilon, self.x_limits[1] + epsilon) y_limits = (self.y_limits[0] - epsilon, self.y_limits[1] + epsilon) 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 vertices class _RectangularProjection(Projection, metaclass=ABCMeta): """ The abstract superclass of projections with a rectangular domain which is symmetric about the origin. """ _wrappable = True def __init__(self, proj4_params, half_width, half_height, globe=None): self._half_width = half_width self._half_height = half_height super().__init__(proj4_params, globe=globe) @property def boundary(self): w, h = self._half_width, self._half_height return sgeom.LinearRing([(-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, metaclass=ABCMeta): """ The abstract class which denotes cylindrical projections where we want to allow x values to wrap around. """ _wrappable = True def _ellipse_boundary(semimajor=2, semiminor=1, easting=0, northing=0, n=201): """ Define a projection boundary using an ellipse. This type of boundary is used by several projections. """ t = np.linspace(0, -2 * np.pi, n) # Clockwise boundary. coords = np.vstack([semimajor * np.cos(t), semiminor * np.sin(t)]) coords += ([easting], [northing]) return coords class PlateCarree(_CylindricalProjection): def __init__(self, central_longitude=0.0, globe=None): globe = globe or Globe(semimajor_axis=WGS84_SEMIMAJOR_AXIS) proj4_params = [('proj', 'eqc'), ('lon_0', central_longitude), ('to_meter', math.radians(1) * ( globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)), ('vto_meter', 1)] x_max = 180 y_max = 90 # Set the threshold around 0.5 if the x max is 180. self.threshold = x_max / 360 super().__init__(proj4_params, x_max, y_max, globe=globe) def _bbox_and_offset(self, other_plate_carree): """ Return 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, -170.0], [-170.0, 180]] >>> print(offset) 10.0 The returned values are longitudes in ``other_plate_carree``'s coordinate system. Warning ------- 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] += self.x_limits[1] - self.x_limits[0] return bbox, lon_0_offset def quick_vertices_transform(self, vertices, src_crs): return_value = super().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() 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 class TransverseMercator(Projection): """ A Transverse Mercator projection. """ _wrappable = True 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, approx=False): """ Parameters ---------- central_longitude: optional The true longitude of the central meridian in degrees. Defaults to 0. central_latitude: optional The true latitude of the planar origin in degrees. Defaults to 0. false_easting: optional X offset from the planar origin in metres. Defaults to 0. false_northing: optional Y offset from the planar origin in metres. Defaults to 0. scale_factor: optional Scale factor at the central meridian. Defaults to 1. globe: optional An instance of :class:`cartopy.crs.Globe`. If omitted, a default globe is created. approx: optional Whether to use Proj's approximate projection (True), or the new Extended Transverse Mercator code (False). Defaults to True, but will change to False in the next release. """ 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')] if approx: proj4_params += [('approx', None)] super().__init__(proj4_params, globe=globe) self.threshold = 1e4 @property def boundary(self): x0, x1 = self.x_limits y0, y1 = self.y_limits return sgeom.LinearRing([(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) class OSGB(TransverseMercator): def __init__(self, approx=False): super().__init__(central_longitude=-2, central_latitude=49, scale_factor=0.9996012717, false_easting=400000, false_northing=-100000, globe=Globe(datum='OSGB36', ellipse='airy'), approx=approx) @property def boundary(self): w = self.x_limits[1] - self.x_limits[0] h = self.y_limits[1] - self.y_limits[0] return sgeom.LinearRing([(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) class OSNI(TransverseMercator): def __init__(self, approx=False): globe = Globe(semimajor_axis=6377340.189, semiminor_axis=6356034.447938534) super().__init__(central_longitude=-8, central_latitude=53.5, scale_factor=1.000035, false_easting=200000, false_northing=250000, globe=globe, approx=approx) @property def boundary(self): w = self.x_limits[1] - self.x_limits[0] h = self.y_limits[1] - self.y_limits[0] return sgeom.LinearRing([(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) class UTM(Projection): """ Universal Transverse Mercator projection. """ def __init__(self, zone, southern_hemisphere=False, globe=None): """ Parameters ---------- zone The numeric zone of the UTM required. southern_hemisphere: optional Set to True if the zone is in the southern hemisphere. Defaults to False. globe: optional An instance of :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'utm'), ('units', 'm'), ('zone', zone)] if southern_hemisphere: proj4_params.append(('south', None)) super().__init__(proj4_params, globe=globe) self.threshold = 1e2 @property def boundary(self): x0, x1 = self.x_limits y0, y1 = self.y_limits return sgeom.LinearRing([(x0, y0), (x0, y1), (x1, y1), (x1, y0), (x0, y0)]) @property def x_limits(self): easting = 5e5 # allow 50% overflow return (0 - easting / 2, 2 * easting + easting / 2) @property def y_limits(self): northing = 1e7 # allow 50% overflow return (0 - northing, 2 * northing + northing / 2) class EuroPP(UTM): """ UTM Zone 32 projection for EuroPP domain. Ellipsoid is International 1924, Datum is ED50. """ def __init__(self): globe = Globe(ellipse='intl') super().