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improved algorithm

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This commit is contained in:
Johannes Schauer Marin Rodrigues 2021-10-14 20:43:32 +02:00
parent a4ced15215
commit d3692ff587
Signed by: josch
GPG key ID: F2CBA5C78FBD83E1
2 changed files with 359 additions and 340 deletions
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34
README.md
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@ -14,3 +14,37 @@ which will individually be transformed into rectangles which are also plotted.
On Debian systems you need the following packages:
apt-get install python python-pil python-scipy python-tk python-matplotlib python-numpy
how to setup postgresql+postgis locally without root
----------------------------------------------------
/usr/lib/postgresql/14/bin/initdb -D /tmp/postgres
/usr/lib/postgresql/14/bin/postgres --port=5433 --unix_socket_directories=/tmp/postgres -D /tmp/postgres &
/usr/lib/postgresql/14/bin/createdb --port=5433 --host=/tmp/postgres gis
/usr/lib/postgresql/14/bin/psql --port=5433 --host=/tmp/postgres gis -c 'CREATE EXTENSION postgis;' -c 'CREATE EXTENSION hstore;'
osm2pgsql --port=5433 --host=/tmp/postgres -d gis --create --slim -G --hstore --tag-transform-script /tmp/openstreetmap-carto/openstreetmap-carto.lua -S /tmp/openstreetmap-carto/openstreetmap-carto.style ~/Downloads/map.xml
/usr/lib/postgresql/14/bin/psql --port=5433 --host=/tmp/postgres gis -f /tmp/openstreetmap-carto/indexes.sql
openstreetmap-carto:
scripts/get-external-data.py --port=5433 --host=/tmp/postgres
diff --git a/project.mml b/project.mml
index 7fb3d47..d8014f8 100644
--- a/project.mml
+++ b/project.mml
@@ -27,6 +27,8 @@ _parts:
osm2pgsql: &osm2pgsql
type: "postgis"
dbname: "gis"
+ port: "5433"
+ host: "/tmp/postgres"
key_field: ""
geometry_field: "way"
extent: "-20037508,-20037508,20037508,20037508"
# the database connection settings are part of the style xml!
carto project.mml > mapnik.xml
nik4 --url https://www.openstreetmap.org/\#map\=12/49.7731/9.6726 /tmp/openstreetmap-carto/mapnik.xml screenshot.svg

547
mapbender.py
View file

@ -1,4 +1,4 @@
#!/usr/bin/env python
#!/usr/bin/env python3
#
# Copyright (C) 2014 - 2021 Johannes Schauer Marin Rodrigues <josch@mister-muffin.de>
#
@ -15,32 +15,47 @@
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import os
import math
from math import sqrt
import numpy as np
import matplotlib.pyplot as plt
import numpy
from scipy import interpolate
from itertools import tee
from matplotlib.patches import Polygon
from matplotlib.collections import PatchCollection
import matplotlib
from PIL import Image
from PIL import Image, ImageDraw
import urllib.request
import matplotlib.path
import matplotlib.transforms
import xml.etree.ElementTree as ET
TILESIZE = 256
EARTHRADIUS = 6378137
def y2lat(a):
def haversine(lon1, lat1, lon2, lat2):
lon1 = math.radians(lon1)
lat1 = math.radians(lat1)
lon2 = math.radians(lon2)
lat2 = math.radians(lat2)
dlon = lon2 - lon1
dlat = lat2 - lat1
a = (
math.sin(dlat / 2) ** 2
+ math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2) ** 2
)
return EARTHRADIUS * 2 * math.asin(math.sqrt(a))
