[PPL-devel] visualizing polyhedra

[Enea Zaffanella]

On 01/08/2014 03:41 AM, Piotr Mardziel wrote:
> Hello ppl developers. I’m trying to visualize (draw) polyhedra but am finding it hard to do so with the representations provided in ppl. Is there some reasonable way to get from ppl or (easily) compute the faces of a polyhedron so that it can be drawn?
>
> Best,
> Piotr (Peter) Mardziel <piotrm at cs.umd.edu>
> http://www.cs.umd.edu/~piotrm
>
>
>
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Hello Piotr.

For the sake of ease of exposition, let me consider a fully dimensional, 
topologically closed and bounded polyhedron. A minimized representation 
in the PPL will then consist of a minimal set of constraints (the facets 
of the polyhedron), a minimal set of generators (the vertices of the 
polyhedron) and a saturation matrix telling, for each constaint, which 
of the vertices are saturating that constraint. Hence, using this 
saturation matrix, knowing which vertices form the facets of the 
polyhedron should be quite immediate and reasonably efficient. 
Currently, however, there is no public method providing this info to the 
user in the most efficient way (adding it should not be a big issue ... 
the only problem is the design of a proper interface).
Is that what you were meaning when asking to "compute the faces of a 
polyhedron"?

I should also mention that, a few years ago, a couple of Leeds' students 
(Leigh Finegold and Gerard Howard) worked on a web-based application for 
the visualization of (lower dimension projections of) polyhedra, based 
on the PPL. You may find the following links useful as a starting point 
to obtain further info:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98.9838&rep=rep1&type=pdf

http://www.cems.uwe.ac.uk/~gdhoward/Howard-MSC.pdf

Regards,
Enea.