__init__(32, globe=globe) @property def x_limits(self): return (-1.4e6, 2e6) @property def y_limits(self): return (4e6, 7.9e6) class Mercator(Projection): """ A Mercator projection. """ _wrappable = True def __init__(self, central_longitude=0.0, min_latitude=-80.0, max_latitude=84.0, globe=None, latitude_true_scale=None, false_easting=0.0, false_northing=0.0, scale_factor=None): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to 0. min_latitude: optional The maximum southerly extent of the projection. Defaults to -80 degrees. max_latitude: optional The maximum northerly extent of the projection. Defaults to 84 degrees. globe: A :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. latitude_true_scale: optional The latitude where the scale is 1. Defaults to 0 degrees. false_easting: optional X offset from the planar origin in metres. Defaults to 0. false_northing: optional Y offset from the planar origin in metres. Defaults to 0. scale_factor: optional Scale factor at natural origin. Defaults to unused. Notes ----- Only one of ``latitude_true_scale`` and ``scale_factor`` should be included. """ proj4_params = [('proj', 'merc'), ('lon_0', central_longitude), ('x_0', false_easting), ('y_0', false_northing), ('units', 'm')] # If it's None, we don't pass it to Proj4, in which case its default # of 0.0 will be used. if latitude_true_scale is not None: proj4_params.append(('lat_ts', latitude_true_scale)) if scale_factor is not None: if latitude_true_scale is not None: raise ValueError('It does not make sense to provide both ' '"scale_factor" and "latitude_true_scale". ') else: proj4_params.append(('k_0', scale_factor)) super().__init__(proj4_params, globe=globe) # Need to have x/y limits defined for the initial hash which # gets used within transform_points for caching self._x_limits = self._y_limits = None # Calculate limits. minlon, maxlon = self._determine_longitude_bounds(central_longitude) limits = self.transform_points(self.as_geodetic(), np.array([minlon, maxlon]), np.array([min_latitude, max_latitude])) self._x_limits = tuple(limits[..., 0]) self._y_limits = tuple(limits[..., 1]) self.threshold = min(np.diff(self.x_limits)[0] / 720, np.diff(self.y_limits)[0] / 360) def __eq__(self, other): res = super().__eq__(other) if hasattr(other, "_y_limits") and hasattr(other, "_x_limits"): res = res and self._y_limits == other._y_limits and \ self._x_limits == other._x_limits return res def __ne__(self, other): return not self == other def __hash__(self): return hash((self.proj4_init, self._x_limits, self._y_limits)) @property def boundary(self): x0, x1 = self.x_limits y0, y1 = self.y_limits return sgeom.LinearRing([(x0, y0), (x0, y1), (x1, y1), (x1, y0), (x0, y0)]) @property def x_limits(self): return self._x_limits @property def y_limits(self): return self._y_limits # Define a specific instance of a Mercator projection, the Google mercator. Mercator.GOOGLE = Mercator(min_latitude=-85.0511287798066, max_latitude=85.0511287798066, globe=Globe(ellipse=None, semimajor_axis=WGS84_SEMIMAJOR_AXIS, semiminor_axis=WGS84_SEMIMAJOR_AXIS, nadgrids='@null')) # Deprecated form GOOGLE_MERCATOR = Mercator.GOOGLE class LambertCylindrical(_RectangularProjection): def __init__(self, central_longitude=0.0, globe=None): globe = globe or Globe(semimajor_axis=WGS84_SEMIMAJOR_AXIS) proj4_params = [('proj', 'cea'), ('lon_0', central_longitude), ('to_meter', math.radians(1) * ( globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS))] super().__init__(proj4_params, 180, math.degrees(1), globe=globe) 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, standard_parallels=(33, 45), globe=None, cutoff=-30): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to -96. central_latitude: optional The central latitude. Defaults to 39. false_easting: optional X offset from planar origin in metres. Defaults to 0. false_northing: optional Y offset from planar origin in metres. Defaults to 0. standard_parallels: optional Standard parallel latitude(s). Defaults to (33, 45). globe: optional A :class:`cartopy.crs.Globe`. If omitted, a default globe is created. cutoff: optional 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)] n_parallels = len(standard_parallels) if not 1 <= n_parallels <= 2: raise ValueError('1 or 2 standard parallels must be specified. ' f'Got {n_parallels} ({standard_parallels})') proj4_params.append(('lat_1', standard_parallels[0])) if n_parallels == 2: proj4_params.append(('lat_2', standard_parallels[1])) super().__init__(proj4_params, globe=globe) # Compute whether this projection is at the "north pole" or the # "south pole" (after the central lon/lat have been taken into # account). if n_parallels == 1: plat = 90 if standard_parallels[0] > 0 else -90 else: # Which pole are the parallels closest to? That is the direction # that the cone converges. if abs(standard_parallels[0]) > abs(standard_parallels[1]): poliest_sec = standard_parallels[0] else: poliest_sec = standard_parallels[1] plat = 90 if poliest_sec > 0 else -90 self.cutoff = cutoff n = 91 lons = np.empty(n + 2) lats = np.full(n + 2, float(cutoff)) lons[0] = lons[-1] = 0 lats[0] = lats[-1] = plat if plat == 90: # Ensure clockwise lons[1:-1] = np.linspace(central_longitude + 180 - 0.001, central_longitude - 180 + 0.001, n) else: lons[1:-1] = np.linspace(central_longitude - 180 + 0.001, central_longitude + 180 - 0.001, n) points = self.transform_points(self.as_geodetic(), lons, lats) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = 1e5 def __eq__(self, other): res = super().