def lat2y(a, zoom):
return (
180.0
/ math.pi
* (2.0 * math.atan(math.exp(a * math.pi / 180.0)) - math.pi / 2.0)
(1.0 - math.asinh(math.tan(math.radians(a))) / math.pi)
/ 2.0
* 2 ** zoom
* TILESIZE
)
def lat2y(a):
return (
180.0
/ math.pi
* math.log(math.tan(math.pi / 4.0 + a * (math.pi / 180.0) / 2.0))
)
def lon2x(a, zoom):
return (a + 180.0) / 360.0 * (2 ** zoom * TILESIZE)
def pairwise(iterable):
@ -59,120 +74,54 @@ def triplewise(iterable):
return zip(a, b, c)
# using barycentric coordinates
def ptInTriangle(p, p0, p1, p2):
A = 0.5 * (
-p1[1] * p2[0]
+ p0[1] * (-p1[0] + p2[0])
+ p0[0] * (p1[1] - p2[1])
+ p1[0] * p2[1]
)
sign = -1 if A < 0 else 1
s = (
p0[1] * p2[0] - p0[0] * p2[1] + (p2[1] - p0[1]) * p[0] + (p0[0] - p2[0]) * p[1]
) * sign
t = (
p0[0] * p1[1] - p0[1] * p1[0] + (p0[1] - p1[1]) * p[0] + (p1[0] - p0[0]) * p[1]
) * sign
return s >= 0 and t >= 0 and (s + t) <= 2 * A * sign
def intersects(p0, p1, p2, p3):
s10_x = p1[0] - p0[0]
s10_y = p1[1] - p0[1]
s32_x = p3[0] - p2[0]
s32_y = p3[1] - p2[1]
denom = s10_x * s32_y - s32_x * s10_y
if denom == 0:
return False # collinear
denom_is_positive = denom > 0
s02_x = p0[0] - p2[0]
s02_y = p0[1] - p2[1]
s_numer = s10_x * s02_y - s10_y * s02_x
if (s_numer < 0) == denom_is_positive:
return False # no collision
t_numer = s32_x * s02_y - s32_y * s02_x
if (t_numer < 0) == denom_is_positive:
return False # no collision
if (s_numer > denom) == denom_is_positive or (t_numer > denom) == denom_is_positive:
return False # no collision
return True
def getxing(p0, p1, p2, p3):
ux = p1[0] - p0[0]
uy = p1[1] - p0[1]
vx = p2[0] - p3[0]
vy = p2[1] - p3[1]
# get multiplicity of u at which u meets v
a = vy * ux - vx * uy
if a == 0:
# lines are parallel and never meet
return None
s = (vy * (p3[0] - p0[0]) + vx * (p0[1] - p3[1])) / a
if 0.0 < s < 1.0:
return (p0[0] + s * ux, p0[1] + s * uy)
else:
return None
# the line p0-p1 is the upper normal to the path
# the line p2-p3 is the lower normal to the path
#
# | | |
# p0--------|--------p1
# | | |
# | | |
# p3--------|--------p2
# | | |
def ptInQuadrilateral(p, p0, p1, p2, p3):
# it might be that the two normals cross at some point
# in that case the two triangles are created differently
cross = getxing(p0, p1, p2, p3)
if cross:
return ptInTriangle(p, p0, cross, p3) or ptInTriangle(p, p2, cross, p1)
else:
return ptInTriangle(p, p0, p1, p2) or ptInTriangle(p, p2, p3, p0)
def get_st(Ax, Ay, Bx, By, Cx, Cy, Dx, Dy, Xx, Xy):
d = Bx - Ax - Cx + Dx
e = By - Ay - Cy + Dy
l = Dx - Ax
g = Dy - Ay
h = Cx - Dx
m = Cy - Dy
i = Xx - Dx
j = Xy - Dy
n = g * h - m * l
# calculation for s
a1 = m * d - h * e
b1 = n - j * d + i * e
c1 = l * j - g * i
# calculation for t
a2 = g * d - l * e
b2 = n + j * d - i * e
c2 = h * j - m * i
s = []
if a1 == 0:
s.append(-c1 / b1)
else:
r1 = b1 * b1 - 4 * a1 * c1
if r1 >= 0:
r11 = (-b1 + sqrt(r1)) / (2 * a1)
if -0.0000000001 <= r11 <= 1.0000000001:
s.append(r11)
r12 = (-b1 - sqrt(r1)) / (2 * a1)
if -0.0000000001 <= r12 <= 1.0000000001:
s.append(r12)
t = []
if a2 == 0:
t.append(-c2 / b2)
else:
r2 = b2 * b2 - 4 * a2 * c2
if r2 >= 0:
r21 = (-b2 + sqrt(r2)) / (2 * a2)
if -0.0000000001 <= r21 <= 1.0000000001:
