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qsomap/qsomap.py

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#!/usr/bin/env python3
import sys
import svgwrite
import numpy as np
import matplotlib.pyplot as pp
from matplotlib.colors import hsv_to_rgb
import json
import random
import argparse
REF_LATITUDE = 49.58666
REF_LONGITUDE = 11.01250
# REF_LATITUDE = -30
# REF_LONGITUDE = 90
def map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R=1):
""" Azimuthal equidistant projection.
This function takes a point to map in latitude/longitude format as well as
a reference point which becomes the "center" of the map.
It then projects the point into the 2D plane such that the distance from
the center is proportional to the distance on the Great Circle through the
projected and the reference point. The angle represents the azimuthal
direction of the projected point.
Args:
lat(numpy.array): Latitudes of the point to project.
lon(numpy.array): Longitudes of the point to project.
ref_lat(float): Latitude of the reference point.
ref_lon(float): Longitude of the reference point.
R(float): Radius (scale) of the map.
Returns:
x(numpy.array): The calculated x coordinates.
y(numpy.array): The calculated y coordinates.
"""
dlon = lon - ref_lon
rho_linear_norm = np.arccos(np.sin(ref_lat) * np.sin(lat)
+ np.cos(ref_lat)
* np.cos(lat) * np.cos(dlon)) / np.pi
rho = R * rho_linear_norm
theta = np.arctan2(np.cos(lat) * np.sin(dlon),
(np.cos(ref_lat) * np.sin(lat)
- np.sin(ref_lat) * np.cos(lat)
* np.cos(dlon)))
x = rho * np.sin(theta)
y = -rho * np.cos(theta)
return x, y
def random_country_color():
h = random.random()
s = 0.7
v = 0.8
r, g, b = [int(255.99*x) for x in hsv_to_rgb([h, s, v])]
return f"#{r:02x}{g:02x}{b:02x}"
def is_point_in_polygon(point, polygon):
# Idea: draw an infinite line from the test point along the x axis to the
# right. Then check how many polygon edges this line intersects. If the
# number is even, the point is outside the polygon.
edges = [] # list of lists, containing two points each
for i in range(len(polygon)-1):
edges.append([polygon[i], polygon[i+1]])
# the closing edge
edges.append([polygon[-1], polygon[0]])
num_intersects = 0
test_x, test_y = point
for edge in edges:
start_x = edge[0][0]
start_y = edge[0][1]
end_x = edge[1][0]
end_y = edge[1][1]
# quick exclusion tests
if start_x < test_x and end_x < test_x:
continue # edge is completely left of the test point
if start_y < test_y and end_y < test_y:
continue # edge is completely below the test point
if start_y > test_y and end_y > test_y:
continue # edge is completely above the test point
# calculate the x coordinate where the edge intersects the whole
# horizontal line
intersect_x = start_x + (end_x - start_x) \
* (test_y - start_y) \
/ (end_y - start_y)
if intersect_x > test_x:
# we found an intersection!
num_intersects += 1
if num_intersects % 2 == 0:
return False # even number of intersects -> outside polygon
else:
return True # odd number of intersects -> inside polygon
def svg_make_inverse_country_path(doc, map_radius, polygon, **kwargs):
# build a closed circle path covering the whole map
commands = [f"M 0, {map_radius}",
f"a {map_radius},{map_radius} 0 1,0 {map_radius*2},0",
f"a {map_radius},{map_radius} 0 1,0 {-map_radius*2},0",
"z"]
# "subtract" the country polygon
commands.append(f"M {polygon[0][0]} {polygon[0][1]}")
# add lines for each polygon point
for point in polygon[1:]:
commands.append(f"L {point[0]} {point[1]}")
# ensure straight closing line
commands.append(f"L {polygon[0][0]} {polygon[0][1]}")
# close the inner path
commands.append("z")
return doc.path(commands, **kwargs)
def render(ref_lat, ref_lon, output_stream):
random.seed(0)
print("Loading Geodata…", file=sys.stderr)
with open('geo-countries/data/countries.geojson', 'r') as jfile:
geojson = json.load(jfile)
print("Finding boundaries…", file=sys.stderr)
