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mapbender
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port to py3 and format with black

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Johannes Schauer Marin Rodrigues 3 years ago
parent dffa71bbdd
commit a4ced15215
Signed by: josch
GPG Key ID: F2CBA5C78FBD83E1
1 changed files with 223 additions and 169 deletions
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mapbender.py
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@ -20,56 +20,80 @@ from math import sqrt
import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
from itertools import tee, izip
from itertools import tee
from matplotlib.patches import Polygon
from matplotlib.collections import PatchCollection
import matplotlib
from PIL import Image
def y2lat(a):
return 180.0/math.pi*(2.0*math.atan(math.exp(a*math.pi/180.0))-math.pi/2.0)
return (
180.0
/ math.pi
* (2.0 * math.atan(math.exp(a * math.pi / 180.0)) - math.pi / 2.0)
)
def lat2y(a):
return 180.0/math.pi*math.log(math.tan(math.pi/4.0+a*(math.pi/180.0)/2.0))
return (
180.0
/ math.pi
* math.log(math.tan(math.pi / 4.0 + a * (math.pi / 180.0) / 2.0))
)
def pairwise(iterable):
"s -> (s0,s1), (s1,s2), (s2,s3), ..."
a, b = tee(iterable, 2)
next(b, None)
return izip(a, b)
return zip(a, b)
def triplewise(iterable):
"s -> (s0,s1,s2), (s1,s2,s3), (s2,s3,s4), ..."
a,b,c = tee(iterable, 3)
a, b, c = tee(iterable, 3)
next(b, None)
next(c, None)
next(c, None)
return izip(a,b,c)
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;
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 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]
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
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
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)
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
#
@ -88,134 +112,138 @@ def ptInQuadrilateral(p, p0, p1, p2, p3):
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
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
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
a2 = g * d - l * e
b2 = n + j * d - i * e
c2 = h * j - m * i
s = []
if a1 == 0:
s.append(-c1/b1)
s.append(-c1 / b1)
else:
r1 = b1*b1-4*a1*c1
r1 = b1 * b1 - 4 * a1 * c1
if r1 >= 0:
r11 = (-b1+sqrt(r1))/(2*a1)
r11 = (-b1 + sqrt(r1)) / (2 * a1)
if -0.0000000001 <= r11 <= 1.0000000001:
s.append(r11)
r12 = (-b1-sqrt(r1))/(2*a1)
r12 = (-b1 - sqrt(r1)) / (2 * a1)
if -0.0000000001 <= r12 <= 1.0000000001:
s.append(r12)
t = []
if a2 == 0:
t.append(-c2/b2)
t.append(-c2 / b2)
else:
r2 = b2*b2-4*a2*c2
r2 = b2 * b2 - 4 * a2 * c2
if r2 >= 0:
r21 = (-b2+sqrt(r2))/(2*a2)
r21 = (-b2 + sqrt(r2)) / (2 * a2)
if -0.0000000001 <= r21 <= 1.0000000001:
t.append(r21)
r22 = (-b2-sqrt(r2))/(2*a2)
r22 = (-b2 - sqrt(r2)) / (2 * a2)
if -0.0000000001 <= r22 <= 1.0000000001:
t.append(r22)
if not s or not t:
return [],[]
return [], []
if len(s) == 1 and len(t) == 2:
s = [s[0],s[0]]
s = [s[0], s[0]]
if len(s) == 2 and len(t) == 1:
t = [t[0],t[0]]
t = [t[0], t[0]]
return s, t
def main(x,y,width,smoothing,subdiv):
halfwidth = width/2.0
tck,u = interpolate.splprep([x,y],s=smoothing)
unew = np.linspace(0,1.0,subdiv+1)
out = interpolate.splev(unew,tck)
def main(x, y, width, smoothing, subdiv):
halfwidth = width / 2.0
tck, u = interpolate.splprep([x, y], s=smoothing)
unew = np.linspace(0, 1.0, subdiv + 1)
out = interpolate.splev(unew, tck)
heights = []
offs = []
height = 0.0
for (ax,ay),(bx,by) in pairwise(zip(*out)):
s = ax-bx
t = ay-by
l = sqrt(s*s+t*t)
for (ax, ay), (bx, by) in pairwise(list(zip(*out))):
s = ax - bx
t = ay - by
l = sqrt(s * s + t * t)
offs.append(height)
height += l
heights.append(l)
# the border of the first segment is just perpendicular to the path
cx = -out[1][1]+out[1][0]
cy = out[0][1]-out[0][0]
cl = sqrt(cx*cx+cy*cy)/halfwidth
dx = out[1][1]-out[1][0]
dy = -out[0][1]+out[0][0]
dl = sqrt(dx*dx+dy*dy)/halfwidth
px = [out[0][0]+cx/cl]
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(zip(*out)):
cx = -out[1][1] + out[1][0]
cy = out[0][1] - out[0][0]
cl = sqrt(cx * cx + cy * cy) / halfwidth
dx = out[1][1] - out[1][0]
dy = -out[0][1] + out[0][0]
dl = sqrt(dx * dx + dy * dy) / halfwidth
px = [out[0][0] + cx / cl]
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))):
# get adjacent line segment vectors
ax = ux-ubx
ay = uy-uby
bx = uax-ux
by = uay-uy
ax = ux - ubx
ay = uy - uby
bx = uax - ux
by = uay - uy
# normalize length
al = sqrt(ax*ax+ay*ay)
bl = sqrt(bx*bx+by*by)
ax = ax/al
ay = ay/al
bx = bx/bl
by = by/bl