t.append(r21)
r22 = (-b2 - sqrt(r2)) / (2 * a2)
if -0.0000000001 <= r22 <= 1.0000000001:
t.append(r22)
if not s or not t:
return [], []
if len(s) == 1 and len(t) == 2:
s = [s[0], s[0]]
if len(s) == 2 and len(t) == 1:
t = [t[0], t[0]]
return s, t
def main(x, y, width, smoothing, subdiv):
def main(path, width, subdiv, zoom):
halfwidth = width / 2.0
tck, u = interpolate.splprep([x, y], s=smoothing)
unew = np.linspace(0, 1.0, subdiv + 1)
found_smoothing = False
for smoothing in [2 ** i for i in range(30)]:
tck, u = interpolate.splprep(list(zip(*path)), s=smoothing)
unew = numpy.linspace(0, 1.0, subdiv + 1)
out = interpolate.splev(unew, tck)
# prepend and append a segment
out = (
[2 * out[0][0] - out[0][1]] + list(out[0]) + [2 * out[0][-1] - out[0][-2]],
[2 * out[1][0] - out[1][1]] + list(out[1]) + [2 * out[1][-1] - out[1][-2]],
)
heights = []
offs = []
height = 0.0
for (ax, ay), (bx, by) in pairwise(list(zip(*out))):
for (ax, ay), (bx, by) in pairwise(zip(*out)):
s = ax - bx
t = ay - by
l = sqrt(s * s + t * t)
@ -190,7 +139,7 @@ def main(x, y, width, smoothing, subdiv):
py = [out[1][0] + cy / cl]
qx = [out[0][0] + dx / dl]
qy = [out[1][0] + dy / dl]
for (ubx, uby), (ux, uy), (uax, uay) in triplewise(list(zip(*out))):
for (ubx, uby), (ux, uy), (uax, uay) in triplewise(zip(*out)):
# get adjacent line segment vectors
ax = ux - ubx
ay = uy - uby
@ -227,52 +176,48 @@ def main(x, y, width, smoothing, subdiv):
qx.append(out[0][-1] + dx / dl)
qy.append(out[1][-1] + dy / dl)
quads = []
patches = []
for (p3x, p3y, p2x, p2y), (p0x, p0y, p1x, p1y) in pairwise(
list(zip(px, py, qx, qy))
):
for (p2x, p2y, p1x, p1y), (p3x, p3y, p0x, p0y) in pairwise(zip(px, py, qx, qy)):
quads.append(((p0x, p0y), (p1x, p1y), (p2x, p2y), (p3x, p3y)))
polygon = Polygon(((p0x, p0y), (p1x, p1y), (p2x, p2y), (p3x, p3y)), True)
patches.append(polygon)
containingquad = []
for pt in zip(x, y):
# for each point, find the quadrilateral that contains it
found = []
for i, (p0, p1, p2, p3) in enumerate(quads):
if ptInQuadrilateral(pt, p0, p1, p2, p3):
found.append(i)
if found:
if len(found) > 1:
print("point found in two quads")
return None
containingquad.append(found[0])
else:
containingquad.append(None)
# check if the only points for which no quad could be found are in the
# beginning or in the end
# find the first missing ones:
for i, q in enumerate(containingquad):
if q != None:
# check for convex quads (sides intersect)
have_convex = False
for (p0, p1, p2, p3) in quads:
if intersects(p0, p3, p1, p2):
have_convex = True
break
# find the last missing ones
for j, q in zip(range(len(containingquad) - 1, -1, -1), reversed(containingquad)):
if q != None:
if have_convex:
continue
## check for quads that look too much like a triangle
# have_triangle = False
# for ((p00, p01), (p10, p11), (p20, p21), (p30, p31)) in quads:
# len1 = sqrt((p10-p00)**2+(p11-p01)**2)
# len2 = sqrt((p30-p20)**2+(p31-p21)**2)
# if len1/len2 > 100:
# have_triangle = True
# break
# if len2/len1 < 1/100:
# have_triangle = True
# break
# if have_triangle:
# continue
# draw
polygon = []
for ((p00, p01), (p10, p11), (p20, p21), (p30, p31)) in quads:
polygon.append((p10, p11))
