Thomas Kolb
e965ec9032
The positions are still a bit off, because they are simply calculated as the average of all polygon coordinates. That causes a bias towards detailed borderlines. A better way would be to calculate the center of mass for each polygon, but that is not implemented yet.
537 lines
17 KiB
Python
Executable file
537 lines
17 KiB
Python
Executable file
#!/usr/bin/env python3
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import sys
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import svgwrite
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import numpy as np
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import matplotlib.pyplot as pp
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from matplotlib.colors import hsv_to_rgb
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import json
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import random
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import argparse
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LABEL_MIN_FONT_SIZE = 2
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def map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R=1):
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""" Azimuthal equidistant projection.
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This function takes a point to map in latitude/longitude format as well as
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a reference point which becomes the "center" of the map.
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It then projects the point into the 2D plane such that the distance from
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the center is proportional to the distance on the Great Circle through the
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projected and the reference point. The angle represents the azimuthal
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direction of the projected point.
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Args:
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lat(numpy.array): Latitudes of the point to project.
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lon(numpy.array): Longitudes of the point to project.
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ref_lat(float): Latitude of the reference point.
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ref_lon(float): Longitude of the reference point.
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R(float): Radius (scale) of the map.
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Returns:
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x(numpy.array): The calculated x coordinates.
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y(numpy.array): The calculated y coordinates.
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"""
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dlon = lon - ref_lon
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rho_linear_norm = np.arccos(np.sin(ref_lat) * np.sin(lat)
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+ np.cos(ref_lat)
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* np.cos(lat) * np.cos(dlon)) / np.pi
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rho = R * rho_linear_norm
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theta = np.arctan2(np.cos(lat) * np.sin(dlon),
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(np.cos(ref_lat) * np.sin(lat)
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- np.sin(ref_lat) * np.cos(lat)
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* np.cos(dlon)))
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x = rho * np.sin(theta)
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y = -rho * np.cos(theta)
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return x, y
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def is_point_in_polygon(point, polygon):
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# Idea: draw an infinite line from the test point along the x axis to the
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# right. Then check how many polygon edges this line intersects. If the
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# number is even, the point is outside the polygon.
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edges = [] # list of lists, containing two points each
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for i in range(len(polygon)-1):
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edges.append([polygon[i], polygon[i+1]])
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# the closing edge
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edges.append([polygon[-1], polygon[0]])
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num_intersects = 0
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test_x, test_y = point
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for edge in edges:
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start_x = edge[0][0]
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start_y = edge[0][1]
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end_x = edge[1][0]
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end_y = edge[1][1]
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# quick exclusion tests
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if start_x < test_x and end_x < test_x:
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continue # edge is completely left of the test point
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if start_y < test_y and end_y < test_y:
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continue # edge is completely below the test point
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if start_y > test_y and end_y > test_y:
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continue # edge is completely above the test point
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# calculate the x coordinate where the edge intersects the whole
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# horizontal line
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intersect_x = start_x + (end_x - start_x) \
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* (test_y - start_y) \
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/ (end_y - start_y)
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if intersect_x > test_x:
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# we found an intersection!
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num_intersects += 1
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if num_intersects % 2 == 0:
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return False # even number of intersects -> outside polygon
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else:
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return True # odd number of intersects -> inside polygon
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def svg_make_inverse_country_path(doc, map_radius, polygon, **kwargs):
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# build a closed circle path covering the whole map
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commands = [f"M 0, {map_radius}",
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f"a {map_radius},{map_radius} 0 1,0 {map_radius*2},0",
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f"a {map_radius},{map_radius} 0 1,0 {-map_radius*2},0",
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"z"]
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# "subtract" the country polygon
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commands.append(f"M {polygon[0][0]} {polygon[0][1]}")
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# add lines for each polygon point
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for point in polygon[1:]:
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commands.append(f"L {point[0]} {point[1]}")
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# ensure straight closing line
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commands.append(f"L {polygon[0][0]} {polygon[0][1]}")
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# close the inner path
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commands.append("z")
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return doc.path(commands, **kwargs)
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def simplify_geojson(geojson):
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# key: 3-letter country identifier
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# data: {full_name,
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# numpy.array(coordinates),
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# numpy.array(proj_coordinates)}.
