       Re: VectorPlot on a Circle

• To: mathgroup at smc.vnet.net
• Subject: [mg114798] Re: VectorPlot on a Circle
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 17 Dec 2010 03:30:17 -0500 (EST)

```Look at Boole or RegionFunction

With[{d = .041},
VectorPlot[{y, -x} Boole[1 - d < Sqrt[x^2 + y^2] < 1 + d],
{x, -1, 1}, {y, -1, 1}]]

With[{d = .041}, VectorPlot[{y, -x},
{x, -1, 1}, {y, -1, 1},
RegionFunction ->
Function[{x, y}, 1 - d < Sqrt[x^2 + y^2] < 1 + d]]]

Bob Hanlon

=============
Hi,

I'm trying to do a vector plot but confine the vectors to a unit circle.

VectorPlot[
If[Abs[x^2 + y^2 - 1] == 0, {x, y}, {0, 0}], {x, -1, 1}, {y, -1, 1}]
only plots a couple of vectors, not the dense set of vectors that I want.

and
VectorPlot[
If[Abs[x^2 + y^2 - 1] <.1, {x, y}, {0, 0}], {x, -1, 1}, {y, -1, 1}]
plots lots of vectors but they're on an annulus rather than a circle.

Is there any way to do this?

Or more generally is there any way to confine the vectors to a curve.
Or, kicking the dimension up by 1, can VectorPlot3D confine the vectors
to a surface?

Thanks,