polygon.append((p00, p01))
for ((p00, p01), (p10, p11), (p20, p21), (p30, p31)) in reversed(quads):
polygon.append((p30, p31))
polygon.append((p20, p21))
polygon.append(polygon[0])
# check if path is inside polygon
if matplotlib.path.Path(polygon).contains_path(
matplotlib.path.Path(path)
):
found_smoothing = True
break
# remove the first and last missing ones
if i != 0 or j != len(containingquad) - 1:
containingquad = containingquad[i : j + 1]
x = x[i : j + 1]
y = y[i : j + 1]
# check if there are any remaining missing ones:
if None in containingquad:
print("cannot find quad for point")
return None
for off, h in zip(offs, heights):
targetquad = ((0, off + h), (width, off + h), (width, off), (0, off))
patches.append(Polygon(targetquad, True))
tx = []
ty = []
assert len(containingquad) == len(x) == len(y)
if not found_smoothing:
print("cannot find smoothing")
exit(1)
assert (
len(out[0])
== len(out[1])
@ -284,136 +229,176 @@ def main(x, y, width, smoothing, subdiv):
== len(heights) + 1
== len(offs) + 1
)
for (rx, ry), i in zip(list(zip(x, y)), containingquad):
if i == None:
minx = math.inf
maxx = -1
miny = math.inf
maxy = -1
for (xi, yi) in polygon:
if xi < minx:
minx = xi
if xi > maxx:
maxx = xi
if yi < miny:
miny = yi
if yi > maxy:
maxy = yi
im1 = Image.new("RGB", (int(maxx - minx), int(maxy - miny)))
im2 = Image.new("RGB", (int(maxx - minx), int(maxy - miny)))
opener = urllib.request.build_opener()
opener.addheaders = [("User-agent", "mapbender")]
urllib.request.install_opener(opener)
todl = []
for i in range(int(minx / TILESIZE) - 1, int(maxx / TILESIZE) + 2):
for j in range(int(miny / TILESIZE) - 1, int(maxy / TILESIZE) + 2):
os.makedirs("%d/%d" % (zoom, i), exist_ok=True)
fname = "%d/%d/%d.png" % (zoom, i, j)
if not matplotlib.path.Path(numpy.array(polygon)).intersects_bbox(
matplotlib.transforms.Bbox(
[
(i * TILESIZE, j * TILESIZE),
(
(i + 1) * TILESIZE,
(j + 1) * TILESIZE,
),
]
)
):
continue
(ax, ay), (bx, by), (cx, cy), (dx, dy) = quads[i]
s, t = get_st(ax, ay, bx, by, cx, cy, dx, dy, rx, ry)
# if more than one solution, take second
# TODO: investigate if this is always the right solution
if len(s) != 1 or len(t) != 1:
s = s[1]
t = t[1]
else:
s = s[0]
t = t[0]
u = s * width
v = offs[i] + t * heights[i]
tx.append(u)
ty.append(v)
# sx = []
# sy = []
# for ((x1,y1),(x2,y2)),((ax,ay),(bx,by),(cx,cy),(dx,dy)),off,h in zip(pairwise(zip(*out)),quads,offs,heights):
# s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x1,y1)
# if len(s) != 1 or len(t) != 1:
# return None
# u = s[0]*width
# v = off+t[0]*h
# sx.append(u)
# sy.append(v)
# s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x2,y2)
# if len(s) != 1 or len(t) != 1:
# return None
# u = s[0]*width
# v = off+t[0]*h
# sx.append(u)
# sy.append(v)
# create map with
# python -c 'import logging; logging.basicConfig(level=logging.DEBUG); from landez import ImageExporter; ie = ImageExporter(tiles_url="http://{s}.tile.opencyclemap.org/cycle/{z}/{x}/{y}.png"); ie.export_image(bbox=(8.0419921875,51.25160146817652,10.074462890625,54.03681240523652), zoomlevel=14, imagepath="image.png")'
im = Image.open("map.png")
