460 lines
14 KiB
Python
Executable file
460 lines
14 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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REF_LATITUDE = 49.58666
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REF_LONGITUDE = 11.01250
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# REF_LATITUDE = -30
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# REF_LONGITUDE = 90
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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 random_country_color():
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h = random.random()
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s = 0.7
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v = 0.8
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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 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 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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# 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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ref_lat = ref_lat * np.pi / 180
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ref_lon = ref_lon * np.pi / 180
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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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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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# 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, R)
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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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# 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 {
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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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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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for k, v in simplegeodata.items():
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print(f"Exporting {k}…", file=sys.stderr)
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color = random_country_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 + R # 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, R, 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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# 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 = R * distance / d_max
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doc.add(doc.circle(center=(R, R), r=r,
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**{'class': 'dist_circle'}))
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doc.add(doc.text(f"{distance} km", (R, R-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 = R + R * np.cos(azimuth-np.pi/2)
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start_y = R + R * np.sin(azimuth-np.pi/2)
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end_x = R - R * np.cos(azimuth-np.pi/2)
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end_y = R - R * np.sin(azimuth-np.pi/2)
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doc.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*R - 10, R - 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=(R, R))
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doc.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=(R, R))
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doc.add(txt)
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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, R)
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points = np.array([x, y]).T + R
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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, R)
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points = np.array([x, y]).T + R
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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, R)
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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 + R, ty + R),
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**{'class': 'maidenhead_label',
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'font-size': font_size}))
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doc.add(group)
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"""
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for x in range(0, 26):
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for y in range(0, 26):
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sectorname = chr(ord('A')+x) + chr(ord('A')+y)
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"""
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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, :])
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pp.plot([-1, 1], [0, 0], 'k', linewidth=0.5)
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pp.plot([0, 0], [-1, 1], 'k', linewidth=0.5)
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t = np.linspace(-np.pi, np.pi, 256)
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ct, st = np.cos(t), np.sin(t)
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pp.plot(ct, st, 'k', linewidth=0.5)
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U = 40075
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for distance in np.arange(0, U/2, 2000):
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f = distance / (U/2)
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pp.plot(f*ct, f*st, 'k', linewidth=0.2)
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pp.axis('equal')
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pp.show()
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if __name__ == "__main__":
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parser = argparse.ArgumentParser(
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description="Render an azimuthal equidistant map of the world " +
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"centered on the given point")
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parser.add_argument(metavar='ref-lat', type=float, dest='ref_lat',
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help='Reference Latitude')
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parser.add_argument(metavar='ref-lon', type=float, dest='ref_lon',
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help='Reference Longitude')
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parser.add_argument('-o', '--output-file', type=argparse.FileType('w'),
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help='The output SVG file (default: print to stdout)',
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default=sys.stdout)
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args = parser.parse_args()
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render(args.ref_lat, args.ref_lon, args.output_file)
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