Calculate Angle Between Three 3D Points

Anonymous Monk has asked for the wisdom of the Perl Monks concerning the following question:

I'm trying to calculate the angle between three 3D points.
The results are not what I expect.
Can anyone please tell me where the code may be incorrect and how to fix it?

# points are A, B, C each with 3 coordinates (x, y, z)
#   stored as array elements [0],[1],[2]
# value desired is cos(theta) between AB and BC that
#   should range 0 to 1, where 1 is a straight line A to C
# Calculate by cos(theta) = AB*BC (dot product)

@AB = ($B[0]-$A[0], $B[1]-$A[1], $B[2]-$A[2]);
@BC = ($C[0]-$B[0], $C[1]-$B[1], $C[2]-$B[2]);

$lengthAB = sqrt((($AB[0])**2)+(($AB[1])**2)+(($AB[2])**2);
$lengthBC = sqrt((($BC[0])**2)+(($BC[1])**2)+(($BC[2])**2);

@unitvectorAB=($AB[0]/$lengthAB, $AB[1]/$lengthAB, $AB[2]/$lengthAB);
@unitvectorBC=($BC[0]/$lengthBC, $BC[1]/$lengthBC, $BC[2]/$lengthBC);

$costheta = ($unitvectorAB[0]*$unitvectorBC[0])+($unitvectorAB[1]*$uni
+tvectorBC[1])+($unitvectorAB[2]*$unitvectorBC[2]);
[download]

Thank you!

Comment on Calculate Angle Between Three 3D Points Download Code

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Re: Calculate Angle Between Three 3D Points by dws (Chancellor) on Aug 20, 2003 at 18:41 UTC
I'm trying to calculate the angle between three 3D points. The results are not what I expect. It looks like you're on the right track: prior to normalizing the vectors, translate the vectors such that B is at (0,0,0). But your translation looks wrong. Think `@BA` instead of `@AB`, walk through your math again, and see if you can spot the problem.	[reply] [d/l] [select]
Re: Re: Calculate Angle Between Three 3D Points by Anonymous Monk on Aug 20, 2003 at 19:22 UTC
THANK YOU! It works when I reverse @AB into @BA. The expected answers for cos(theta) from dot product are now -1 to 0, and that is fine with me. Thanks again!	[reply]
Re: Calculate Angle Between Three 3D Points by Zeroth (Beadle) on Aug 20, 2003 at 18:21 UTC
How about using something like this: Math::VectorReal ?	[reply]
Re: Re: Calculate Angle Between Three 3D Points by Anonymous Monk on Aug 20, 2003 at 18:48 UTC
Thanks for the advice (and the rapid response!) However, I cannot get Math::VectorReal to work with my Perl. It gives the error message: Can't locate Math/VectorReal.pm in @INC I think it would be easier for now to fix the code written above, so does anyone see a mistake and know how to fix it?	[reply]
Re3: Calculate Angle Between Three 3D Points by dragonchild (Archbishop) on Aug 20, 2003 at 19:06 UTC
That's because you have to install it from CPAN. It's not a module that comes standard with Perl. Click on the link: Math::VectorReal and download it. ------ We are the carpenters and bricklayers of the Information Age. The idea is a little like C++ templates, except not quite so brain-meltingly complicated. -- TheDamian, Exegesis 6 Please remember that I'm crufty and crochety. All opinions are purely mine and all code is untested, unless otherwise specified.	[reply]