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An origami program needs routines to compute where to fold the paper. The most complex fold is Beloch’s Fold, in which two points P and Q are given along with two lines M and N. The problem is to find a fold which takes P onto line M and simultaneously, takes Q onto line N. In the figure below, folding along the line K is one possible solution.
Write a program to compute the fold line K, which takes point P to line M and point Q to line N, given points P and Q and lines M and N. Point P will not be on line M, point Q will not be on line N and lines M and N will not be parallel.
nput consists of a single line of input. The line contains 10 space separated floating point values between -10000 and 10000: Px, Py, Ma, Mb, Mc, Qx, Qy, Na, Nb, Nc where:
The output consists of a single line containing 3 space separated floating point values to 4 decimal places: Ka, Kb, Kc where:
Ka*x + Kb*y + Kc = 0 is a fold line which takes P onto M and Q onto N.
-4 5 6 7 8 9 10 -1 3 4
1.7691 1.1979 3.3690
4 5 6 7 8 9 10 -3 2 1
4.4949 5.7186 -20.1193