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Re: How to ParametricPlot3D a plane given Normal and Distance

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84686] Re: How to ParametricPlot3D a plane given Normal and Distance
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 10 Jan 2008 02:22:10 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <fm22bj$94u$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

the implicit version would be
when n={nx,ny,nz}

n.{x,y,z}-d==0

and if you solve this equation for say
z than
{x,y,z /. Solve[n.{x,y,z}-d==0,z][[1]]}

is your parameric form.

Regards
   Jens

John Rivers wrote:
> hello
> 
> this has eluded me for some reason ...
> 
> 
> nx = 0; ny = 0; nz = 1; (* plane's surface normal *)
> 
> dist = 0; (* distance of plane from origin *)
> 
> fx1 = ???;
> fx2 = ???;
> fx3 = ???;
> 
> ParametricPlot3D[
>  {fx1, fx2, fx3},  (* functions for x y and z coordinates *)
>  {t, -10, 10},
>  {u, -10, 10}
> ]
> 
> what should the functions fx1 fx2 and fx3 be ?
> 
> i have been playing around with:
> 
> Ax + By + Cz = D
> - and -
> <x, y, z> dot <nx, ny, nz> = D
> 
> but not got anywhere yet
> 
> thanks
> 
> John
> 


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