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MathGroup Archive 2005

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Re: Plotting polyhedra

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62223] Re: [mg62207] Plotting polyhedra
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 16 Nov 2005 02:28:26 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Peter,

How about this?

v1 = {0, 0, 0};
v2 = {1, 0, 0};
v3 = {0, 1, 0};
v4 = {0, 0, 1};

Show[Graphics3D[{Polygon[{v1, v2, v3}], Polygon[{v1, v2, v4}], 
        Polygon[{v1, v4, v3}], Polygon[{v4, v2, v3}]}]];

But if you are going to plot many tetrahedrons...

tetrahedron[{v1_, v2_, v3_, v4_}] := {Polygon[{v1, v2, v3}], 
      Polygon[{v1, v2, v4}], Polygon[{v1, v4, v3}], Polygon[{v4, v2, v3}]};

Show[Graphics3D[
      {tetrahedron[{v1, v2, v3, v4}],
        tetrahedron[{{1, 1, 1}, {1, 2, 3}, {2, 4, 1}, {3, 2, 1}}]}]
    ];

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 


From: King, Peter R [mailto:peter.king at imperial.ac.uk]
To: mathgroup at smc.vnet.net



I wish to be able to plot polyhedra given a table of (xyz) coordinates
for vertices. I'd be happy if I was restricted to tetrahedra, but would
prefer to be able to deal with general polyhedra. I can always plot the
polygons that make up the faces of the polyhedron but this seems a bit
tedious, is there a more efficient way than (for example)

Show[Graphics3D[{Polygon[{{0,0,0},{1,0,0},{0,1,0}}],Polygon[{{0,0,0},{1,
0,0},{0,0,1}}],Polygon[{{0,0,0},{0,0,1},{0,1,0}}],Polygon[{{0,0,1},{1,0,
0},{0,1,0}}]}]]

Which involves putting in the coordinates of each vertex 3 times.

Thanks.




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