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# coordinates is a list of 2xN arrays, where N is the number of points.
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# Row 0 contains the longitude, Row 1 the latitude.
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# proj_coordinates is a list of 2xN arrays, where N is the number of
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# points. Row 0 contains the projected x, Row 1 the projected y.
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simplegeodata = {}
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features = geojson['features']
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for feature in features:
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name = feature['properties']['ADMIN']
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key = feature['properties']['ISO_A2']
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# handle duplicate keys (can happen for small countries)
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if key in simplegeodata.keys():
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key = name
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print(f"Preparing {key} ({name})…", file=sys.stderr)
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multipoly = feature['geometry']['coordinates']
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conv_polys = []
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for poly in multipoly:
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for subpoly in poly:
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coords_list = [] # list of lists
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assert(len(subpoly[0]) == 2)
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coords_list += subpoly
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# convert coordinates to numpy array and radians
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coords = np.array(coords_list).T * np.pi / 180
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conv_polys.append(coords)
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simplegeodata[key] = {"name": name, "coordinates": conv_polys}
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return simplegeodata
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def map_all_polygons(simplegeodata, ref_lat, ref_lon, map_radius):
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# apply azimuthal equidistant projection
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for k, v in simplegeodata.items():
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proj_polys = []
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for poly in v['coordinates']:
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lat = poly[1, :]
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lon = poly[0, :]
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x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon,
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map_radius)
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coords = np.array([x, y])
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# remove any points that contain a NaN coordinate
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coords = coords[:, np.any(np.invert(np.isnan(coords)), axis=0)]
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proj_polys.append(coords)
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v['proj_coordinates'] = proj_polys
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def hsv_to_svgstr(h, s, v):
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r, g, b = [int(255.99*x) for x in hsv_to_rgb([h, s, v])]
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return f"#{r:02x}{g:02x}{b:02x}"
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def assign_country_colors(simplegeodata):
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for k, v in simplegeodata.items():
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hue = random.random()
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v['polygon_color'] = hsv_to_svgstr(hue, 0.7, 0.8)
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v['label_color'] = hsv_to_svgstr(hue, 0.5, 0.4)
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def svg_add_countries(doc, simplegeodata, ref_lat, ref_lon, map_radius):
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antipodal_lat = -ref_lat
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antipodal_lon = ref_lon + np.pi
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if antipodal_lon > np.pi:
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antipodal_lon -= 2*np.pi
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for k, v in simplegeodata.items():
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print(f"Mapping {k}…", file=sys.stderr)
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color = v['polygon_color']
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group = doc.g()
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for i in range(len(v['proj_coordinates'])):
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poly = v['proj_coordinates'][i]
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points = poly.T + map_radius # shift to the center of the drawing
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# check if the antipodal point is inside this polygon. If so, it
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# needs to be "inverted", i.e. subtracted from the surrounding map
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# circle.
