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@ -67,6 +67,56 @@ def ptInQuadrilateral(p, p0, p1, p2, p3):
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# return ptInTriangle(p, p0, p1, p2) or ptInTriangle(p, p2, p3, p0)
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return ptInTriangle(p, p0, p1, p2) or ptInTriangle(p, p2, p3, p0)
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def get_st(Ax,Ay,Bx,By,Cx,Cy,Dx,Dy,Xx,Xy):
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d = Bx-Ax-Cx+Dx
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e = By-Ay-Cy+Dy
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l = Dx-Ax
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g = Dy-Ay
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h = Cx-Dx
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m = Cy-Dy
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i = Xx-Dx
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j = Xy-Dy
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n = g*h-m*l
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# calculation for s
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a1 = m*d-h*e
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b1 = n-j*d+i*e
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c1 = l*j-g*i
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# calculation for t
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a2 = g*d-l*e
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b2 = n+j*d-i*e
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c2 = h*j-m*i
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s = []
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if a1 == 0:
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s.append(-c1/b1)
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else:
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r1 = b1*b1-4*a1*c1
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if r1 >= 0:
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r11 = (-b1+sqrt(r1))/(2*a1)
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if -0.0000000001 <= r11 <= 1.0000000001:
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s.append(r11)
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r12 = (-b1-sqrt(r1))/(2*a1)
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if -0.0000000001 <= r12 <= 1.0000000001:
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s.append(r12)
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t = []
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if a2 == 0:
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t.append(-c2/b2)
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else:
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r2 = b2*b2-4*a2*c2
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if r2 >= 0:
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r21 = (-b2+sqrt(r2))/(2*a2)
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if -0.0000000001 <= r21 <= 1.0000000001:
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t.append(r21)
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r22 = (-b2-sqrt(r2))/(2*a2)
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if -0.0000000001 <= r22 <= 1.0000000001:
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t.append(r22)
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if not s or not t:
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return None
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if len(s) == 1 and len(t) == 2:
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s = [s[0],s[0]]
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if len(s) == 2 and len(t) == 1:
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t = [t[0],t[0]]
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return s, t
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def find_coeffs(pa, pb):
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matrix = []
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for p1, p2 in zip(pa, pb):
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@ -152,28 +202,18 @@ def main():
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qy.append(out[1][-1]+dy/dl)
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quads = []
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patches = []
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# a unified quad p0,p2,p5,p3 does not work because then after perspective
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# projection, the line p1,p4 is not in the center anymore
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#
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# p0----p1---p2
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# | | |
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# p3----p4---p5
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#
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for (p3x,p3y,p4x,p4y,p5x,p5y),(p0x,p0y,p1x,p1y,p2x,p2y) in pairwise(zip(px,py,out[0],out[1],qx,qy)):
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q1 = ((p0x,p0y),(p1x,p1y),(p4x,p4y),(p3x,p3y))
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q2 = ((p1x,p1y),(p2x,p2y),(p5x,p5y),(p4x,p4y))
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quads.append((q1,q2))
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patches.append(Polygon(q1, True))
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patches.append(Polygon(q2, True))
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#for (p0x,p0y,p1x,p1y),(p3x,p3y,p2x,p2y) in pairwise(zip(px,py,qx,qy)):
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for (p3x,p3y,p2x,p2y),(p0x,p0y,p1x,p1y) in pairwise(zip(px,py,qx,qy)):
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quads.append(((p0x,p0y),(p1x,p1y),(p2x,p2y),(p3x,p3y)))
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polygon = Polygon(((p0x,p0y),(p1x,p1y),(p2x,p2y),(p3x,p3y)), True)
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patches.append(polygon)
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containingquad = []
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for pt in zip(x,y):
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# for each point, find the quadrilateral that contains it
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found = []
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for i,(q1,q2) in enumerate(quads):
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if ptInQuadrilateral(pt,*q1):
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found.append((i,0))
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if ptInQuadrilateral(pt,*q2):
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found.append((i,1))
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for i,(p0,p1,p2,p3) in enumerate(quads):
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if ptInQuadrilateral(pt,p0,p1,p2,p3):
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found.append(i)
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if found:
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if len(found) > 2:
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print found
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@ -185,15 +225,12 @@ def main():
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print containingquad
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trans = []
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print width, height
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for off,h,(q1,q2) in zip(offs,heights,quads):
