My Math Forum Calculate distance between two limited length vectors

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 April 12th, 2013, 07:55 AM #1 Newbie   Joined: Apr 2013 Posts: 1 Thanks: 0 Calculate distance between two limited length vectors Hello, I am working on a system to avoid collisions for cranes, and I have an idea how I would like to do parts of this system, however, I cannot find the solutions in any of my math books from the university. The problem is to calculate the closest distance between two vectors in a 3D coordinate system. Now, to start with, I would like to solve the problem in 2D since it is easier to verify and the theory should be possible to apply on the 3D case. In my algebra / geometry books solutions exist to calculate minimum distance between two vectors of infinite length, but my problem is that the vectors need to a have a certain defined length. I would give an example of what I would like to achieve: AB is a vector between the coordinates A=(x1,y1) and B=(x2,y2). AB is only a line between these two points and does not extend outside the points. CD is a vector between the coordinates C=(x3,y3) and D=(x4,y4). CD is also only a line between these two points and does not extend outside the points. How do I calculate the minimum distance between these two vectors? Best regards, Eric
 April 12th, 2013, 04:38 PM #2 Global Moderator   Joined: May 2007 Posts: 6,661 Thanks: 648 Re: Calculate distance between two limited length vectors It is a step wise process. First, calculate the minimum distance for the infinite lines (extensions of the given vectors). Find the points on the two lines which are the end points of the minimum. If they are both in the interior of the given segments, you are done. If either point is outside the segment, get the nearer segment end point. The distance will be the distance between the segment point(s) chosen.

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