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Re: Plotting feasible region of a linear programme

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112822] Re: Plotting feasible region of a linear programme
  • From: Yaroslav Bulatov <yaroslavvb at gmail.com>
  • Date: Sat, 2 Oct 2010 05:43:55 -0400 (EDT)
  • References: <i81j79$a07$1@smc.vnet.net>

On Sep 30, 1:54 am, Yaroslav Bulatov <yarosla... at gmail.com> wrote:
> What is a good way to visualize feasible region of a 3-variable linear
> programme in Mathematica? I tried RegionPlot3D but you can see the
> result is lacking in aesthetics
>
> randomCons := Module[{},
>    hadamard = KroneckerProduct @@ Table[{{1, 1}, {1, -1}}, {3}];
>    invHad = Inverse[hadamard];
>    vs = Range[8];
>    m = mm /@ vs;
>    sectionAnchors = Subsets[vs, {1, 7}];
>    randomSection :=
>     Mean[hadamard[[#]] & /@ #] & /@
>      Prepend[RandomChoice[sectionAnchors, 3], vs]; {p0, p1, p2, p3} =
>     randomSection;
>    section =
>     Thread[m ->
>       p0 + {x, y, z}.Orthogonalize[{p1 - p0, p2 - p0, p3 - p0}]];
>    And @@ Thread[invHad.m >= 0 /. section]
>    ];
> Table[RegionPlot3D @@ {randomCons, {x, -3, 3}, {y, -3, 3}, {z, -3,
>     3}}, {10}]

I got a suggestion from Maxim Rytin to use a legacy package
InequalityPlot, and it works much better than RegionPlot3D for this
problem. I've put comparison in parallel stackoverflow thread --
http://stackoverflow.com/questions/3815496/plotting-linear-inequalities-in-mathematica.

Two issues remain -- 1) it creates more polygons than necessary, so
can't use EdgeForm to outline edges of the region 2) sometimes faces
are missed


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