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bend raster map

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josch 2014-04-02 16:39:22 +02:00
parent 54ec6a7b6c
commit 437de19643
1 changed files with 127 additions and 97 deletions
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224
fitbspline.py
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@ -1,6 +1,7 @@
#!/usr/bin/env python
import sys
import math
from math import sqrt
import numpy as np
import matplotlib.pyplot as plt
@ -9,6 +10,13 @@ from itertools import tee, izip
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)
def lat2y(a):
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), ..."
@ -43,7 +51,7 @@ def getxing(p0, p1, p2, p3):
# lines are parallel and never meet
return None
s = (vy*(p3[0]-p0[0])+vx*(p0[1]-p3[1]))/a
if s < 1.0:
if 0.0 < s < 1.0:
return (p0[0]+s*ux, p0[1]+s*uy)
else:
return None
@ -61,11 +69,10 @@ 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)
return ptInTriangle(p, p0, p1, p2) or ptInTriangle(p, p2, p3, p0)
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
@ -110,38 +117,17 @@ def get_st(Ax,Ay,Bx,By,Cx,Cy,Dx,Dy,Xx,Xy):
if -0.0000000001 <= r22 <= 1.0000000001:
t.append(r22)
if not s or not t:
return None
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 find_coeffs(pa, pb):
matrix = []
for p1, p2 in zip(pa, pb):
matrix.append([p1[0], p1[1], 1, 0, 0, 0, -p2[0]*p1[0], -p2[0]*p1[1]])
matrix.append([0, 0, 0, p1[0], p1[1], 1, -p2[1]*p1[0], -p2[1]*p1[1]])
A = np.matrix(matrix, dtype=np.float)
B = np.array(pb).reshape(8)
#res = np.dot(np.linalg.inv(A), B)
res = np.dot(np.linalg.inv(A.T * A) * A.T, B)
return np.array(res).reshape(8)
def main():
width = 2/5.0
def main(x,y,width,smoothing,subdiv):
halfwidth = width/2.0
x = []
y = []
with open(sys.argv[1]) as f:
for l in f:
a,b = l.split()
x.append(float(a))
y.append(float(b))
tck,u = interpolate.splprep([x,y],s=10)
unew = np.arange(0,1.1,0.1)
tck,u = interpolate.splprep([x,y],s=smoothing)
unew = np.linspace(0,1.0,subdiv+1)
out = interpolate.splev(unew,tck)
heights = []
offs = []
@ -202,7 +188,6 @@ def main():
qy.append(out[1][-1]+dy/dl)
quads = []
patches = []
#for (p0x,p0y,p1x,p1y),(p3x,p3y,p2x,p2y) in pairwise(zip(px,py,qx,qy)):
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)
@ -215,77 +200,77 @@ def main():
if ptInQuadrilateral(pt,p0,p1,p2,p3):
found.append(i)
if found:
if len(found) > 2:
print found
containingquad.append(found)
if len(found) > 1:
print "point found in two quads"
return None
containingquad.append(found[0])
else:
print "can't find quad for point"
containingquad.append(None)
#exit(1)
print containingquad
trans = []
print width, height
srcquads = []
for off,h,srcquad in zip(offs,heights,quads):
#targetquad = ((0,height-off),(width,height-off),(width,height-off-h),(0,height-off-h))
# 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:
break
# find the last missing ones
for j,q in izip(xrange(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]
# 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))
trans.append(find_coeffs(srcquad,targetquad))
patches.append(Polygon(targetquad,True))
tx = []
ty = []
#targetquad = (0,height),(width,height),(width,0),(0,0)
#srcquad = (min(x),max(y)),(max(x),max(y)),(max(x),min(y)),(min(x),min(y))
#trans = find_coeffs(srcquad,targetquad)
#for (rx,ry) in zip(x,y):
# a,b,c,d,e,f,g,h = trans
# u = (a*rx + b*ry + c)/(g*rx + h*ry + 1)
# v = (d*rx + e*ry + f)/(g*rx + h*ry + 1)
# tx.append(u)
# ty.append(v)
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 == len(trans)+1
for (rx,ry),l in zip(zip(x,y),containingquad):
if not l:
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):
if i == None:
continue
for i in l[:1]:
(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 len(s) != 1 or len(t) != 1:
print "fail"
exit(1)
#a,b,c,d,e,f,g,h = trans[i]
##den = -a*e+a*h*ry+b*d-b*g*ry-d*h*rx+e*g*rx
##tx.append((-b*f+b*ry+c*e-c*h*ry-e*rx+f*h*rx)/den)
##ty.append((a*f-a*ry-c*d+c*g*ry+d*rx-f*g*rx)/den)
#u = (a*rx + b*ry + c)/(g*rx + h*ry + 1)
#v = (d*rx + e*ry + f)/(g*rx + h*ry + 1)
u = s[0]*width
v = offs[i]+t[0]*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)
(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:
print "fail"
exit(1)
#u = (a*ax + b*ay + c)/(g*ax + h*ay + 1)
#v = (d*ax + e*ay + f)/(g*ax + h*ay + 1)
u = s[0]*width
v = off+t[0]*h
sx.append(u)
sy.append(v)
#u = (a*bx + b*by + c)/(g*bx + h*by + 1)
#v = (d*bx + e*by + f)/(g*bx + h*by + 1)
s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x2,y2)
if len(s) != 1 or len(t) != 1:
print "fail"
exit(1)
u = s[0]*width
v = off+t[0]*h
sx.append(u)
sy.append(v)
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)
im1 = Image.open("out.png")
im2 = Image.open("map.png")
bbox = [8.4320068359375,51.34090729023285,9.7119140625,53.556626004824615]
bbox[1] = lat2y(bbox[1])
bbox[3] = lat2y(bbox[3])
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))
@ -295,9 +280,54 @@ def main():
fig, ax = plt.subplots()
ax.add_collection(p)
ax.set_aspect('equal')
plt.plot(x,y,out[0],out[1],px,py,qx,qy,sx,sy,tx,ty)
#plt.plot(tx,ty)
plt.imshow(np.asarray(im1),extent=[0,width,0,height])
plt.imshow(np.asarray(im2),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()
iw,ih = im2.size
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=(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 = im2.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")
return True
if __name__ == '__main__':
main()
x = []
y = []
with open(sys.argv[1]) as f:
for l in f:
a,b = l.split()
# apply mercator projection
b = lat2y(float(b))
x.append(float(a))
y.append(b)
width = 2.0/7.0
main(x,y,width,6,20)
#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