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From: Parag Katira on 15 Mar 2010 15:35
I have the vertices of a polyhedron. I need to determine the individual facets and their surface areas. Does an code or a predefined function exist that can help me with this.

Any help is greatly appreciated.

Thanks.
From: Walter Roberson on 15 Mar 2010 15:39
Parag Katira wrote:
> I have the vertices of a polyhedron. I need to determine the individual
> facets and their surface areas. Does an code or a predefined function
> exist that can help me with this.

Are the polyhedra *definitely* convex? Are they Regular? In how many
dimensions? Do you have the good fortune to be restricted to the Platonic solids?

The facets and their surface areas is a much different question if you are
using stellated polyhedra, especially as you increase into higher dimensions.

Do you have some of H. M. Coxter's works on polytopes?
From: Bruno Luong on 15 Mar 2010 16:09
If the polyhedron is convex, you can use convexHull (of DelaunayTri class) or convhulln to determine the vertices of all faces. For each face, project on a plane to get 2D coordinates, then use function POLYAREA to compute the its surface area.

Otherwise look in FEX, especially files from Luigi Giaccari.

Bruno
From: Luigi Giaccari on 16 Mar 2010 12:37
"Parag Katira" <paragkatira(a)gmail.com> wrote in message <hnm25d$97o$1(a)fred.mathworks.com>...
> I have the vertices of a polyhedron. I need to determine the individual facets and their surface areas. Does an code or a predefined function exist that can help me with this.
>
> Any help is greatly appreciated.
>
> Thanks.


I hope one of these works

http://www.mathworks.com/matlabcentral/newsreader/create_message?reply_id=711429

http://www.advancedmcode.org/how-to-plot-a-coloured-surface-from-3d-scatter.html

http://www.advancedmcode.org/surface-recostruction-from-scattered-points-cloud-mycrustopen.html

http://www.advancedmcode.org/surface-recostruction-from-scattered-points-cloud-mycrust-robust.html



http://www.advancedmcode.org
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