       Re: making a plane

• To: mathgroup at smc.vnet.net
• Subject: [mg24228] Re: making a plane
• Date: Sat, 1 Jul 2000 03:22:00 -0400 (EDT)
• References: <8jhcqf\$q1i@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You need to use "Polygon" in the Graphics3D routine.  See the following
code snippet.  I defined your 4 points with names "data#"

data1 = {0.0517, 0.0847, 0.1004}
data2 = {0.0517 , -0.0187 , 0.0344}
data3 = {-0.0517 , 0.0187 , 0.0690}
data4 = {-0.0517 , -0.0847 , 0.0030}

Show[Graphics3D[
{Polygon[{data1, data2, data3}],
Polygon[{data2, data3, data4}]}]]

This turns out looking fine.  I am always cautious about using a graph
to judge if two things are coplanar - They might be close enough to
look like it, but in reality are slightly "off".  You should confirm
that they are indeed coplanar by checking the cross products of the
vectors to see if they yield the same normal vector defining the
plane.  Here is my (inelegant) way:

line12 = line12/Sqrt[(line12.line12)]
line13 = line13/Sqrt[(line13.line13)]
line34 = line34/Sqrt[(line34.line34)]
line24 = line24/Sqrt[(line24.line24)]

In:=
Cross[line12, line24]

Out=
{0.0714131, -0.439356, 0.688325}

In:=
Cross[line13, line34]

Out=
{0.0714131, -0.439356, 0.688325}

As we see the two cross products yield the same results - confirming
the the 4 points do indeed lie in the same plane.

In article <8jhcqf\$q1i at smc.vnet.net>,
"KHS" <khs at procd.sogang.ac.kr> 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
>