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@cs.umd.edu http://www.cs.umd.edu/~piotrm
PPL-devel mailing list PPL-devel@cs.unipr.it http://www.cs.unipr.it/mailman/listinfo/ppl-devel
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=rep...
http://www.cems.uwe.ac.uk/~gdhoward/Howard-MSC.pdf
Regards, Enea.