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srcquads = []
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for off,h,srcquad in zip(offs,heights,quads):
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#targetquad = ((0,height-off),(width,height-off),(width,height-off-h),(0,height-off-h))
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t1 = ((0,off+h),(halfwidth,off+h),(halfwidth,off),(0,off))
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t2 = ((halfwidth,off+h),(width,off+h),(width,off),(halfwidth,off))
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c1 = find_coeffs(q1,t1)
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c2 = find_coeffs(q2,t2)
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trans.append((c1,c2))
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patches.append(Polygon(t1,True))
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patches.append(Polygon(t2,True))
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targetquad = ((0,off+h),(width,off+h),(width,off),(0,off))
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trans.append(find_coeffs(srcquad,targetquad))
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patches.append(Polygon(targetquad,True))
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tx = []
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ty = []
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#targetquad = (0,height),(width,height),(width,0),(0,0)
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@ -210,26 +247,45 @@ def main():
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for (rx,ry),l in zip(zip(x,y),containingquad):
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if not l:
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continue
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for i,j in l[:1]:
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a,b,c,d,e,f,g,h = trans[i][j]
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#den = -a*e+a*h*ry+b*d-b*g*ry-d*h*rx+e*g*rx
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#tx.append((-b*f+b*ry+c*e-c*h*ry-e*rx+f*h*rx)/den)
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#ty.append((a*f-a*ry-c*d+c*g*ry+d*rx-f*g*rx)/den)
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u = (a*rx + b*ry + c)/(g*rx + h*ry + 1)
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v = (d*rx + e*ry + f)/(g*rx + h*ry + 1)
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for i in l[:1]:
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(ax,ay),(bx,by),(cx,cy),(dx,dy) = quads[i]
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s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,rx,ry)
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if len(s) != 1 or len(t) != 1:
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print "fail"
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exit(1)
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#a,b,c,d,e,f,g,h = trans[i]
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##den = -a*e+a*h*ry+b*d-b*g*ry-d*h*rx+e*g*rx
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##tx.append((-b*f+b*ry+c*e-c*h*ry-e*rx+f*h*rx)/den)
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##ty.append((a*f-a*ry-c*d+c*g*ry+d*rx-f*g*rx)/den)
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#u = (a*rx + b*ry + c)/(g*rx + h*ry + 1)
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#v = (d*rx + e*ry + f)/(g*rx + h*ry + 1)
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u = s[0]*width
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v = offs[i]+t[0]*heights[i]
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tx.append(u)
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ty.append(v)
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#sx = []
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#sy = []
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#for (((ax,ay),(bx,by)),(a,b,c,d,e,f,g,h)) in zip(pairwise(zip(*out)),trans):
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# u = (a*ax + b*ay + c)/(g*ax + h*ay + 1)
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# v = (d*ax + e*ay + f)/(g*ax + h*ay + 1)
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# sx.append(u)
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# sy.append(v)
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# u = (a*bx + b*by + c)/(g*bx + h*by + 1)
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# v = (d*bx + e*by + f)/(g*bx + h*by + 1)
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# sx.append(u)
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# sy.append(v)
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sx = []
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sy = []
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for ((x1,y1),(x2,y2)),((ax,ay),(bx,by),(cx,cy),(dx,dy)),off,h in zip(pairwise(zip(*out)),quads,offs,heights):
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s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x1,y1)
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if len(s) != 1 or len(t) != 1:
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print "fail"
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exit(1)
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#u = (a*ax + b*ay + c)/(g*ax + h*ay + 1)
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#v = (d*ax + e*ay + f)/(g*ax + h*ay + 1)
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u = s[0]*width
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v = off+t[0]*h
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sx.append(u)
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sy.append(v)
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#u = (a*bx + b*by + c)/(g*bx + h*by + 1)
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#v = (d*bx + e*by + f)/(g*bx + h*by + 1)
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s,t = get_st(ax,ay,bx,by,cx,cy,dx,dy,x2,y2)
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if len(s) != 1 or len(t) != 1:
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print "fail"
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exit(1)
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u = s[0]*width
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v = off+t[0]*h
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sx.append(u)
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sy.append(v)
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colors = 100*np.random.rand(len(patches)/2)+100*np.random.rand(len(patches)/2)
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p = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=0.4)
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p.set_array(np.array(colors))
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@ -239,7 +295,7 @@ def main():
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fig, ax = plt.subplots()
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ax.add_collection(p)
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ax.set_aspect('equal')
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plt.plot(x,y,out[0],out[1],px,py,qx,qy,tx,ty)
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plt.plot(x,y,out[0],out[1],px,py,qx,qy,sx,sy,tx,ty)
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#plt.plot(tx,ty)
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plt.show()
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