__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 x_limits(self): return self._x_limits @property def y_limits(self): return self._y_limits class LambertZoneII(Projection): """ Lambert zone II (extended) projection (https://epsg.io/27572), a legacy projection that covers hexagonal France and Corsica. """ def __init__(self): crs = pyproj.CRS.from_epsg(27572) super().__init__(crs.to_wkt()) # Projected bounds from https://epsg.io/27572 self.bounds = [-5242.32, 1212512.16, 1589155.51, 2706796.21] class LambertAzimuthalEqualArea(Projection): """ A Lambert Azimuthal Equal-Area projection. """ _wrappable = True def __init__(self, central_longitude=0.0, central_latitude=0.0, false_easting=0.0, false_northing=0.0, globe=None): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to 0. central_latitude: optional The central latitude. Defaults to 0. false_easting: optional X offset from planar origin in metres. Defaults to 0. false_northing: optional Y offset from planar origin in metres. Defaults to 0. globe: optional A :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'laea'), ('lon_0', central_longitude), ('lat_0', central_latitude), ('x_0', false_easting), ('y_0', false_northing)] super().__init__(proj4_params, globe=globe) a = float(self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS) # Find the antipode, and shift it a small amount in latitude to # approximate the extent of the projection: lon = central_longitude + 180 sign = np.sign(central_latitude) or 1 lat = -central_latitude + sign * 0.01 x, max_y = self.transform_point(lon, lat, self.as_geodetic()) coords = _ellipse_boundary(a * 1.9999, max_y - false_northing, false_easting, false_northing, 61) self._boundary = sgeom.polygon.LinearRing(coords.T) mins = np.min(coords, axis=1) maxs = np.max(coords, axis=1) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = np.diff(self._x_limits)[0] * 1e-3 @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 class Miller(_RectangularProjection): _handles_ellipses = False def __init__(self, central_longitude=0.0, globe=None): if globe is None: globe = Globe(semimajor_axis=WGS84_SEMIMAJOR_AXIS, ellipse=None) a = globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS proj4_params = [('proj', 'mill'), ('lon_0', central_longitude)] # See Snyder, 1987. Eqs (11-1) and (11-2) substituting maximums of # (lambda-lambda0)=180 and phi=90 to get limits. super().__init__(proj4_params, a * np.pi, a * 2.303412543376391, globe=globe) class RotatedPole(_CylindricalProjection): """ A rotated latitude/longitude projected coordinate system with cylindrical topology and projected distance. Coordinates are measured in projection metres. The class uses proj to perform an ob_tran operation, using the pole_longitude to set a lon_0 then performing two rotations based on pole_latitude and central_rotated_longitude. This is equivalent to setting the new pole to a location defined by the pole_latitude and pole_longitude values in the GeogCRS defined by globe, then rotating this new CRS about it's pole using the central_rotated_longitude value. """ def __init__(self, pole_longitude=0.0, pole_latitude=90.0, central_rotated_longitude=0.0, globe=None): """ Parameters ---------- pole_longitude: optional Pole longitude position, in unrotated degrees. Defaults to 0. pole_latitude: optional Pole latitude position, in unrotated degrees. Defaults to 0. central_rotated_longitude: optional Longitude rotation about the new pole, in degrees. Defaults to 0. globe: optional An optional :class:`cartopy.crs.Globe`. Defaults to a "WGS84" datum. """ globe = globe or Globe(semimajor_axis=WGS84_SEMIMAJOR_AXIS) proj4_params = [('proj', 'ob_tran'), ('o_proj', 'latlon'), ('o_lon_p', central_rotated_longitude), ('o_lat_p', pole_latitude), ('lon_0', 180 + pole_longitude), ('to_meter', math.radians(1) * ( globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS))] super().__init__(proj4_params, 180, 90, globe=globe) class Gnomonic(Projection): _handles_ellipses = False def __init__(self, central_latitude=0.0, central_longitude=0.0, globe=None): proj4_params = [('proj', 'gnom'), ('lat_0', central_latitude), ('lon_0', central_longitude)] super().__init__(proj4_params, globe=globe) self._max = 5e7 self.threshold = 1e5 @property def boundary(self): return sgeom.Point(0, 0).buffer(self._max).exterior @property def x_limits(self): return (-self._max, self._max) @property def y_limits(self): return (-self._max, self._max) class Stereographic(Projection): _wrappable = True def __init__(self, central_latitude=0.0, central_longitude=0.0, false_easting=0.0, false_northing=0.0, true_scale_latitude=None, scale_factor=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 is not None: if central_latitude not in (-90., 90.): warnings.warn('"true_scale_latitude" parameter is only used ' 'for polar stereographic projections. Consider ' 'the use of "scale_factor" instead.', stacklevel=2) proj4_params.append(('lat_ts', true_scale_latitude)) if scale_factor is not None: if true_scale_latitude is not None: raise ValueError('It does not make sense to provide both ' '"scale_factor" and "true_scale_latitude". ' 'Ignoring "scale_factor".') else: proj4_params.append(('k_0', scale_factor)) super().__init__(proj4_params, globe=globe) # TODO: Let the globe return the semimajor axis always. a = float(self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS) b = float(self.ellipsoid.semi_minor_metre or WGS84_SEMIMINOR_AXIS) # 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 / WGS84_SEMIMAJOR_AXIS y_axis_offset = 5e7 / WGS84_SEMIMINOR_AXIS 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) coords = _ellipse_boundary(self._x_limits[1], self._y_limits[1], false_easting, false_northing, 91) self._boundary = sgeom.LinearRing(coords.T) self.threshold = np.diff(self._x_limits)[0] * 1e-3 @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 class NorthPolarStereo(Stereographic): def __init__(self, central_longitude=0.0, true_scale_latitude=None, globe=None): super().