# key: 3-letter country identifier
# data: {full_name,
# numpy.array(coordinates),
# numpy.array(proj_coordinates)}.
# coordinates is a list of 2xN arrays, where N is the number of points.
# Row 0 contains the longitude, Row 1 the latitude.
# proj_coordinates is a list of 2xN arrays, where N is the number of
# points. Row 0 contains the projected x, Row 1 the projected y.
simplegeodata = {}
features = geojson['features']
for feature in features:
name = feature['properties']['ADMIN']
key = feature['properties']['ISO_A2']
# handle duplicate keys (can happen for small countries)
if key in simplegeodata.keys():
key = name
print(f"Preparing {key} ({name})…", file=sys.stderr)
multipoly = feature['geometry']['coordinates']
conv_polys = []
for poly in multipoly:
for subpoly in poly:
coords_list = [] # list of lists
assert(len(subpoly[0]) == 2)
coords_list += subpoly
# convert coordinates to numpy array and radians
coords = np.array(coords_list).T * np.pi / 180
conv_polys.append(coords)
simplegeodata[key] = {"name": name, "coordinates": conv_polys}
ref_lat = ref_lat * np.pi / 180
ref_lon = ref_lon * np.pi / 180
antipodal_lat = -ref_lat
antipodal_lon = ref_lon + np.pi
if antipodal_lon > np.pi:
antipodal_lon -= 2*np.pi
R = 500
"""
# Override data with test coordinate system
coords = []
N = 128
# constant-latitude circles
coords.append(np.array([np.linspace(-np.pi, np.pi, N),
np.ones(N) * np.pi/4]))
coords.append(np.array([np.linspace(-np.pi, np.pi, N),
np.ones(N) * 0]))
coords.append(np.array([np.linspace(-np.pi, np.pi, N),
np.ones(N) * -np.pi/4]))
# constant-longitude half-circles
coords.append(np.array([np.ones(N) * -4*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * -3*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * -2*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * -1*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * 0*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * 1*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * 2*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
coords.append(np.array([np.ones(N) * 3*np.pi/4,
np.linspace(-np.pi/2, np.pi/2, N)]))
simplegeodata = {"XY": {'name': 'test', 'coordinates': coords}}
"""
# apply azimuthal equidistant projection
for k, v in simplegeodata.items():
proj_polys = []
for poly in v['coordinates']:
lat = poly[1, :]
lon = poly[0, :]
x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R)
coords = np.array([x, y])
# remove any points that contain a NaN coordinate
coords = coords[:, np.any(np.invert(np.isnan(coords)), axis=0)]
proj_polys.append(coords)
v['proj_coordinates'] = proj_polys
# generate the SVG
doc = svgwrite.Drawing("/tmp/test.svg", size=(2*R, 2*R))
doc.defs.add(doc.style("""
.country {
stroke: black;
stroke-width: 0.01px;
}
.dist_circle_label, .azimuth_line_label {
font-size: 3px;
font-family: sans-serif;
text-anchor: middle;
}
.dist_circle, .azimuth_line {
fill: none;
stroke: black;
stroke-width: 0.1px;
}
.maidenhead_line {
fill: none;
stroke: red;
stroke-width: 0.1px;
opacity: 0.5;
}
.maidenhead_label {
font-family: sans-serif;
dominant-baseline: middle;
text-anchor: middle;
fill: red;
opacity: 0.25;
}
"""))
doc.add(doc.circle(center=(R, R), r=R, fill='#ddeeff',
stroke_width=1, stroke='black'))
for k, v in simplegeodata.items():
print(f"Exporting {k}…", file=sys.stderr)
color = random_country_color()
group = doc.g()
for i in range(len(v['proj_coordinates'])):
poly = v['proj_coordinates'][i]
points = poly.T + R # shift to the center of the drawing
# check if the antipodal point is inside this polygon. If so, it
# needs to be "inverted", i.e. subtracted from the surrounding map
# circle.
if is_point_in_polygon((antipodal_lon, antipodal_lat),
v['coordinates'][i].T):
print("!!! Found polygon containing the antipodal point!",
file=sys.stderr)
obj = svg_make_inverse_country_path(doc, R, np.flipud(points),
**{'class': 'country',
'fill': color})
else:
obj = doc.polygon(points, **{
'class': 'country',
'fill': color})
group.add(obj)
group.set_desc(title=v['name'])
doc.add(group)
# generate equidistant circles
d_max = 40075/2
for distance in [500, 1000, 2000, 3000, 4000, 5000, 6000, 8000, 10000,
12000, 14000, 16000, 18000, 20000]:
r = R * distance / d_max
doc.add(doc.circle(center=(R, R), r=r,
**{'class': 'dist_circle'}))
doc.add(doc.text(f"{distance} km", (R, R-r+5),
**{'class': 'dist_circle_label'}))
# generate azimuth lines in 30° steps
for azimuth in np.arange(0, np.pi, np.pi/6):
start_x = R + R * np.cos(azimuth-np.pi/2)
start_y = R + R * np.sin(azimuth-np.pi/2)
end_x = R - R * np.cos(azimuth-np.pi/2)
end_y = R - R * np.sin(azimuth-np.pi/2)
doc.add(doc.line((start_x, start_y), (end_x, end_y),
**{'class': 'azimuth_line'}))
azimuth_deg = int(np.round(azimuth * 180 / np.pi))
textpos = (2*R - 10, R - 2)
txt = doc.text(f"{azimuth_deg:d} °", textpos,
**{'class': 'azimuth_line_label'})
txt.rotate(azimuth_deg - 90, center=(R, R))
doc.add(txt)
txt = doc.text(f"{azimuth_deg+180:d} °", textpos,
**{'class': 'azimuth_line_label'})
txt.rotate(azimuth_deg - 90 + 180, center=(R, R))
doc.add(txt)
# generate Maidenhead locator grid (first two letters only)
group = doc.g()
N = 18 # subdivisions of Earth
resolution = 4096
for x in range(0, N):
lon = x * 2 * np.pi / N
lat = np.linspace(-np.pi/2, np.pi/2, resolution)
x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R)
points = np.array([x, y]).T + R
group.add(doc.polyline(points, **{'class': 'maidenhead_line'}))
for y in range(0, N):
lon = np.linspace(-np.pi, np.pi, resolution)
lat = y * np.pi / N - np.pi/2
x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R)
points = np.array([x, y]).T + R
group.add(doc.polyline(points, **{'class': 'maidenhead_line'}))
for x in range(0, N):
for y in range(0, N):
sectorname = chr(ord('A') + (x + N//2) % N) \
+ chr(ord('A') + y)
lon = (x + 0.5) * 2 * np.pi / N
lat = (y + 0.5) * np.pi / N - np.pi/2
tx, ty = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, R)
font_size = 10
if y == 0 or y == N-1:
font_size = 3
group.add(doc.text(sectorname, (tx + R, ty + R),
**{'class': 'maidenhead_label',
'font-size': font_size}))
doc.add(group)
"""
for x in range(0, 26):
for y in range(0, 26):
sectorname = chr(ord('A')+x) + chr(ord('A')+y)
"""
print("Writing output…", file=sys.stderr)
doc.write(output_stream, pretty=True)
return
# Debug Plot
for k, v in simplegeodata.items():
for poly in v['proj_coordinates']:
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)
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