On Sunday, April 15, 2018 at 6:44:46 AM UTC-7, john.smith wrote:
> 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.
Thanks. I just found out that in the last line of my code, I have to swap cos
and sin, then the answer seems to be right.
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