__init__( central_latitude=90, central_longitude=central_longitude, true_scale_latitude=true_scale_latitude, # None is +90 globe=globe) class SouthPolarStereo(Stereographic): def __init__(self, central_longitude=0.0, true_scale_latitude=None, globe=None): super().__init__( central_latitude=-90, central_longitude=central_longitude, true_scale_latitude=true_scale_latitude, # None is -90 globe=globe) class Orthographic(Projection): _handles_ellipses = False def __init__(self, central_longitude=0.0, central_latitude=0.0, azimuth=0.0, globe=None): proj4_params = [('proj', 'ortho'), ('lon_0', central_longitude), ('lat_0', central_latitude), ('alpha', azimuth)] if pyproj.__proj_version__ < '9.5.0' and azimuth != 0.0: warnings.warn( 'Setting azimuth is not supported with PROJ versions < 9.5.0. ' 'Assuming azimuth=0. ' 'Current PROJ version: %s' % pyproj.__proj_version__) super().__init__(proj4_params, globe=globe) # TODO: Let the globe return the semimajor axis always. a = float(self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS) # To stabilise the projection of geometries, we reduce the boundary by # a tiny fraction at the cost of the extreme edges. coords = _ellipse_boundary(a * 0.99999, a * 0.99999, n=61) self._boundary = sgeom.polygon.LinearRing(coords.T) mins = np.min(coords, axis=1) maxs = np.max(coords, axis=1) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = np.diff(self._x_limits)[0] * 0.02 @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 class _WarpedRectangularProjection(Projection, metaclass=ABCMeta): _wrappable = True def __init__(self, proj4_params, central_longitude, false_easting=None, false_northing=None, globe=None): if false_easting is not None: proj4_params += [('x_0', false_easting)] if false_northing is not None: proj4_params += [('y_0', false_northing)] super().__init__(proj4_params, globe=globe) # Obtain boundary points minlon, maxlon = self._determine_longitude_bounds(central_longitude) n = 91 lon = np.empty(2 * n + 1) lat = np.empty(2 * n + 1) lon[:n] = minlon lat[:n] = np.linspace(-90, 90, n) lon[n:2 * n] = maxlon lat[n:2 * n] = np.linspace(90, -90, n) lon[-1] = minlon lat[-1] = -90 points = self.transform_points(self.as_geodetic(), lon, lat) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] @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 class Aitoff(_WarpedRectangularProjection): """ An Aitoff projection. This projection is a modified azimuthal equidistant projection, balancing shape and scale distortion. There are no standard lines and only the central point is free of distortion. """ _handles_ellipses = False def __init__(self, central_longitude=0, false_easting=None, false_northing=None, globe=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ proj_params = [('proj', 'aitoff'), ('lon_0', central_longitude)] super().__init__(proj_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e5 class _Eckert(_WarpedRectangularProjection, metaclass=ABCMeta): """ An Eckert projection. This class implements all the methods common to the Eckert family of projections. """ _handles_ellipses = False def __init__(self, central_longitude=0, false_easting=None, false_northing=None, globe=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ proj4_params = [('proj', self._proj_name), ('lon_0', central_longitude)] super().__init__(proj4_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e5 class EckertI(_Eckert): """ An Eckert I projection. This projection is pseudocylindrical, but not equal-area. Both meridians and parallels are straight lines. Its equal-area pair is :class:`EckertII`. """ _proj_name = 'eck1' class EckertII(_Eckert): """ An Eckert II projection. This projection is pseudocylindrical, and equal-area. Both meridians and parallels are straight lines. Its non-equal-area pair with equally-spaced parallels is :class:`EckertI`. """ _proj_name = 'eck2' class EckertIII(_Eckert): """ An Eckert III projection. This projection is pseudocylindrical, but not equal-area. Parallels are equally-spaced straight lines, while meridians are elliptical arcs up to semicircles on the edges. Its equal-area pair is :class:`EckertIV`. """ _proj_name = 'eck3' class EckertIV(_Eckert): """ An Eckert IV projection. This projection is pseudocylindrical, and equal-area. Parallels are unequally-spaced straight lines, while meridians are elliptical arcs up to semicircles on the edges. Its non-equal-area pair with equally-spaced parallels is :class:`EckertIII`. It is commonly used for world maps. """ _proj_name = 'eck4' class EckertV(_Eckert): """ An Eckert V projection. This projection is pseudocylindrical, but not equal-area. Parallels are equally-spaced straight lines, while meridians are sinusoidal arcs. Its equal-area pair is :class:`EckertVI`. """ _proj_name = 'eck5' class EckertVI(_Eckert): """ An Eckert VI projection. This projection is pseudocylindrical, and equal-area. Parallels are unequally-spaced straight lines, while meridians are sinusoidal arcs. Its non-equal-area pair with equally-spaced parallels is :class:`EckertV`. It is commonly used for world maps. """ _proj_name = 'eck6' class EqualEarth(_WarpedRectangularProjection): """ An Equal Earth projection. This projection is pseudocylindrical, and equal area. Parallels are unequally-spaced straight lines, while meridians are equally-spaced arcs. It is intended for world maps. Note ---- To use this projection, you must be using Proj 5.2.0 or newer. References ---------- Bojan Šavrič, Tom Patterson & Bernhard Jenny (2018) The Equal Earth map projection, International Journal of Geographical Information Science, DOI: 10.1080/13658816.2018.1504949 """ def __init__(self, central_longitude=0, false_easting=None, false_northing=None, globe=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. """ proj_params = [('proj', 'eqearth'), ('lon_0', central_longitude)] super().