Re: making a plane

• To: mathgroup at smc.vnet.net
• Subject: [mg24226] Re: [mg24194] making a plane
• From: "Preston Nichols" <pnichols at wittenberg.edu>
• Date: Sat, 1 Jul 2000 03:21:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm guessing a "Polygon" got dropped from your message:

c = Show[Graphics3D[
Polygon[{
{0.0517 , 0.0847 , 0.1004},
{0.0517 , -0.0187 , 0.0344},
{-0.0517 , 0.0187 , 0.0690},
{-0.0517, -0.0847, 0.0030}
}]],
Axes -> Automatic,
PlotRange -> {{-0.15, 0.15}, {-0.15, 0.15}, {-0.15, 0.15}}
];

Your points are coplanar, but they are listed in the wrong order to make a
non-intersecting polygon.  (You are getting a "folded" polygon.)

The following produces a satisfactory picture:

Show[Graphics3D[
Polygon[{
{0.0517 , 0.0847 , 0.1004},
{0.0517 , -0.0187 , 0.0344},
{-0.0517 , 0.0187 , 0.0690},
{-0.0517, -0.0847, 0.0030}
}]],
Axes -> Automatic,
PlotRange -> {{-0.15, 0.15}, {-0.15, 0.15}, {-0.15, 0.15}}
];

It's always hard to interpret pictures of linear objects (lines and planes)
in 3D if you use only one ViewPoint.  Here's an animation that strongly
hints at the solution to your problem:

Needs["Graphics`Animation`];
SpinShow[c]

(After the pictures appear, just double-click on one of them.)

The folded polygon does lie in a plane, but due to an optical illusion, it
looks like two independent planes.  (Part of the explanation for the
illusion is that Mathematica's simulated light sources don't produce shadows!)

Preston Nichols
Mathematics and Computer Science
Wittenberg University

At 01:57 AM 06/30/2000 -0400, KHS wrote:
>For given 4 points like this,
>
>    0.0517  ,  0.0847  ,  0.1004
>    0.0517  , -0.0187  ,  0.0344
>   -0.0517  ,  0.0187  ,  0.0690
>   -0.0517  , -0.0847  ,  0.0030
>
>I thought these points should be on the one plane....
>so I make
>
>
>c=Show[Graphics3D[
>
>[{{
>         0.0517  ,  0.0847  ,  0.1004},{   0.0517  , -0.0187  ,  0.0344},{
>                 -0.0517  ,  0.0187  ,  0.0690},{    -0.0517  , -0.0847  ,
>            0.0030}}]],Axes->Automatic,
>    PlotRange->{{-0.15,0.15},{-0.15,0.15},{-0.15,0.15}}];
>
>
>But, the figure is so strange....It looks like 2 planes...I don't