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if is_point_in_polygon((antipodal_lon, antipodal_lat),
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v['coordinates'][i].T):
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print("!!! Found polygon containing the antipodal point!",
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file=sys.stderr)
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obj = svg_make_inverse_country_path(doc, map_radius,
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np.flipud(points),
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**{'class': 'country',
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'fill': color})
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else:
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obj = doc.polygon(points, **{
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'class': 'country',
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'fill': color})
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group.add(obj)
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group.set_desc(title=v['name'])
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doc.add(group)
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def svg_add_maidenhead_grid(doc, ref_lat, ref_lon, map_radius):
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# generate Maidenhead locator grid (first two letters only)
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group = doc.g()
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N = 18 # subdivisions of Earth
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resolution = 4096
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for x in range(0, N):
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lon = x * 2 * np.pi / N
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lat = np.linspace(-np.pi/2, np.pi/2, resolution)
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x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, map_radius)
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points = np.array([x, y]).T + map_radius
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group.add(doc.polyline(points, **{'class': 'maidenhead_line'}))
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for y in range(0, N):
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lon = np.linspace(-np.pi, np.pi, resolution)
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lat = y * np.pi / N - np.pi/2
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x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon,
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map_radius)
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points = np.array([x, y]).T + map_radius
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group.add(doc.polyline(points, **{'class': 'maidenhead_line'}))
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for x in range(0, N):
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for y in range(0, N):
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sectorname = chr(ord('A') + (x + N//2) % N) \
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+ chr(ord('A') + y)
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lon = (x + 0.5) * 2 * np.pi / N
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lat = (y + 0.5) * np.pi / N - np.pi/2
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tx, ty = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon,
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map_radius)
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font_size = 10
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if y == 0 or y == N-1:
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font_size = 3
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group.add(doc.text(sectorname, (tx + map_radius, ty + map_radius),
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**{'class': 'maidenhead_label',
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'font-size': font_size}))
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doc.add(group) # Maidenhead grid
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def svg_add_country_names(doc, simplegeodata, map_radius):
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group = doc.g()
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for k, v in simplegeodata.items():
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print(f"Labeling {k} ", end='')
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for poly in v['proj_coordinates']:
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x = poly[0, :]
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y = poly[1, :]
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w = np.max(x) - np.min(x)
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h = np.max(y) - np.min(y)
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# FIXME: calculate center of mass
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center_x = np.median(x) + map_radius
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center_y = np.median(y) + map_radius
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kwargs = {
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'class': 'country_label',
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'fill': v['label_color']
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}
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# rotate text by 90 degrees if polygon is higher than wide
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if h > w:
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font_size = h / len(v['name'])
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rotate = True
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else:
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font_size = w / len(v['name'])
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rotate = False
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if font_size < LABEL_MIN_FONT_SIZE:
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print('.', end='', flush=True)
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continue # too small
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else:
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print('#', end='', flush=True)
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kwargs['font-size'] = font_size
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txt = doc.text(v['name'], (center_x, center_y),
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**kwargs)
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if rotate:
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txt.rotate(90, center=(center_x, center_y))
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group.add(txt)
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print()
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doc.add(group)
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def svg_add_distance_azimuth_lines(doc, ref_lat, ref_lon, map_radius):
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group = doc.g()
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# generate equidistant circles
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d_max = 40075/2
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for distance in [500, 1000, 2000, 3000, 4000, 5000, 6000, 8000, 10000,
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12000, 14000, 16000, 18000, 20000]:
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r = map_radius * distance / d_max
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group.add(doc.circle(center=(map_radius, map_radius), r=r,
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**{'class': 'dist_circle'}))
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group.add(doc.text(f"{distance} km", (map_radius, map_radius-r+5),
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**{'class': 'dist_circle_label'}))
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# generate azimuth lines in 30° steps
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for azimuth in np.arange(0, np.pi, np.pi/6):
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start_x = map_radius + map_radius * np.cos(azimuth-np.pi/2)
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start_y = map_radius + map_radius * np.sin(azimuth-np.pi/2)
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end_x = map_radius - map_radius * np.cos(azimuth-np.pi/2)
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end_y = map_radius - map_radius * np.sin(azimuth-np.pi/2)
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group.add(doc.line((start_x, start_y), (end_x, end_y),
