Re: Vector Field
- To: mathgroup at smc.vnet.net
- Subject: [mg16332] Re: Vector Field
- From: adam.smith at hillsdale.edu
- Date: Sun, 7 Mar 1999 01:05:50 -0500
- Organization: Deja News - The Leader in Internet Discussion
- References: <7bg1g5$5l8@smc.vnet.net> <7bntqq$diq@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I seem to be having trouble posting things. This is about my third try.
Hopefully it worked.
Below, Jens provided an easy way to do this. However, as I read your message,
you just want a set of vectors which "sits" on the sphere and is normal to it.
I have a solution which does just this. First, note that the equation for a
sphere is f = x^2 + y^2 + z^2. The gradient of this produces normals to this
curve. In this case the gradient of f = {2 x, 2 y, 2 z}. I dropped the
constant factor of two - it makes the display "nicer". Then the task is to
great a list of a vector {x,y,z} at specific points {x,y,z} corresponding to
the sphere you chose. This is done in the
normals = Flatten[Table....]command.
Then this list is plotted. Here is the Mathematica input I used:
<<Graphics`PlotField3D`
sphere = ParametricPlot3D[{Sin[x]*Cos[y],Sin[x]*Sin[y],Cos[x]},{x,0,Pi},
{y,0,2*Pi},DisplayFunction->Identity]
normals = Flatten[
Table[
{{Sin[u]*Cos[v],Sin[u]*Sin[v],Cos[u]},
{Sin[u]*Cos[v],Sin[u]*Sin[v],Cos[u]}},
{u,0,Pi, Pi/4},{v,0,2 Pi, Pi/4}],1];
vec = ListPlotVectorField3D[normals,Axes->True,VectorHeads->True,
DisplayFunction->Identity]
Show[{sphere,vec},DisplayFunction->$DisplayFunction]
You can adjust the limits in the table to suit your preferences. I hope that
this is helpful.
Adam Smith
In article <7bntqq$diq at smc.vnet.net>,
Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:
> Hi Luke,
>
> why to use Photoshop to overlay the images ? The combination is easy:
>
> field = PlotGradientField3D[1/(1 + x^2 + y^2 + z^2), {x, -1.2, 1.2},
> {y, 0, 1.2}, {z, -1.2, 1.2}, VectorHeads ->
> True,DisplayFunction->Identity]
>
> sph = ParametricPlot3D[{Cos[phi]*Sin[th], Sin[phi]*Sin[th], Cos[th]},
> {phi, 0, Pi}, {th, 0, Pi},DisplayFunction->Identity]
>
> Show[{sph, field},DisplayFunction->$DisplayFunction]
>
> Hope that helps
> Jens
>
> Luke wrote:
> >
> > I am trying to create a picture of a sphere with Normal vectors on the
> > surface to demonstrate the Divergence Theorum. I am quite new to Mathematica
> > and I was wondering if it could be done.
> >
> > I have created the sphere using:
> >
> > ParametricPlot3D[{Sin[x]*Cos[y],Sin[x]*Sin[y],Cos[x]},{x,0,Pi},{y,0,2*Pi}]
> >
> > I am hoping to be able to use PlotVectorField3D to create a vector field and
> > overlay in on the image using Photoshop where I could remove the vector
> > which should not be in view. I'm not sure how to plot the field desired.
> >
> > Anyone have any suggestions?
> >
> > Luke
>
>
-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own