       Hatching triangle interior

• To: mathgroup at smc.vnet.net
• Subject: [mg124282] Hatching triangle interior
• From: Chris Young <cy56 at comcast.net>
• Date: Mon, 16 Jan 2012 17:03:26 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```If the number of plot points is kept down, this does a pretty fast
hatching of the triangle interior. Green for positive orientation, red
for negative.

I'm hoping this can be generalized to any convex polygon via permuting
the indices for a list of points.

http://home.comcast.net/~cy56/TriHatch.nb
http://home.comcast.net/~cy56/TriHatchPic1.png
http://home.comcast.net/~cy56/TriHatchPic2.png

\[HorizontalLine]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},
ColorFunction -> (White &),
Mesh -> Round[mesh Norm[P3 - P2], 1],
MeshStyle ->
If[orient > 0, Lighter[Green, light], Lighter[Red, light]],
MeshFunctions -> {{x, y} \[Function] Det[{Q - P1, {x, y} - P1}]},
PlotPoints -> plotPts
]
]

Chris Young

```

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