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josch
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233
fitbspline.py
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233
fitbspline.py
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#!/usr/bin/env python
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import sys
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from math import sqrt
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import interpolate
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from itertools import tee, izip
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from matplotlib.patches import Polygon
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from matplotlib.collections import PatchCollection
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import matplotlib
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def pairwise(iterable):
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"s -> (s0,s1), (s1,s2), (s2,s3), ..."
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a, b = tee(iterable, 2)
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next(b, None)
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return izip(a, b)
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def triplewise(iterable):
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"s -> (s0,s1,s2), (s1,s2,s3), (s2,s3,s4), ..."
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a,b,c = tee(iterable, 3)
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next(b, None)
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next(c, None)
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next(c, None)
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return izip(a,b,c)
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# using barycentric coordinates
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def ptInTriangle(p, p0, p1, p2):
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A = 0.5 * (-p1[1] * p2[0] + p0[1] * (-p1[0] + p2[0]) + p0[0] * (p1[1] - p2[1]) + p1[0] * p2[1]);
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sign = -1 if A < 0 else 1;
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s = (p0[1] * p2[0] - p0[0] * p2[1] + (p2[1] - p0[1]) * p[0] + (p0[0] - p2[0]) * p[1]) * sign;
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t = (p0[0] * p1[1] - p0[1] * p1[0] + (p0[1] - p1[1]) * p[0] + (p1[0] - p0[0]) * p[1]) * sign;
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return s >= 0 and t >= 0 and (s + t) <= 2 * A * sign;
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def getxing(p0, p1, p2, p3):
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ux = p1[0]-p0[0]
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uy = p1[1]-p0[1]
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vx = p2[0]-p3[0]
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vy = p2[1]-p3[1]
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# get multiplicity of u at which u meets v
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a = vy*ux-vx*uy
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if a == 0:
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# lines are parallel and never meet
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return None
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s = (vy*(p3[0]-p0[0])+vx*(p0[1]-p3[1]))/a
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if s < 1.0:
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return (p0[0]+s*ux, p0[1]+s*uy)
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else:
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return None
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# the line p0-p1 is the upper normal to the path
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# the line p2-p3 is the lower normal to the path
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#
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# | | |
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# p0--------|--------p1
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# | | |
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# | | |
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# p3--------|--------p2
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# | | |
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def ptInQuadrilateral(p, p0, p1, p2, p3):
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# it might be that the two normals cross at some point
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# in that case the two triangles are created differently
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cross = getxing(p0, p1, p2, p3)
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#if cross:
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# return ptInTriangle(p, p0, cross, p3) or ptInTriangle(p, p2, cross, p1)
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#else:
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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 find_coeffs(pa, pb):
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matrix = []
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for p1, p2 in zip(pa, pb):
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matrix.append([p1[0], p1[1], 1, 0, 0, 0, -p2[0]*p1[0], -p2[0]*p1[1]])
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matrix.append([0, 0, 0, p1[0], p1[1], 1, -p2[1]*p1[0], -p2[1]*p1[1]])
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A = np.matrix(matrix, dtype=np.float)
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B = np.array(pb).reshape(8)
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#res = np.dot(np.linalg.inv(A), B)
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res = np.dot(np.linalg.inv(A.T * A) * A.T, B)
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return np.array(res).reshape(8)
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def main():
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width = 2/5.0
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halfwidth = width/2.0
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x = []
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y = []
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with open(sys.argv[1]) as f:
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for l in f:
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a,b = l.split()
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x.append(float(a))
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y.append(float(b))
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tck,u = interpolate.splprep([x,y],s=10)
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unew = np.arange(0,1.1,0.1)
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out = interpolate.splev(unew,tck)
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heights = []
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offs = []
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height = 0.0
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for (ax,ay),(bx,by) in pairwise(zip(*out)):
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s = ax-bx
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t = ay-by
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l = sqrt(s*s+t*t)
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offs.append(height)
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height += l
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heights.append(l)
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# the border of the first segment is just perpendicular to the path
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cx = -out[1][1]+out[1][0]
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cy = out[0][1]-out[0][0]
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cl = sqrt(cx*cx+cy*cy)/halfwidth
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dx = out[1][1]-out[1][0]
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dy = -out[0][1]+out[0][0]
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dl = sqrt(dx*dx+dy*dy)/halfwidth
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px = [out[0][0]+cx/cl]
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py = [out[1][0]+cy/cl]
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qx = [out[0][0]+dx/dl]
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qy = [out[1][0]+dy/dl]
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for (ubx,uby),(ux,uy),(uax,uay) in triplewise(zip(*out)):
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# get adjacent line segment vectors
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ax = ux-ubx
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ay = uy-uby
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bx = uax-ux
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by = uay-uy
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# normalize length
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al = sqrt(ax*ax+ay*ay)
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bl = sqrt(bx*bx+by*by)
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ax = ax/al
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ay = ay/al
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bx = bx/bl
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by = by/bl
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# get vector perpendicular to sum
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cx = -ay-by
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cy = ax+bx
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cl = sqrt(cx*cx+cy*cy)/halfwidth
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px.append(ux+cx/cl)
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py.append(uy+cy/cl)
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# and in the other direction
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dx = ay+by
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dy = -ax-bx
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dl = sqrt(dx*dx+dy*dy)/halfwidth
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qx.append(ux+dx/dl)
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qy.append(uy+dy/dl)
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# the border of the last segment is just perpendicular to the path
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cx = -out[1][-1]+out[1][-2]
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cy = out[0][-1]-out[0][-2]
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cl = sqrt(cx*cx+cy*cy)/halfwidth
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dx = out[1][-1]-out[1][-2]
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dy = -out[0][-1]+out[0][-2]
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dl = sqrt(dx*dx+dy*dy)/halfwidth
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px.append(out[0][-1]+cx/cl)
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py.append(out[1][-1]+cy/cl)
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qx.append(out[0][-1]+dx/dl)
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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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#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,(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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containingquad.append(found)
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else:
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print "can't find quad for point"
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containingquad.append(None)
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#exit(1)
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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,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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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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#srcquad = (min(x),max(y)),(max(x),max(y)),(max(x),min(y)),(min(x),min(y))
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#trans = find_coeffs(srcquad,targetquad)
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#for (rx,ry) in zip(x,y):
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# a,b,c,d,e,f,g,h = trans
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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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# tx.append(u)
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# ty.append(v)
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assert len(containingquad) == len(x) == len(y)
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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
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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 in l[: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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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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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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plt.figure()
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plt.axes().set_aspect('equal')
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#plt.axhspan(0, height, xmin=0, xmax=width)
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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,sx,sy)
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#plt.plot(tx,ty)
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plt.show()
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if __name__ == '__main__':
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main()
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