__init__(proj_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e5 class Hammer(_WarpedRectangularProjection): """ A Hammer projection. This projection is a modified `.LambertAzimuthalEqualArea` projection, similar to `.Aitoff`, and intended to reduce distortion in the outer meridians compared to `.Mollweide`. There are no standard lines and only the central point is free of distortion. """ _handles_ellipses = False def __init__(self, central_longitude=0, false_easting=None, false_northing=None, globe=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ proj4_params = [('proj', 'hammer'), ('lon_0', central_longitude)] super().__init__(proj4_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e5 class Mollweide(_WarpedRectangularProjection): """ A Mollweide projection. This projection is pseudocylindrical, and equal area. Parallels are unequally-spaced straight lines, while meridians are elliptical arcs up to semicircles on the edges. Poles are points. It is commonly used for world maps, or interrupted with several central meridians. """ _handles_ellipses = False def __init__(self, central_longitude=0, globe=None, false_easting=None, false_northing=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ proj4_params = [('proj', 'moll'), ('lon_0', central_longitude)] super().__init__(proj4_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e5 class Robinson(_WarpedRectangularProjection): """ A Robinson projection. This projection is pseudocylindrical, and a compromise that is neither equal-area nor conformal. Parallels are unequally-spaced straight lines, and meridians are curved lines of no particular form. It is commonly used for "visually-appealing" world maps. """ _handles_ellipses = False def __init__(self, central_longitude=0, globe=None, false_easting=None, false_northing=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. false_easting: float, optional X offset from planar origin in metres. Defaults to 0. false_northing: float, optional Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ proj4_params = [('proj', 'robin'), ('lon_0', central_longitude)] super().__init__(proj4_params, central_longitude, false_easting=false_easting, false_northing=false_northing, globe=globe) self.threshold = 1e4 def transform_point(self, x, y, src_crs, trap=True): """ 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().transform_point(x, y, src_crs, trap=trap) return result def transform_points(self, src_crs, x, y, z=None, trap=False): """ 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().transform_points(src_crs, x, y, z, trap=trap) 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 class InterruptedGoodeHomolosine(Projection): """ Composite equal-area projection emphasizing either land or ocean features. Original Reference: Goode, J. P., 1925: The Homolosine Projection: A new device for portraying the Earth's surface entire. Annals of the Association of American Geographers, 15:3, 119-125, DOI: 10.1080/00045602509356949 A central_longitude value of -160 is recommended for the oceanic view. """ _wrappable = True def __init__(self, central_longitude=0, globe=None, emphasis='land'): """ Parameters ---------- central_longitude : float, optional The central longitude, by default 0 globe : :class:`cartopy.crs.Globe`, optional If omitted, a default Globe object is created, by default None emphasis : str, optional Options 'land' and 'ocean' are available, by default 'land' """ if emphasis == 'land': proj4_params = [('proj', 'igh'), ('lon_0', central_longitude)] super().__init__(proj4_params, globe=globe) elif emphasis == 'ocean': proj4_params = [('proj', 'igh_o'), ('lon_0', central_longitude)] super().__init__(proj4_params, globe=globe) else: msg = '`emphasis` needs to be either \'land\' or \'ocean\'' raise ValueError(msg) minlon, maxlon = self._determine_longitude_bounds(central_longitude) epsilon = 1e-10 # Obtain boundary points n = 31 if emphasis == 'land': top_interrupted_lons = (-40.0,) bottom_interrupted_lons = (80.0, -20.0, -100.0) elif emphasis == 'ocean': top_interrupted_lons = (-90.0, 60.0) bottom_interrupted_lons = (90.0, -60.0) lons = np.empty( (2 + 2 * len(top_interrupted_lons + bottom_interrupted_lons)) * n + 1) lats = np.empty( (2 + 2 * len(top_interrupted_lons + bottom_interrupted_lons)) * n + 1) end = 0 # Left boundary lons[end:end + n] = minlon lats[end:end + n] = np.linspace(-90, 90, n) end += n # Top boundary for lon in top_interrupted_lons: lons[end:end + n] = lon - epsilon + central_longitude lats[end:end + n] = np.linspace(90, 0, n) end += n lons[end:end + n] = lon + epsilon + central_longitude lats[end:end + n] = np.linspace(0, 90, n) end += n # Right boundary lons[end:end + n] = maxlon lats[end:end + n] = np.linspace(90, -90, n) end += n # Bottom boundary for lon in bottom_interrupted_lons: lons[end:end + n] = lon + epsilon + central_longitude lats[end:end + n] = np.linspace(-90, 0, n) end += n lons[end:end + n] = lon - epsilon + central_longitude lats[end:end + n] = np.linspace(0, -90, n) end += n # Close loop lons[-1] = minlon lats[-1] = -90 points = self.transform_points(self.as_geodetic(), lons, lats) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = 2e4 @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 class _Satellite(Projection): def __init__(self, projection, satellite_height=35785831, central_longitude=0.0, central_latitude=0.0, false_easting=0, false_northing=0, globe=None, sweep_axis=None): proj4_params = [('proj', projection), ('lon_0', central_longitude), ('lat_0', central_latitude), ('h', satellite_height), ('x_0', false_easting), ('y_0', false_northing), ('units', 'm')] if sweep_axis: proj4_params.append(('sweep', sweep_axis)) super().