Re: Polygon with holes

• To: mathgroup at smc.vnet.net
• Subject: [mg97330] Re: Polygon with holes
• From: ragfield <ragfield at gmail.com>
• Date: Wed, 11 Mar 2009 04:22:27 -0500 (EST)
• References: <gp5fn9\$9mc\$1@smc.vnet.net>

```On Mar 10, 5:34 am, Harrie Kraai <hakr... at xs4all.nl> wrote:
> Does anyone know of a facility for Polygons (graphics) with holes inside?
> I guess there is no such thing as an oriented polygon in Mathematica?
> Or a polygon consisting of disjoint lines (inner and outer contours,
> clockwise and counterclockwise)?
>
> I can see that it is possible to connect outer and inner contours using
> a dummy line, but that is not so easy to program in a generic way.

This is currently the only way to achieve the desired affect.

MultiContourPolygon[polys_List] := Module[
{contours = Append[#, First[#]] & /@ polys},
{
Polygon@Join[Join @@ contours, Reverse[First /@ contours]],
Line[contours]
}
]

Graphics@MultiContourPolygon[{{{0, 0}, {0, 1}, {1, 1}, {1,
0}}, {{.25, .25}, {.75, .25}, {.75, .75}, {.25, .75}}, {{.4, \
.4}, {.6, .4}, {.6, .6}, {.4, .6}}}]

> Solutions such as creating an artificial hole by another Polygon in the
> background colour are not really acceptable.
>
> Polygon's with holes would be very useful for maps etc.

Agreed.

-Rob

```

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