bbox = [8.0419921875, 51.25160146817652, 10.074462890625, 54.03681240523652]
# apply mercator projection
bbox[1] = lat2y(bbox[1])
bbox[3] = lat2y(bbox[3])
iw, ih = im.size
if not os.path.exists(fname):
todl.append((i, j))
for n, (i, j) in enumerate(todl):
print("%d/%d" % (n, len(todl)))
fname = "%d/%d/%d.png" % (zoom, i, j)
urllib.request.urlretrieve(
#"https://tile.openstreetmap.org/%d/%d/%d.png" % (zoom, i, j),
#https://a.tile.thunderforest.com/cycle/17/68690/44518.png?apikey=6170aad10dfd42a38d4d8c709a53
"https://tile.thunderforest.com/cycle/%d/%d/%d.png?apikey=d8f470ce7a8e4dd0acf39cc8fd3cf979" % (zoom, i, j),
#"https://tile.thunderforest.com/outdoors/%d/%d/%d.png?apikey=d8f470ce7a8e4dd0acf39cc8fd3cf979" % (zoom, i, j),
#"https://tile.thunderforest.com/landscape/%d/%d/%d.png?apikey=d8f470ce7a8e4dd0acf39cc8fd3cf979" % (zoom, i, j),
#"https://tile.thunderforest.com/atlas/%d/%d/%d.png?apikey=d8f470ce7a8e4dd0acf39cc8fd3cf979" % (zoom, i, j),
filename=fname,
)
for i in range(int(minx / TILESIZE) - 1, int(maxx / TILESIZE) + 2):
for j in range(int(miny / TILESIZE) - 1, int(maxy / TILESIZE) + 2):
if not matplotlib.path.Path(numpy.array(polygon)).intersects_bbox(
matplotlib.transforms.Bbox(
[
(i * TILESIZE, j * TILESIZE),
(
(i + 1) * TILESIZE,
(j + 1) * TILESIZE,
),
]
)
):
continue
fname = "%d/%d/%d.png" % (zoom, i, j)
with Image.open(fname) as tile:
im1.paste(tile, (int(i * TILESIZE - minx), int(j * TILESIZE - miny)))
im2.paste(tile, (int(i * TILESIZE - minx), int(j * TILESIZE - miny)))
draw2 = ImageDraw.Draw(im2)
draw2.line([(xi - minx, yi - miny) for xi, yi in path], fill=(255, 0, 0), width=4)
draw1 = ImageDraw.Draw(im1)
draw1.line([(xi - minx, yi - miny) for xi, yi in path], fill=(255, 0, 0), width=4)
draw1.line([(xi - minx, yi - miny) for xi, yi in zip(*out)], fill=(0, 255, 0))
for ((p00, p01), (p10, p11), (p20, p21), (p30, p31)) in quads:
draw1.polygon(
[
(p00 - minx, p01 - miny),
(p10 - minx, p11 - miny),
(p20 - minx, p21 - miny),
(p30 - minx, p31 - miny),
]
)
draw1.polygon([(xi - minx, yi - miny) for xi, yi in polygon], outline=(0, 0, 255))
im1.save("out2.png")
data = []
for i, (off, h, (p0, p1, p2, p3)) in enumerate(zip(offs, heights, quads)):
# first, account for the offset of the input image
p0 = p0[0] - bbox[0], p0[1] - bbox[1]
p1 = p1[0] - bbox[0], p1[1] - bbox[1]
p2 = p2[0] - bbox[0], p2[1] - bbox[1]
p3 = p3[0] - bbox[0], p3[1] - bbox[1]
# PIL expects coordinates in counter clockwise order
p1, p3 = p3, p1
# x lon
# ----- = -----
# w bbox[2]-bbox[0]
# translate to pixel coordinates
p0 = (iw * p0[0]) / (bbox[2] - bbox[0]), (ih * p0[1]) / (bbox[3] - bbox[1])
p1 = (iw * p1[0]) / (bbox[2] - bbox[0]), (ih * p1[1]) / (bbox[3] - bbox[1])
p2 = (iw * p2[0]) / (bbox[2] - bbox[0]), (ih * p2[1]) / (bbox[3] - bbox[1])
p3 = (iw * p3[0]) / (bbox[2] - bbox[0]), (ih * p3[1]) / (bbox[3] - bbox[1])
# PIL starts coordinate system at the upper left corner, swap y coord
p0 = int(p0[0]), int(ih - p0[1])
p1 = int(p1[0]), int(ih - p1[1])
p2 = int(p2[0]), int(ih - p2[1])
p3 = int(p3[0]), int(ih - p3[1])
box = (
data.append(
(
(
0,
int(ih * (height - off - h) / (bbox[3] - bbox[1])),
int(iw * width / (bbox[2] - bbox[0])),
int(ih * (height - off) / (bbox[3] - bbox[1])),
