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### plot of implicit function

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```Hello, I have an analitical 3D streamfunction, and I want to plot it.
I looked here http://www.dfanning.com/tips/particle_3d.html and it's
exactly what I want, but I have an a implicit definition of
coordinates:
f(R,phi,z)=t
g(R,phi,z)=t
h(R,phi,z)=t

Anyone have an idea for implicit function plot?
```
 0
Reply negri.andre (1) 11/19/2010 9:24:28 AM

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```On Fri, 19 Nov 2010 01:24:28 -0800 (PST), Andrea
<negri.andre@gmail.com> wrote:

>Hello, I have an analitical 3D streamfunction, and I want to plot it.
>I looked here http://www.dfanning.com/tips/particle_3d.html and it's
>exactly what I want,

Isn't a streamfunction like a vectorfield? Shouldn't you be using
something like this (but then in 3D):
http://michaelgalloy.com/2008/03/19/overview-of-flow-visualization-in-idl.html

> but I have an a implicit definition of
>coordinates:
>f(R,phi,z)=t
>g(R,phi,z)=t
>h(R,phi,z)=t

I don't understand. So you have coordinates (R,phi,z) which can be
easily transformed to (x,y,z). f,g and h aren't defining the
vectorfield are they? So what are they and how is your vectorfield
based upon them? Maybe I'm missing something obvious here...
```
 0

```On Nov 19, 11:08=A0am, Wox <s...@nomail.com> wrote:
> On Fri, 19 Nov 2010 01:24:28 -0800 (PST), Andrea
>
> <negri.an...@gmail.com> wrote:
> >Hello, I have an analitical 3D streamfunction, and I want to plot it.
> >I looked herehttp://www.dfanning.com/tips/particle_3d.htmland it's
> >exactly what I want,
>
> Isn't a streamfunction like a vectorfield? Shouldn't you be using
> something like this (but then in 3D):http://michaelgalloy.com/2008/03/19/=
overview-of-flow-visualization-in...
>
> > but I have an a implicit definition of
> >coordinates:
> >f(R,phi,z)=3Dt
> >g(R,phi,z)=3Dt
> >h(R,phi,z)=3Dt
>
> I don't understand. So you have coordinates (R,phi,z) which can be
> easily transformed to (x,y,z). f,g and h aren't defining the
> vectorfield are they? So what are they and how is your vectorfield
> based upon them? Maybe I'm missing something obvious here...

Sorry for my bad explanation. I have an analitical vector field (ie
the mathematical formula) and I have integrated it in order to obtain
the analitical formula of streamlines (in 3D, in this case) ie now I
have the trajectory of a point in the vector field in function of a
parameter t (the time, if you want) in cylindric coordinates.
The problem is that: the trajectory is not defined as explicit
function of time only like this

R=3Df(t)
phi=3Dg(t)
z=3Dh(t)

but are defined as implicit function of time, and the function
involved are a non-invertible function. So, I need the idl equivalent
of implicitplot3d maple command.
```
 0

```On Fri, 19 Nov 2010 02:34:04 -0800 (PST), Andrea
<negri.andre@gmail.com> wrote:

>> >f(R,phi,z)=t
>> >g(R,phi,z)=t
>> >h(R,phi,z)=t

Ah, I see. So for each t you need to solve a non-linear system of
equations (3 eq., 3 var.) in order to get the position (R,phi,z) of
the particle (or whatever) at time t.

You could use NEWTON or BROYDEN to find (R,phi,z) for each t. Off
course your "Vecfunc" changes every time (for each t), so you have to
use a global variable t.

Can't think of anything else...
```
 0

```On Nov 19, 11:56=A0am, Wox <s...@nomail.com> wrote:
> On Fri, 19 Nov 2010 02:34:04 -0800 (PST), Andrea
>
> <negri.an...@gmail.com> wrote:
> >> >f(R,phi,z)=3Dt
> >> >g(R,phi,z)=3Dt
> >> >h(R,phi,z)=3Dt
>
> Ah, I see. So for each t you need to solve a non-linear system of
> equations (3 eq., 3 var.) in order to get the position (R,phi,z) of
> the particle (or whatever) at time t.
>
> You could use NEWTON or BROYDEN to find (R,phi,z) for each t. Off
> course your "Vecfunc" changes every time (for each t), so you have to
> use a global variable t.
>
> Can't think of anything else...

Fortunatley the velocity field is stationary.
Thanks a lot for help!

Andrea
```
 0

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