'''oneLinePair.py

   Compute the mapping defined by one pair of lines, according
to Feature-Based Metamorphosis, a la Beier and Neely.
'''

import math
from pointLineDist import *


def perp(dx, dy):
  '''Return a vector the same length as, and perpendicular to the input.'''
  return (dy, -dx)

def findSourceCoords(X, P, Q, Pp, Qp):
  '''Given input point X=(xd,yd) find the source image point Xp=(xs,ys)
     using the line segments (P,Q) and (Pp, Qp) to define the mapping.'''
  (xd,yd) = X  # unpack points...
  (x0,y0) = P
  (x1,y1) = Q
  # Compute u and v
  (u,v) = pointLineDist(xd,yd,x0,y0,x1,y1)
  (x0p,y0p) = Pp
  (x1p,y1p) = Qp
  # denominator in B&N eq 3:
  newhypot = math.sqrt((x1p-x0p)^2+(y1p-y0p)^2)
  # numerator in B&N eq 3:
  (vx,vy)=perp(x1p-x0p, y1p-y0p)
  # overall of eq 3:
  xs = x0p + u*(x1p-x0p) + v * vx / newhypot
  ys = y0p + u*(y1p-y0p) + v * vy / newhypot
  return (xs,ys)

def test():
  P = (0,0); Q=(1,0)
  Pp = (5,5); Qp=(6,5)
  X = (13,18)

  print findSourceCoords(X, P, Q, Pp, Qp)

test()