On Friday, April 13, 2018 at 2:36:19 AM UTC+1, Yupeng Gu wrote:
> from math import sqrt,pi,sin,cos
> tt = int(raw_input())
>
> _mid = sqrt(2.0)
>
> def findRad(lower,upper,target,func):
> if upper-lower<0.00000001:
> return upper
> mid = (upper+lower)/2.0
> if func(mid-0.000001)>func(mid) or target<=func(mid):
> return findRad(lower,mid,target,func)
> else:
> return findRad(mid,upper,target,func)
>
> for t in xrange(1,tt+1):
> area = float(raw_input())
> print "Case #{0}:".format(t)
> if area<_mid-0.000001:
> rad = findRad(0.0,pi/4.0,area,lambda r:cos(r)+sin(r))
> print "{0} {1} {2}".format(cos(rad)/2.0,sin(rad)/2.0,0)
> print "{0} {1} {2}".format(-sin(rad)/2.0,cos(rad)/2.0,0)
> print "0 0 0.5"
> elif abs(area-_mid)<0.000001:
> print "0.3535533905932738 0.3535533905932738 0"
> print "-0.3535533905932738 0.3535533905932738 0"
> print "0 0 0.5"
> else:
> x = sqrt(2.0)/4.0
> rad = findRad(0.0,pi/4.0,area,lambda r:sqrt(2)*cos(r)+sin(r))
> print "{0} {1} {2}".format(x,x*cos(rad),-x*sin(rad))
> print "{0} {1} {2}".format(-x,x*cos(rad),-x*sin(rad))
> print "{0} {1} {2}".format(0,cos(rad)/2.0,sin(rad)/2.0)
Because the the directions to the face centers must be orthogonal.
The answer your code gives for area 1.5 is
0.353553390593 0.352062072584 -0.0324391283414
-0.353553390593 0.352062072584 -0.0324391283414
0 0.497890957846 0.045875855252
but the dot product between the centers of the last two is
(0.352 * 0.497 - 0.032 * 0.045)
which is not zero.
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