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Point of closest approach

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I would like to calculate the point on each of two lines in 3D space at which they are closest. So for example given A = { 0 , 0 , 0 , 1.0 , 1.0 , 1.0 } and B = { 0 , 0 , 0.5 , 1.0 , 1.0 , 0.5 } it would determine that the point of closest approach was at { 0.5 , 0.5 , 0.5 } and { 0.5 , 0.5 , 0.5 }. The lines may not necessarily cross one another.

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Quote:
Original post by abachler
I would like to calculate the point on each of two lines in 3D space at which they are closest. So for example given A = { 0 , 0 , 0 , 1.0 , 1.0 , 1.0 } and B = { 0 , 0 , 0.5 , 1.0 , 1.0 , 0.5 } it would determine that the point of closest approach was at { 0.5 , 0.5 , 0.5 } and { 0.5 , 0.5 , 0.5 }. The lines may not necessarily cross one another.
This problem can be solved pretty easily using minimization (or a geometrical approach).

Here is the first hit from Google for 'closest point two lines'; you should be able to find what you need there.

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