al = sqrt(ax * ax + ay * ay)
bl = sqrt(bx * bx + by * by)
ax = ax / al
ay = ay / al
bx = bx / bl
by = by / bl
# get vector perpendicular to sum
cx = -ay-by
cy = ax+bx
cl = sqrt(cx*cx+cy*cy)/halfwidth
px.append(ux+cx/cl)
py.append(uy+cy/cl)
cx = -ay - by
cy = ax + bx
cl = sqrt(cx * cx + cy * cy) / halfwidth
px.append(ux + cx / cl)
py.append(uy + cy / cl)
# and in the other direction
dx = ay+by
dy = -ax-bx
dl = sqrt(dx*dx+dy*dy)/halfwidth
qx.append(ux+dx/dl)
qy.append(uy+dy/dl)
dx = ay + by
dy = -ax - bx
dl = sqrt(dx * dx + dy * dy) / halfwidth
qx.append(ux + dx / dl)
qy.append(uy + dy / dl)
# the border of the last segment is just perpendicular to the path
cx = -out[1][-1]+out[1][-2]
cy = out[0][-1]-out[0][-2]
cl = sqrt(cx*cx+cy*cy)/halfwidth
dx = out[1][-1]-out[1][-2]
dy = -out[0][-1]+out[0][-2]
dl = sqrt(dx*dx+dy*dy)/halfwidth
px.append(out[0][-1]+cx/cl)
py.append(out[1][-1]+cy/cl)
qx.append(out[0][-1]+dx/dl)
qy.append(out[1][-1]+dy/dl)
cx = -out[1][-1] + out[1][-2]
cy = out[0][-1] - out[0][-2]
cl = sqrt(cx * cx + cy * cy) / halfwidth
dx = out[1][-1] - out[1][-2]
dy = -out[0][-1] + out[0][-2]
dl = sqrt(dx * dx + dy * dy) / halfwidth
px.append(out[0][-1] + cx / cl)
py.append(out[1][-1] + cy / cl)
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(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)
for (p3x, p3y, p2x, p2y), (p0x, p0y, p1x, p1y) in pairwise(
list(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 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):
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"
print("point found in two quads")
return None
containingquad.append(found[0])
else:
@ -223,35 +251,45 @@ def main(x,y,width,smoothing,subdiv):
# 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):
for i, q in enumerate(containingquad):
if q != None:
break
# find the last missing ones
for j,q in izip(xrange(len(containingquad)-1, -1, -1), reversed(containingquad)):
for j, q in zip(range(len(containingquad) - 1, -1, -1), reversed(containingquad)):
if q != None:
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]
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"
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))
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)
assert len(out[0]) == len(out[1]) == len(px) == len(py) == len(qx) == len(qy) == len(quads)+1 == len(heights)+1 == len(offs)+1
for (rx,ry),i in zip(zip(x,y),containingquad):
assert (
len(out[0])
== len(out[1])
== len(px)
== len(py)
== len(qx)
== len(qy)
== len(quads) + 1
== len(heights) + 1
== len(offs) + 1
)
for (rx, ry), i in zip(list(zip(x, y)), containingquad):
if i == None:
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
(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]
@ -259,13 +297,13 @@ def main(x,y,width,smoothing,subdiv):
else:
s = s[0]
t = t[0]
u = s*width
v = offs[i]+t*heights[i]
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):
# 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
@ -283,74 +321,90 @@ def main(x,y,width,smoothing,subdiv):
# 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]
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
iw, ih = im.size
data = []
for i,(off,h,(p0,p1,p2,p3)) in enumerate(zip(offs,heights,quads)):
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]
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
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])
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=(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])))
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]))),Image.MESH,data,Image.BICUBIC)
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 = (
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])),
)
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]))),
Image.MESH,
data,
Image.BICUBIC,
)
im_out.save("out.png")
#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')
# 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()
# 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()
# 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__':
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]
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])
exit(1)
with open(sys.argv[1]) as f:
for l in f:
a,b = l.split()
a, b = l.split()
# apply mercator projection
b = lat2y(float(b))
x.append(float(a))
@ -358,8 +412,8 @@ if __name__ == '__main__':
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]:
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

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