Re: How to ParametricPlot3D a plane given Normal and Distance
- To: mathgroup at smc.vnet.net
- Subject: [mg84693] Re: How to ParametricPlot3D a plane given Normal and Distance
- From: dh <dh at metrohm.ch>
- Date: Thu, 10 Jan 2008 02:25:46 -0500 (EST)
- References: <fm22bj$94u$1@smc.vnet.net>
Hi John,
one way to parametrize a plane uses 2 vectors parallel to the plane
(that are not parallel). You could get thouse using Cross, but it may be
easier using NullSpace. Here is an example:
normal={1,1,1}/Sqrt[3];
dist=2;
m={normal,{0,0,0},{0,0,0}};
ns=NullSpace[m];
ParametricPlot3D[dist normal+{u,v}.ns,{u,0,5},{v,0,5}]
hope this helps, Daniel
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
>