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Re: Polygon with holes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97405] Re: Polygon with holes
  • From: Harrie Kraai <hakraai at xs4all.nl>
  • Date: Thu, 12 Mar 2009 05:42:38 -0500 (EST)
  • References: <gp5fn9$9mc$1@smc.vnet.net> <gp7vsh$1cv$1@smc.vnet.net>

ragfield wrote:
> 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}}}]
> 

Hi Rob,

Thanks for this suggestion. However, (as you are porbably aware) it does 
not work so easily for arbitrary polygons. The connection between inner 
and outer contours is made by a straight line. A general algorithm would 
have to select the points to be connected and make sure that the 
connection itself does not intersect the contours. There should also be 
a check on the orientations. Making two or more holes would complicate 
things further.

As I expected there seems to be no simple facility available. This could 
be a feature request for wolfram. How do I submit one?

HK

>> 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.


T


> 
> -Rob
> 


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