__init__(proj4_params, globe=globe) def _set_boundary(self, coords): self._boundary = sgeom.LinearRing(coords.T) mins = np.min(coords, axis=1) maxs = np.max(coords, axis=1) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = np.diff(self._x_limits)[0] * 0.02 @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 class Geostationary(_Satellite): """ A view appropriate for satellites in Geostationary Earth orbit. Perspective view looking directly down from above a point on the equator. In this projection, the projected coordinates are scanning angles measured from the satellite looking directly downward, multiplied by the height of the satellite. """ def __init__(self, central_longitude=0.0, satellite_height=35785831, false_easting=0, false_northing=0, globe=None, sweep_axis='y'): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. satellite_height: float, optional The height of the satellite. Defaults to 35785831 metres (true geostationary orbit). false_easting: X offset from planar origin in metres. Defaults to 0. false_northing: Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. sweep_axis: 'x' or 'y', optional. Defaults to 'y'. Controls which axis is scanned first, and thus which angle is applied first. The default is appropriate for Meteosat, while 'x' should be used for GOES. """ super().__init__( projection='geos', satellite_height=satellite_height, central_longitude=central_longitude, central_latitude=0.0, false_easting=false_easting, false_northing=false_northing, globe=globe, sweep_axis=sweep_axis) # TODO: Let the globe return the semimajor axis always. a = float(self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS) b = float(self.ellipsoid.semi_minor_metre or WGS84_SEMIMINOR_AXIS) h = float(satellite_height) # To find the bound we trace around where the line from the satellite # is tangent to the surface. This involves trigonometry on a sphere # centered at the satellite. The two scanning angles form two legs of # triangle on this sphere--the hypotenuse "c" (angle arc) is controlled # by distance from center to the edge of the ellipse being seen. # This is one of the angles in the spherical triangle and used to # rotate around and "scan" the boundary angleA = np.linspace(0, -2 * np.pi, 91) # Clockwise boundary. # Convert the angle around center to the proper value to use in the # parametric form of an ellipse th = np.arctan(a / b * np.tan(angleA)) # Given the position on the ellipse, what is the distance from center # to the ellipse--and thus the tangent point r = np.hypot(a * np.cos(th), b * np.sin(th)) sat_dist = a + h # Using this distance, solve for sin and tan of c in the triangle that # includes the satellite, Earth center, and tangent point--we need to # figure out the location of this tangent point on the elliptical # cross-section through the Earth towards the satellite, where the # major axis is a and the minor is r. With the ellipse centered on the # Earth and the satellite on the y-axis (at y = a + h = sat_dist), the # equation for an ellipse and some calculus gives us the tangent point # (x0, y0) as: # y0 = a**2 / sat_dist # x0 = r * np.sqrt(1 - a**2 / sat_dist**2) # which gives: # sin_c = x0 / np.hypot(x0, sat_dist - y0) # tan_c = x0 / (sat_dist - y0) # A bit of algebra combines these to give directly: sin_c = r / np.sqrt(sat_dist ** 2 - a ** 2 + r ** 2) tan_c = r / np.sqrt(sat_dist ** 2 - a ** 2) # Using Napier's rules for right spherical triangles R2 and R6, # (See https://en.wikipedia.org/wiki/Spherical_trigonometry), we can # solve for arc angles b and a, which are our x and y scanning angles, # respectively. coords = np.vstack([np.arctan(np.cos(angleA) * tan_c), # R6 np.arcsin(np.sin(angleA) * sin_c)]) # R2 # Need to multiply scanning angles by satellite height to get to the # actual native coordinates for the projection. coords *= h coords += np.array([[false_easting], [false_northing]]) self._set_boundary(coords) class NearsidePerspective(_Satellite): """ Perspective view looking directly down from above a point on the globe. In this projection, the projected coordinates are x and y measured from the origin of a plane tangent to the Earth directly below the perspective point (e.g. a satellite). """ _handles_ellipses = False def __init__(self, central_longitude=0.0, central_latitude=0.0, satellite_height=35785831, false_easting=0, false_northing=0, globe=None): """ Parameters ---------- central_longitude: float, optional The central longitude. Defaults to 0. central_latitude: float, optional The central latitude. Defaults to 0. satellite_height: float, optional The height of the satellite. Defaults to 35785831 meters (true geostationary orbit). false_easting: X offset from planar origin in metres. Defaults to 0. false_northing: Y offset from planar origin in metres. Defaults to 0. globe: :class:`cartopy.crs.Globe`, optional If omitted, a default globe is created. .. note:: This projection does not handle elliptical globes. """ super().