My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 12th, 2013, 06:55 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
iqbad is offline  
 
April 12th, 2013, 03:38 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,607
Thanks: 616

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.
mathman is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
calculate, distance, length, limited, vectors



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Parametric equations - distance traveled and arc length mwhit Calculus 6 September 29th, 2013 05:12 AM
Looking for a formula to calculate a chord length rainycat Algebra 2 July 23rd, 2013 11:50 PM
Calculate the arc length between 2 points over a hypersphere 7toni7 Real Analysis 1 December 23rd, 2012 08:00 AM
how do I calculate radius of a circle, from chord length? ,, boki-san Algebra 1 February 13th, 2011 10:34 AM
Calculate the length of the side of an irregular tetragon. Mr Spot Algebra 15 November 20th, 2008 05:56 PM





Copyright © 2018 My Math Forum. All rights reserved.