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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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138
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)
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): def find_coeffs(pa, pb):
matrix = [] matrix = []
for p1, p2 in zip(pa, pb): for p1, p2 in zip(pa, pb):
@ -152,28 +202,18 @@ def main():
qy.append(out[1][-1]+dy/dl) qy.append(out[1][-1]+dy/dl)
quads = [] quads = []
patches = [] patches = []
# a unified quad p0,p2,p5,p3 does not work because then after perspective #for (p0x,p0y,p1x,p1y),(p3x,p3y,p2x,p2y) in pairwise(zip(px,py,qx,qy)):
# projection, the line p1,p4 is not in the center anymore 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)))
# p0----p1---p2 polygon = Polygon(((p0x,p0y),(p1x,p1y),(p2x,p2y),(p3x,p3y)), True)
# | | | patches.append(polygon)
# 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))
containingquad = [] containingquad = []
for pt in zip(x,y): for pt in zip(x,y):
# for each point, find the quadrilateral that contains it # for each point, find the quadrilateral that contains it
found = [] found = []
for i,(q1,q2) in enumerate(quads): for i,(p0,p1,p2,p3) in enumerate(quads):
if ptInQuadrilateral(pt,*q1): if ptInQuadrilateral(pt,p0,p1,p2,p3):
found.append((i,0)) found.append(i)
if ptInQuadrilateral(pt,*q2):
found.append((i,1))
if found: if found:
if len(found) > 2: if len(found) > 2:
print found print found
@ -185,15 +225,12 @@ def main():
print containingquad print containingquad
trans = [] trans = []
print width, height 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)) #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)) targetquad = ((0,off+h),(width,off+h),(width,off),(0,off))
t2 = ((halfwidth,off+h),(width,off+h),(width,off),(halfwidth,off)) trans.append(find_coeffs(srcquad,targetquad))
c1 = find_coeffs(q1,t1) patches.append(Polygon(targetquad,True))
c2 = find_coeffs(q2,t2)
trans.append((c1,c2))
patches.append(Polygon(t1,True))
patches.append(Polygon(t2,True))
tx = [] tx = []
ty = [] ty = []
#targetquad = (0,height),(width,height),(width,0),(0,0) #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): for (rx,ry),l in zip(zip(x,y),containingquad):
if not l: if not l:
continue continue
for i,j in l[:1]: for i in l[:1]:
a,b,c,d,e,f,g,h = trans[i][j] (ax,ay),(bx,by),(cx,cy),(dx,dy) = quads[i]
#den = -a*e+a*h*ry+b*d-b*g*ry-d*h*rx+e*g*rx s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,rx,ry)
#tx.append((-b*f+b*ry+c*e-c*h*ry-e*rx+f*h*rx)/den) if len(s) != 1 or len(t) != 1:
#ty.append((a*f-a*ry-c*d+c*g*ry+d*rx-f*g*rx)/den) print "fail"
u = (a*rx + b*ry + c)/(g*rx + h*ry + 1) exit(1)
v = (d*rx + e*ry + f)/(g*rx + h*ry + 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) tx.append(u)
ty.append(v) ty.append(v)
#sx = [] sx = []
#sy = [] sy = []
#for (((ax,ay),(bx,by)),(a,b,c,d,e,f,g,h)) in zip(pairwise(zip(*out)),trans): 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) #u = (a*ax + b*ay + c)/(g*ax + h*ay + 1)
#v = (d*ax + e*ay + f)/(g*ax + h*ay + 1) #v = (d*ax + e*ay + f)/(g*ax + h*ay + 1)
# sx.append(u) u = s[0]*width
# sy.append(v) v = off+t[0]*h
sx.append(u)
sy.append(v)
#u = (a*bx + b*by + c)/(g*bx + h*by + 1) #u = (a*bx + b*by + c)/(g*bx + h*by + 1)
#v = (d*bx + e*by + f)/(g*bx + h*by + 1) #v = (d*bx + e*by + f)/(g*bx + h*by + 1)
# sx.append(u) s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x2,y2)
# sy.append(v) 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) 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 = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=0.4)
p.set_array(np.array(colors)) p.set_array(np.array(colors))
@ -239,7 +295,7 @@ def main():
fig, ax = plt.subplots() fig, ax = plt.subplots()
ax.add_collection(p) ax.add_collection(p)
ax.set_aspect('equal') 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.plot(tx,ty)
plt.show() plt.show()