Re: planar polygon plot
- To: mathgroup at smc.vnet.net
- Subject: [mg16442] Re: planar polygon plot
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Sat, 13 Mar 1999 02:21:50 -0500
- References: <7c6fad$i0s$7@dragonfly.wolfram.com>
- Sender: owner-wri-mathgroup at wolfram.com
Richard S Hsu wrote in message <7c6fad$i0s$7 at dragonfly.wolfram.com>...
>Hi,
>
>I want to plot a planar polygon in 3D with shading.
>when the polygon is concave, the shading could be wrong.
>
>For a simple example:
>
> Show[ Graphics3D[ Polygon[ { {0,0,0}, {1,0.5,0}, {2,0,0},
> {2,2,0}, {1,1.5,0}, {0,2,0} } ] ] ];
>
>I know what Mathematica is doing here, but want to know
>if there is a easy way to get correct shading for general
>3D planar polygons.
>
>Thanks
Richard,
Not a general solution but it works if the polygon is starlike from its
centroid:
Show[ Graphics3D[ Polygon[ { {0,0,0}, {1,0.5,0}, {2,0,0},
{2,2,0}, {1,1.5,0}, {0,2,0} } ] /.Polygon[lst_]:>
{Line[#],EdgeForm[], Polygon[ Prepend[#,
Plus@@lst/Length[lst]]]}&[Append[lst,First[lst]]]] ];
For a general solution see Tom Wickham-Jones's book, Mathematica Graphics
p448.
This uses the accompanying package ExtendGraphics`NonConvexTriangulate` -
available from MathSource.
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565