       Re: Locator points not working in Manipulate calling RegionPlot, etc.

• To: mathgroup at smc.vnet.net
• Subject: [mg124368] Re: Locator points not working in Manipulate calling RegionPlot, etc.
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Tue, 17 Jan 2012 05:58:15 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201162203.RAA15198@smc.vnet.net>

```The problem is that you have two Locator controls which messes things up. You could do something like this instead.

Manipulate[
PolyHatch[pts[[;; 4]], pts[[-1]], mesh, lighter, plotPoints],
{{pts, {{1, 0}, {1, 1}, {2, 1}, {2, 0}, {0, 0}}}, Locator},
{{mesh, 20}, 1, 30},
{{lighter, .3}, 0, 1},
{{plotPoints, 15}, 10, 30, 1}]

By the way, to make the manipulate less laggy you could use for example ParametricPlot to plot the triangles instead of
RegionPlot. For example, this produces the same result but is much more responsive:

TriHatch[P1_, P2_, P3_, mesh_, light_, plotPts_, opts___] :=
Module[{orient, qq },
orient = Sign[Det[{P2 - P1, P3 - P1}]];
qq = Projection[P1 - P2, P3 - P2] + P2;

ParametricPlot[
a P1 + (1 - a) (b P2 + (1 - b) P3), {a, 0, 1}, {b, 0, 1},
PlotStyle -> None,
Mesh -> Round[mesh Norm[P3 - P2], 1],
MeshStyle ->
If[orient > 0, Lighter[Green, light], Lighter[Red, light]],
MeshFunctions -> {Function[{x, y}, Det[{qq - P1, {x, y} - P1}]]},
PlotPoints -> plotPts,
BoundaryStyle -> None, Evaluate[opts]]
]

Manipulate[
PolyHatch[pts[[;; 4]], pts[[-1]], mesh, lighter, plotPoints],
{{pts, {{1, 0}, {1, 1}, {2, 1}, {2, 0}, {0, 0}}}, Locator},
{{mesh, 20}, 1, 30},
{{lighter, .3}, 0, 1},
{{plotPoints, 5}, 2, 20, 1}]

(note that for ParametricPlot the number of PlotPoints can be as  small as small as 2 whereas for RegionPlot you
need at least 20 points for a reasonable plot).

Heike.

On 16 Jan 2012, at 23:03, Chris Young wrote:

> No matter what I do, in terms of wrapping with DynamicModule, avoiding
> using variables from a module in an enclosed Dynamic or Manipulate, I
> can't get this very basic example to work. I just want to be able to
> drag around 4 points to set the quadrilateral, and then hatch all the
> subtriangles formed by drawin lines to the sides of the quadrilateral
> from the point T.  House of trying everything I could think of have
> failed to get the Locator points to work.
>
> Any help hugely appreciated.
>
> http://home.comcast.net/~cy56/PolyHatchFromTestPt.nb
> http://home.comcast.net/~cy56/PolyHatchFromTestPt.png
>
> Chris Young
> cy56 at comcast.net
>
>
> _TriHatch[P1_, P2_, P3_, mesh_, light_, plotPts_, opts___] :=
> Module[
>  {
>   orient,           (* orientation of the triangles *)
>   interior,      (*
>   inequalities for interior of triangle *)
>   Q                          (*
>   projection of first vertex onto opposite side *)
>   },
>  orient = Sign[Det[{P2 - P1, P3 - P1}]];
>
>  interior[P_] :=
>   And @@ (If[orient > 0, # > 0, # < 0] & /@
>      {Det[{P2 - P1, P - P1}],  Det[{P3 - P2, P - P2}],
>       Det[{P1 - P3, P - P3}] });
>
>  Q = Projection[P1 - P2, P3 - P2] + P2;
>
>  RegionPlot[
>   interior[{x, y}],  {x, -2, 2}, {y, -2, 2},
>   PlotStyle -> Opacity[0.1],
>   ColorFunction -> (White &),
>   Mesh -> Round[mesh Norm[P3 - P2], 1],
>   MeshStyle -> If[orient > 0, Lighter[Green, light], Lighter[Red, light]],
>   MeshFunctions -> {{x, y} =E2=8A=82 Det[{Q - P1, {x, y} - P1}]},
>   PlotPoints -> plotPts,
>   BoundaryStyle -> None,
>   Evaluate[opts]
>   ]
>  ]
>
>
>
> \[HorizontalLine]Ctr[P_] := Plus @@ P/Length[P]
>
> \[HorizontalLine]PolyHatch[P_, T_, mesh_, light_, plotPts_] :=
> Module[
>  {C, n},
>
>  C = \[HorizontalLine]Ctr[P];
>  n = Length[P];
>
>  (*Print["n == ",n];*)
>
>  Show[
>   Table[
>    \[HorizontalLine]TriHatch[T, P[[j]], P[[If[j < n, j + 1, 1]]],
>     mesh, light, plotPts],
>    {j, 1, n}
>    ],
>   Graphics[
>    {
>     Table[
>      {Hue[0.85 (j - 1)/n], Thick,
>       Line[{P[[j]], P[[If[j < n, j + 1, 1]]]}]},
>      {j, 1, n}
>      ],
>     Gray, PointSize[Large], Point[C]
>     }
>    ]
>   ]
>  ]
>
>

```

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