int(height - offs[i] - heights[i]),
int(width),
int(height - offs[i]),
),
(
p0[0] - minx,
p0[1] - miny,
p1[0] - minx,
p1[1] - miny,
p2[0] - minx,
p2[1] - miny,
p3[0] - minx,
p3[1] - miny,
),
)
quad = (p0[0], p0[1], p1[0], p1[1], p2[0], p2[1], p3[0], p3[1])
data.append((box, quad))
im_out = im.transform(
(int(iw * width / (bbox[2] - bbox[0])), int(ih * height / (bbox[3] - bbox[1]))),
)
im_out = im2.transform(
(int(width), int(height)),
Image.MESH,
data,
Image.BICUBIC,
)
im_out.save("out.png")
im_out.save("out.jpg", quality=95)
# np.random.seed(seed=0)
# colors = 100*np.random.rand(len(patches)//2)+100*np.random.rand(len(patches)//2)
# p = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=0.4)
# p.set_array(np.array(colors))
# plt.figure()
# plt.axes().set_aspect('equal')
##plt.axhspan(0, height, xmin=0, xmax=width)
# fig, ax = plt.subplots()
##ax.add_collection(p)
# ax.set_aspect('equal')
# plt.axis((0,width,0,height))
# plt.imshow(np.asarray(im_out),extent=[0,width,0,height])
# plt.imshow(np.asarray(im),extent=[bbox[0],bbox[2],bbox[1],bbox[3]])
# plt.plot(x,y,out[0],out[1],px,py,qx,qy,tx,ty)
# plt.show()
return True
if __name__ == "__main__":
x = []
y = []
import sys
if len(sys.argv) != 5:
print("usage: %s data.csv width smoothing N" % sys.argv[0])
print("")
print(
" data.csv whitespace delimited lon/lat pairs of points along the path"
)
print(" width width of the resulting map in degrees")
print(
" smoothing curve smoothing from 0 (exact fit) to higher values (looser fit)"
)
print(" N amount of quads to split the path into")
print("")
print(" example usage:")
print(" %s Weser-Radweg-Hauptroute.csv 0.286 6 20" % sys.argv[0])
if len(sys.argv) != 4:
print("usage: %s data.gpx mapwidth paperwidth" % sys.argv[0])
exit(1)
zoom = 10
latmin = math.inf
latmax = -1
path = []
with open(sys.argv[1]) as f:
for l in f:
a, b = l.split()
root = ET.parse(f)
for trkpt in root.findall(
"./gpx:trk/gpx:trkseg/gpx:trkpt",
{"gpx": "http://www.topografix.com/GPX/1/1"},
):
lat = float(trkpt.attrib["lat"])
lon = float(trkpt.attrib["lon"])
if lat < latmin:
latmin = lat
if lat > latmax:
latmax = lat
# apply mercator projection
b = lat2y(float(b))
x.append(float(a))
y.append(b)
width = float(sys.argv[2])
smoothing = float(sys.argv[3])
N = int(sys.argv[4])
main(x, y, width, smoothing, N)
# for smoothing in [1,2,4,8,12]:
# for subdiv in range(10,30):
# if main(x,y,width,smoothing,subdiv):
# print width,smoothing,subdiv
path.append((lon, lat))
length = 0
for (lon1, lat1), (lon2, lat2) in pairwise(path):
length += haversine(lon1, lat1, lon2, lat2)
dpi = 96 # because we use bitmap tiles instead of vectors
mapwidthm = float(sys.argv[2]) # map width in m
paperwidthm = float(sys.argv[3]) # paper width in m
earth = 6378137 # earth equator radius in m
widthpx = dpi / 0.0254 * paperwidthm
zoom = math.ceil(
math.log2(
2
* math.pi
* earth
* math.cos(math.radians((latmax + latmin) / 2))
* widthpx
/ (mapwidthm * TILESIZE)
)
)
subdiv = math.ceil(4*length/mapwidthm)
print("zoom:", zoom)
print("length:", length)
print("subdiv:", subdiv)
path = [(lon2x(lon, zoom), lat2y(lat, zoom)) for lon, lat in path]
main(path, widthpx, subdiv, zoom)