__init__( projection='nsper', satellite_height=satellite_height, central_longitude=central_longitude, central_latitude=central_latitude, false_easting=false_easting, false_northing=false_northing, globe=globe) # TODO: Let the globe return the semimajor axis always. a = self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS h = float(satellite_height) max_x = a * np.sqrt(h / (2 * a + h)) coords = _ellipse_boundary(max_x, max_x, false_easting, false_northing, 61) self._set_boundary(coords) class AlbersEqualArea(Projection): """ An Albers Equal Area projection This projection is conic and equal-area, and is commonly used for maps of the conterminous United States. """ def __init__(self, central_longitude=0.0, central_latitude=0.0, false_easting=0.0, false_northing=0.0, standard_parallels=(20.0, 50.0), globe=None): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to 0. central_latitude: optional The central latitude. Defaults to 0. false_easting: optional X offset from planar origin in metres. Defaults to 0. false_northing: optional Y offset from planar origin in metres. Defaults to 0. standard_parallels: optional The one or two latitudes of correct scale. Defaults to (20, 50). globe: optional A :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'aea'), ('lon_0', central_longitude), ('lat_0', central_latitude), ('x_0', false_easting), ('y_0', false_northing)] if standard_parallels is not None: try: proj4_params.append(('lat_1', standard_parallels[0])) try: proj4_params.append(('lat_2', standard_parallels[1])) except IndexError: pass except TypeError: proj4_params.append(('lat_1', standard_parallels)) super().__init__(proj4_params, globe=globe) # bounds minlon, maxlon = self._determine_longitude_bounds(central_longitude) n = 103 lons = np.empty(2 * n + 1) lats = np.empty(2 * n + 1) tmp = np.linspace(minlon, maxlon, n) lons[:n] = tmp lats[:n] = 90 lons[n:-1] = tmp[::-1] lats[n:-1] = -90 lons[-1] = lons[0] lats[-1] = lats[0] points = self.transform_points(self.as_geodetic(), lons, lats) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = 1e5 @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 class AzimuthalEquidistant(Projection): """ An Azimuthal Equidistant projection This projection provides accurate angles about and distances through the central position. Other angles, distances, or areas may be distorted. """ _wrappable = True def __init__(self, central_longitude=0.0, central_latitude=0.0, false_easting=0.0, false_northing=0.0, globe=None): """ Parameters ---------- central_longitude: optional The true longitude of the central meridian in degrees. Defaults to 0. central_latitude: optional The true latitude of the planar origin in degrees. Defaults to 0. false_easting: optional X offset from the planar origin in metres. Defaults to 0. false_northing: optional Y offset from the planar origin in metres. Defaults to 0. globe: optional An instance of :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'aeqd'), ('lon_0', central_longitude), ('lat_0', central_latitude), ('x_0', false_easting), ('y_0', false_northing)] super().__init__(proj4_params, globe=globe) # TODO: Let the globe return the semimajor axis always. a = float(self.ellipsoid.semi_major_metre or WGS84_SEMIMAJOR_AXIS) b = float(self.ellipsoid.semi_minor_metre or a) coords = _ellipse_boundary(a * np.pi, b * np.pi, false_easting, false_northing, 61) self._boundary = sgeom.LinearRing(coords.T) mins = np.min(coords, axis=1) maxs = np.max(coords, axis=1) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = 1e5 @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 class Sinusoidal(Projection): """ A Sinusoidal projection. This projection is equal-area. """ def __init__(self, central_longitude=0.0, false_easting=0.0, false_northing=0.0, globe=None): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to 0. false_easting: optional X offset from planar origin in metres. Defaults to 0. false_northing: optional Y offset from planar origin in metres. Defaults to 0. globe: optional A :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'sinu'), ('lon_0', central_longitude), ('x_0', false_easting), ('y_0', false_northing)] super().__init__(proj4_params, globe=globe) # Obtain boundary points minlon, maxlon = self._determine_longitude_bounds(central_longitude) points = [] n = 91 lon = np.empty(2 * n + 1) lat = np.empty(2 * n + 1) lon[:n] = minlon lat[:n] = np.linspace(-90, 90, n) lon[n:2 * n] = maxlon lat[n:2 * n] = np.linspace(90, -90, n) lon[-1] = minlon lat[-1] = -90 points = self.transform_points(self.as_geodetic(), lon, lat) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = max(np.abs(self.x_limits + self.y_limits)) * 1e-5 @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 # MODIS data products use a Sinusoidal projection of a spherical Earth # https://modis-land.gsfc.nasa.gov/GCTP.html Sinusoidal.MODIS = Sinusoidal(globe=Globe(ellipse=None, semimajor_axis=6371007.181, semiminor_axis=6371007.181)) class EquidistantConic(Projection): """ An Equidistant Conic projection. This projection is conic and equidistant, and the scale is true along all meridians and along one or two specified standard parallels. """ def __init__(self, central_longitude=0.0, central_latitude=0.0, false_easting=0.0, false_northing=0.0, standard_parallels=(20.0, 50.0), globe=None): """ Parameters ---------- central_longitude: optional The central longitude. Defaults to 0. central_latitude: optional The true latitude of the planar origin in degrees. Defaults to 0. false_easting: optional X offset from planar origin in metres. Defaults to 0. false_northing: optional Y offset from planar origin in metres. Defaults to 0. standard_parallels: optional The one or two latitudes of correct scale. Defaults to (20, 50). globe: optional A :class:`cartopy.crs.Globe`. If omitted, a default globe is created. """ proj4_params = [('proj', 'eqdc'), ('lon_0', central_longitude), ('lat_0', central_latitude), ('x_0', false_easting), ('y_0', false_northing)] if standard_parallels is not None: try: proj4_params.append(('lat_1', standard_parallels[0])) try: proj4_params.append(('lat_2', standard_parallels[1])) except IndexError: pass except TypeError: proj4_params.append(('lat_1', standard_parallels)) super().