HI,

Can someone please explain the differences between Potential, Vector, Flow and Force fields for me please. I've had a look around and I'm sure people have different views as in some places they are all referred to interchangeably and in others they are different.

Many Thanks

They are very distinct concepts. Can you give an example where those concepts are referred to interchangeably? Do you understand multivariate calculus?

Thanks for the reply.
In the abstract of this paper:

http://www.araa.asn.au/acra/acra2007/papers/paper187final.pdf

Which is about vector fields they say at the beginning "Vector Field (otherwise known as force vector or force field) navigation......"

Reynolds refers to Vector fields as Flow fields

http://www.red3d.com/cwr/steer/gdc99/

and in this paper which is called "[font=Arial, Helvetica, sans-serif]

Multi-agent navigation using path-based vector fields"
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http://portal.acm.org/citation.cfm?id=1791998
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they then go on to refer to them through the whole paper as potential fields.
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[font="Arial, Helvetica, sans-serif"]I am familiar with[size="5"] [font="Arial, Helvetica, sans-serif"]calculus[font="Arial, Helvetica, sans-serif"][size="5"] but I'm not sure about '[size=2]multivariate calculus&#39; I will look it up.<br /> [size=2]<br /> <br /> [size=2]Thanks

"Flow fields" and "vector fields" are the same thing. They assign a vector to every point in space.

Potential fields are related. A potential field assigns a real number to every point in space. It corresponds to a particular vector field -- the vector field that always points locally in the direction of greatest decrease. This vector field is the (negative) gradient of the potential field.

If a vector field has "vortices" or "loops," (I'm not using precise terminology) it cannot be expressed as the gradient of a potential field.

Thanks for the info,

a very nice explanation of potential fields, I get it now I think.

But does this not mean though that in a lot of situations vector fields could be replaced by potential fields and vice versa as they work in a pretty similar way and almost all techniques used with one method could be applied to the other????? Or am I missing something? What are the benefits of one over the other???

Any useful resources would be much appreciated.

Thanks

But does this not mean though that in a lot of situations vector fields could be replaced by potential fields and vice versa as they work in a pretty similar way and almost all techniques used with one method could be applied to the other????? Or am I missing something? What are the benefits of one over the other???

You're right, the ideas are extremely closely related.

I'd think of it this way: You're always going to be moving along a vector field. What kind of vector field will it be? Is it going to be any vector field? Or is it going to be a vector field that you got by taking the gradient of a potential function? Not all vector fields can be produced in this second way -- which can be a good thing, because it guarantees that your vector field will have certain properties that you might want. In particular, the vector field will have no "loops" or "vortices," and, if your world is bounded, a particle moving along it is guaranteed to eventually stop; it cannot keep moving forever, either along a cycle, or chaotically. That's because it's going to always be moving downhill the potential function, and eventually it'll get stuck in a valley

A good book on the subject, if you've done calculus, is Div, Grad, Curl, and All That.

Cool cool,

Thanks muchly for the info, I shall delve deeper and maybe a bit of implementation will help.............

Thanks again

[Edit] I just ordered that book, looks like its got some useful stuff in there.