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**{'class': 'azimuth_line'}))
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azimuth_deg = int(np.round(azimuth * 180 / np.pi))
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textpos = (2*map_radius - 10, map_radius - 2)
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txt = doc.text(f"{azimuth_deg:d} °", textpos,
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**{'class': 'azimuth_line_label'})
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txt.rotate(azimuth_deg - 90, center=(map_radius, map_radius))
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group.add(txt)
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txt = doc.text(f"{azimuth_deg+180:d} °", textpos,
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**{'class': 'azimuth_line_label'})
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txt.rotate(azimuth_deg - 90 + 180, center=(map_radius, map_radius))
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group.add(txt)
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doc.add(group) # Circles, azimuth lines and labels
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def render(ref_lat, ref_lon, output_stream):
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random.seed(0)
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print("Loading Geodata…", file=sys.stderr)
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with open('geo-countries/data/countries.geojson', 'r') as jfile:
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geojson = json.load(jfile)
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print("Finding boundaries…", file=sys.stderr)
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simplegeodata = simplify_geojson(geojson)
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ref_lat = ref_lat * np.pi / 180
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ref_lon = ref_lon * np.pi / 180
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R = 500
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"""
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# Override data with test coordinate system
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coords = []
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N = 128
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# constant-latitude circles
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coords.append(np.array([np.linspace(-np.pi, np.pi, N),
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np.ones(N) * np.pi/4]))
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coords.append(np.array([np.linspace(-np.pi, np.pi, N),
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np.ones(N) * 0]))
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coords.append(np.array([np.linspace(-np.pi, np.pi, N),
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np.ones(N) * -np.pi/4]))
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# constant-longitude half-circles
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coords.append(np.array([np.ones(N) * -4*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * -3*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * -2*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * -1*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * 0*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * 1*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * 2*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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coords.append(np.array([np.ones(N) * 3*np.pi/4,
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np.linspace(-np.pi/2, np.pi/2, N)]))
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simplegeodata = {"XY": {'name': 'test', 'coordinates': coords}}
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"""
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map_all_polygons(simplegeodata, ref_lat, ref_lon, R)
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assign_country_colors(simplegeodata)
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# generate the SVG
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doc = svgwrite.Drawing("/tmp/test.svg", size=(2*R, 2*R))
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doc.defs.add(doc.style("""
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.country {
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stroke: black;
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stroke-width: 0.01px;
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}
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.dist_circle_label, .azimuth_line_label {
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font-size: 3px;
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font-family: sans-serif;
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text-anchor: middle;
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}
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.dist_circle, .azimuth_line {
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fill: none;
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stroke: black;
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stroke-width: 0.1px;
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}
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.maidenhead_line {
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fill: none;
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stroke: red;
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stroke-width: 0.1px;
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opacity: 0.5;
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}
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.maidenhead_label, .country_label {
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font-family: sans-serif;
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dominant-baseline: middle;
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text-anchor: middle;
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}
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.maidenhead_label {
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fill: red;
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opacity: 0.25;
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}
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"""))
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doc.add(doc.circle(center=(R, R), r=R, fill='#ddeeff',
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stroke_width=1, stroke='black'))
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svg_add_countries(doc, simplegeodata, ref_lat, ref_lon, R)
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svg_add_country_names(doc, simplegeodata, R)
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svg_add_maidenhead_grid(doc, ref_lat, ref_lon, R)
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svg_add_distance_azimuth_lines(doc, ref_lat, ref_lon, R)
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print("Writing output…", file=sys.stderr)
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doc.write(output_stream, pretty=True)
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return
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# Debug Plot
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for k, v in simplegeodata.items():
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for poly in v['proj_coordinates']:
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pp.plot(poly[0, :], poly[1, :])
|
|
|
|
pp.plot([-1, 1], [0, 0], 'k', linewidth=0.5)
|
|
pp.plot([0, 0], [-1, 1], 'k', linewidth=0.5)
|
|
|
|
t = np.linspace(-np.pi, np.pi, 256)
|
|
ct, st = np.cos(t), np.sin(t)
|
|
pp.plot(ct, st, 'k', linewidth=0.5)
|
|
|
|
U = 40075
|
|
for distance in np.arange(0, U/2, 2000):
|
|
f = distance / (U/2)
|
|
pp.plot(f*ct, f*st, 'k', linewidth=0.2)
|
|
|
|
pp.axis('equal')
|
|
|
|
pp.show()
|
|
|
|
|
|
if __name__ == "__main__":
|
|
parser = argparse.ArgumentParser(
|
|
description="Render an azimuthal equidistant map of the world " +
|
|
"centered on the given point")
|
|
|
|
parser.add_argument(metavar='ref-lat', type=float, dest='ref_lat',
|
|
help='Reference Latitude')
|
|
parser.add_argument(metavar='ref-lon', type=float, dest='ref_lon',
|
|
help='Reference Longitude')
|
|
parser.add_argument('-o', '--output-file', type=argparse.FileType('w'),
|
|
help='The output SVG file (default: print to stdout)',
|
|
default=sys.stdout)
|
|
|
|
args = parser.parse_args()
|
|
|
|
render(args.ref_lat, args.ref_lon, args.output_file)
|