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[Peter Hachenberger <>]

Yes, I refer to Nef_nary_union_3. It only stores log(n) of n given polyhedra.
I know that it looks very simple, but there is more to it than you see on first sight.
You would not be the first one that I have to convince that it does something useful
and clever.

Peter

----- wrote: -----

To:
From:
Date: 05/11/2009 09:57PM
Subject: Re: [cgal-discuss] Nef_3 Question


Hi Peter,

>In the n-ary union operation that I offer, which tries to use
> binary operations in a clever way,
> I keep only few of the Nef polyhedra in memory.

I can only assume you're not referring to Nef_nary_union_3, which appears
to requires all the source polyhedrons to be in memory as well as the
incremental union at each step. Maybe I don't understand the memory
implications here?

> If you keep them all, the
> operation will be clearly slower.

I'm not sure what the approaches are that you're comparing.

> I actually also thought of performing as many non-intersecting unions
> first,  but I only found
> few time to experiment with that. The code for non-intersecting unions
> exists somewhere on my hard-drive.

Is this some way to perform "cheap" unions of nefs which are guaranteed
not to intersect?

> In case of n-ary intersections, the chances should be higher to do
> something more efficient than consecutive
> binary operations, but I don't have it.

Surely I have a poor understanding of the workings of Nef3, but can't nary
operations or even complex boolean operations be performed within the
framework of the "overlay, selection, simplification" pipeline? Couldn't
the overlay of N polyhedrons be computed, and then an arbitrarily complex
boolean _expression_ evaluated for each feature? At this point it seems like
simplification would work in the same way as after a binary operation.

I guess that my assumption here is that what's costing a lot in my
chain-union scenario is the continual ground-up recomputation of external
structure (and perhaps some other spatial data structures) for the
cumulative nef, and that this could be avoided by overlaying everything at
once.

Best regards,
Fred


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