You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
304 lines
9.5 KiB
Python
304 lines
9.5 KiB
Python
#!/usr/bin/env python
|
|
|
|
import sys
|
|
from math import sqrt
|
|
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
from scipy import interpolate
|
|
from itertools import tee, izip
|
|
from matplotlib.patches import Polygon
|
|
from matplotlib.collections import PatchCollection
|
|
import matplotlib
|
|
|
|
def pairwise(iterable):
|
|
"s -> (s0,s1), (s1,s2), (s2,s3), ..."
|
|
a, b = tee(iterable, 2)
|
|
next(b, None)
|
|
return izip(a, b)
|
|
|
|
def triplewise(iterable):
|
|
"s -> (s0,s1,s2), (s1,s2,s3), (s2,s3,s4), ..."
|
|
a,b,c = tee(iterable, 3)
|
|
next(b, None)
|
|
next(c, None)
|
|
next(c, None)
|
|
return izip(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 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 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)
|
|
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 None
|
|
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
|
|
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)
|
|
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)
|
|
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)):
|
|
# get adjacent line segment vectors
|
|
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
|
|
# 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)
|
|
# 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)
|
|
# 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)
|
|
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)
|
|
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) > 2:
|
|
print found
|
|
containingquad.append(found)
|
|
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))
|
|
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:
|
|
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)
|
|
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)
|
|
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.plot(x,y,out[0],out[1],px,py,qx,qy,sx,sy,tx,ty)
|
|
#plt.plot(tx,ty)
|
|
plt.show()
|
|
|
|
if __name__ == '__main__':
|
|
main()
|