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MathGroup Archive 2000

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Re: RegionPlot ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23496] Re: [mg23489] RegionPlot ?
  • From: BobHanlon at aol.com
  • Date: Sun, 14 May 2000 16:59:59 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 5/12/2000 11:12:28 PM, SChandler at uh.edu writes:

>Right now, the function Experimental`CylindricalAlgebraicDecomposition
>yields a list of inequalities. For inequalities with two variables, I would
>like to be able to plot the region showing where that inequality is
>satisfied.
>
>By way of simple example:
>
>In[69]:=
>ecad = Experimental`CylindricalAlgebraicDecomposition[{x + y <= 3, x -
>y
>> -4,
>       x >= 0, y >= 1}, {x, y}]
>
>Out[69]=
>0 <= x < 2 && 1 <= y <= 3 - x || x == 2 && y == 1
>
>What I would like to do is something like:
>
>RegionPlot[ecad,{x,-3,5},{y,-3,7}].
>
>The output would be Polygon primitives, Line primitives,  and a Point
>primitive
>
>Any thoughts on how to implement this?
>
>Obviously, one could approximate the matter by creating a table of x,y
>values and plotting at {x,y} a primitive of some shape and size for each
>table element satisfying the set of inequalities.  I was hoping someone
>might come up with something more elegant, however. (Maybe ContourPlot
>used
>in some way?)
>

Here is an approach that makes use of FilledPlot. I haven't tested it much, 
but it should give you an idea for one approach.

Needs["Graphics`FilledPlot`"]

regionPlot[ecad_, 
      {x_Symbol, xMin_?NumericQ, xMax_?NumericQ}, 
      {y_Symbol, yMin_?NumericQ, yMax_?NumericQ}] := 
    Module[{xmask, funcs, pts, plts},
      xmask = (UnitStep[x - First[#]] - UnitStep[x - Last[#]]) & /@ 
          Cases[ecad, 
            Inequality[lower___, x, upper___] -> {lower, upper}, {1, 
              Infinity}];
      funcs =  {First[#], Last[#]} & /@ 
          Cases[ecad, 
            Inequality[lower___, y, upper___] -> {lower, upper}, {1, 
              Infinity}];
      pts = 
        Cases[ecad, And[Equal[x, x0_], Equal[y, y0_]] ->  Point[{x0, y0}]];
      plts = 
        MapThread[
          FilledPlot[#1*#2, {x, xMin, xMax}, PlotRange -> {yMin, yMax}, 
              Curves -> None, 
              Epilog -> {AbsolutePointSize[5], RGBColor[1, 0, 0], pts}, 
              DisplayFunction -> Identity] &, {funcs, xmask}];
      Show[plts, DisplayFunction -> $DisplayFunction]
      ];

ecad = Experimental`CylindricalAlgebraicDecomposition[{x + y <= 3, x - y > -4,
       x >= 0, y >= 1}, {x, y}]

regionPlot[ecad, {x, -3, 5}, {y, -3, 7}];

ecad = Experimental`CylindricalAlgebraicDecomposition[{x + y <= 6, x - y > -4,
       x >= 0, y >= -2}, {x, y}]

regionPlot[ecad, {x, -3, 10}, {y, -3, 6}];


Bob

BobHanlon at aol.com


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