Basic Examples
Basic Examples
Find the Monge point and six midplanes for a tetrahedron:
[{{-1,0,3},{1,-1,1},{2,0,-2},{-2,-2,1}}]
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A graphic of a tetrahedron, the Monge point, and the six midplanes:
tet={{0,1,-2},{1,3,3},{3,-1,0},{-1,0,0}};monge=
[tet];Graphics3D[{Tube[#]&/@Subsets[tet,{2}],Green,Sphere[monge[[1]],.2],Opacity[.6],Red,Polygon/@Subsets[tet,{3}],Yellow,Opacity[.2],monge[[2]]}]
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Scope
Scope
The Monge point can be outside of the tetrahedron:
tet={{2,-2,3},{1,0,0},{2,2,1},{3,-1,-2}};monge=
[tet];Graphics3D[{Tube[#]&/@Subsets[tet,{2}],Green,Sphere[monge[[1]],.2],Opacity[.6],Red,Polygon/@Subsets[tet,{3}],Yellow,Opacity[.2],monge[[2]]}]
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