__init__(proj4_params, globe=globe) # bounds n = 103 lons = np.empty(2 * n + 1) lats = np.empty(2 * n + 1) minlon, maxlon = self._determine_longitude_bounds(central_longitude) tmp = np.linspace(minlon, maxlon, n) lons[:n] = tmp lats[:n] = 90 lons[n:-1] = tmp[::-1] lats[n:-1] = -90 lons[-1] = lons[0] lats[-1] = lats[0] points = self.transform_points(self.as_geodetic(), lons, lats) self._boundary = sgeom.LinearRing(points) mins = np.min(points, axis=0) maxs = np.max(points, axis=0) self._x_limits = mins[0], maxs[0] self._y_limits = mins[1], maxs[1] self.threshold = 1e5 @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 class ObliqueMercator(Projection): """ An Oblique Mercator projection. """ _wrappable = True def __init__(self, central_longitude=0.0, central_latitude=0.0, false_easting=0.0, false_northing=0.0, scale_factor=1.0, azimuth=0.0, globe=None): """ Parameters ---------- central_longitude: optional The true longitude of the central meridian in degrees. Defaults to 0. central_latitude: optional The true latitude of the planar origin in degrees. Defaults to 0. false_easting: optional X offset from the planar origin in metres. Defaults to 0. false_northing: optional Y offset from the planar origin in metres. Defaults to 0. scale_factor: optional Scale factor at the central meridian. Defaults to 1. azimuth: optional Azimuth of centerline clockwise from north at the center point of the centre line. Defaults to 0. globe: optional An instance of :class:`cartopy.crs.Globe`. If omitted, a default globe is created. Notes ----- The 'Rotated Mercator' projection can be achieved using Oblique Mercator with `azimuth` ``=90``. """ if np.isclose(azimuth, 90): # Exactly 90 causes coastline 'folding'. azimuth -= 1e-3 proj4_params = [('proj', 'omerc'), ('lonc', central_longitude), ('lat_0', central_latitude), ('k', scale_factor), ('x_0', false_easting), ('y_0', false_northing), ('alpha', azimuth), ('units', 'm')] super().__init__(proj4_params, globe=globe) # Couple limits to those of Mercator - delivers acceptable plots, and # Mercator has been through much more scrutiny. mercator = Mercator( central_longitude=central_longitude, globe=globe, false_easting=false_easting, false_northing=false_northing, scale_factor=scale_factor, ) self._x_limits = mercator.x_limits self._y_limits = mercator.y_limits self.threshold = mercator.threshold @property def boundary(self): x0, x1 = self.x_limits y0, y1 = self.y_limits return sgeom.LinearRing([(x0, y0), (x0, y1), (x1, y1), (x1, y0), (x0, y0)]) @property def x_limits(self): return self._x_limits @property def y_limits(self): return self._y_limits class Spilhaus(Projection): """ Spilhaus World Ocean Map in a Square. This is a projection based on Adams World in a Square II projection with the two major antipodal areas on land: South China (115°E and 30°N) and Argentina (65°W and 30°S). See https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f19f4d5cb3d """ def __init__(self, rotation=45, false_easting=0.0, false_northing=0.0, globe=None): """ Parameters ---------- rotation : optional Clockwise rotation of the map in degrees. Defaults to 45. false_easting : optional X offset from the planar origin in metres. Defaults to 0.0. false_northing : optional Y offset from the planar origin in metres. Defaults to 0.0. """ proj4_params = [('proj', 'spilhaus'), ('rot',rotation), ('x_0', false_easting), ('y_0', false_northing)] super().__init__(proj4_params, globe=globe) # The boundary on https://epsg.io/54099 are wrong # The following bounds are calculated based on #[-65.00000012, -29.99999981] # and [115.00000024, 30.00000036] self.bounds = [ -11802684.083372328, 11802683.949222516, -11801129.925928915, 11801129.925928915 ] class _BoundaryPoint: def __init__(self, distance, kind, data): """ A representation for a geometric object which is connected to the boundary. Parameters ---------- distance: float The distance along the boundary that this object can be found. kind: bool Whether this object represents a point from the pre-computed boundary. data: point or namedtuple The actual data that this boundary object represents. """ self.distance = distance self.kind = kind self.data = data def __repr__(self): return f'_BoundaryPoint({self.distance!r}, {self.kind!r}, {self.data})' def _find_first_ge(a, x): for v in a: if v.distance >= x: return v # We've gone all the way around, so pick the first point again. return a[0] def epsg(code): """ Return the projection which corresponds to the given EPSG code. The EPSG code must correspond to a "projected coordinate system", so EPSG codes such as 4326 (WGS-84) which define a "geodetic coordinate system" will not work. Note ---- The conversion is performed by pyproj.CRS. """ import cartopy._epsg return cartopy._epsg._EPSGProjection(code)