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josch 2014-04-02 07:37:23 +02:00
parent 89a7a9801d
commit 54ec6a7b6c
1 changed files with 101 additions and 45 deletions
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146
fitbspline.py
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@ -67,6 +67,56 @@ def ptInQuadrilateral(p, p0, p1, p2, p3):
# 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):
@ -152,28 +202,18 @@ def main():
qy.append(out[1][-1]+dy/dl)
quads = []
patches = []
# a unified quad p0,p2,p5,p3 does not work because then after perspective
# projection, the line p1,p4 is not in the center anymore
#
# p0----p1---p2
# | | |
# p3----p4---p5
#
for (p3x,p3y,p4x,p4y,p5x,p5y),(p0x,p0y,p1x,p1y,p2x,p2y) in pairwise(zip(px,py,out[0],out[1],qx,qy)):
q1 = ((p0x,p0y),(p1x,p1y),(p4x,p4y),(p3x,p3y))
q2 = ((p1x,p1y),(p2x,p2y),(p5x,p5y),(p4x,p4y))
quads.append((q1,q2))
patches.append(Polygon(q1, True))
patches.append(Polygon(q2, True))
#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,(q1,q2) in enumerate(quads):
if ptInQuadrilateral(pt,*q1):
found.append((i,0))
if ptInQuadrilateral(pt,*q2):
found.append((i,1))
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
@ -185,15 +225,12 @@ def main():
print containingquad
trans = []
print width, height
for off,h,(q1,q2) in zip(offs,heights,quads):
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))
t1 = ((0,off+h),(halfwidth,off+h),(halfwidth,off),(0,off))
t2 = ((halfwidth,off+h),(width,off+h),(width,off),(halfwidth,off))
c1 = find_coeffs(q1,t1)
c2 = find_coeffs(q2,t2)
trans.append((c1,c2))
patches.append(Polygon(t1,True))
patches.append(Polygon(t2,True))
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)
@ -210,26 +247,45 @@ def main():
for (rx,ry),l in zip(zip(x,y),containingquad):
if not l:
continue
for i,j in l[:1]:
a,b,c,d,e,f,g,h = trans[i][j]
#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)
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 (((ax,ay),(bx,by)),(a,b,c,d,e,f,g,h)) in zip(pairwise(zip(*out)),trans):
# u = (a*ax + b*ay + c)/(g*ax + h*ay + 1)
# v = (d*ax + e*ay + f)/(g*ax + h*ay + 1)
# 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)
# sx.append(u)
# sy.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))
@ -239,7 +295,7 @@ 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,tx,ty)
plt.plot(x,y,out[0],out[1],px,py,qx,qy,sx,sy,tx,ty)
#plt.plot(tx,ty)
plt.show()