What Is the Phenomenon of Changing Direction Towards a Moving Target Called?

[Pawnag3]

Hi,
I am just wondering to what this phenomen is called and how I can graph equations for it.
Basically, we have a reference point moving North from origin (with direction vector of 0, k). I'll call it "s"
Then, at "d" distance on the y-axis, we have another object "r".
Now, reference point "s" continues to move north at "v" velocity, while "r" moves towards this point.
Now, the crucial part, every "t" seconds, object "r" looks up and changes its direction based on the position of "s".
Basically, on a plane, this is what I think it looks like the attached picture:

The changes that happen in the direction vector each time are linear. (Basically, the path is a series of straight lines, rather then "curves")

I require your help in determining the new direction vector each time.
And the name of the shape

All help is appreciated :)
Thanks

 

[berkeman]

Hi,
I am just wondering to what this phenomen is called and how I can graph equations for it.
Basically, we have a reference point moving North from origin (with direction vector of 0, k). I'll call it "s"
Then, at "d" distance on the y-axis, we have another object "r".
Now, reference point "s" continues to move north at "v" velocity, while "r" moves towards this point.
Now, the crucial part, every "t" seconds, object "r" looks up and changes its direction based on the position of "s".
Basically, on a plane, this is what I think it looks like the attached picture:

The changes that happen in the direction vector each time are linear. (Basically, the path is a series of straight lines, rather then "curves")

I require your help in determining the new direction vector each time.
And the name of the shape

All help is appreciated :)
Thanks

I believe the general search term for what you are asking about is "target tracking". Here's a Google hit list for that search:

http://www.google.com/search?source...GLL_enUS301US302&q=target+tracking+algorithms

I only had a glance through the list, and many of the hits are for more complex versions of target tracking, but hopefully looking through the list will get you farther along.