# Boost :

Subject: Re: [boost] Formal Review: Boost.Polygon starts today August 24, 2009
From: Jeffrey Hellrung (jhellrung_at_[hidden])
Date: 2009-08-25 13:11:39

Fernando Cacciola wrote:
> Dear Developers,
>
> The formal review of the Boost.Polygon library by Lucanus Simonson
> starts today, August 24, 2009 and will finish September 2, 2009.
>
> I really hope to see your vote and your participation in the discussions on
> the Boost mailing lists!
>
> ---------------------------------------------------
...
> Best Regards
>
> Fernando Cacciola
> Review Manager

I read through the boostcon paper and it all looked very interesting,
but was disappointed to find that coordinates must be of integral type.
Can you comment on the rationale for this limitation? Or, perhaps you
don't consider this a genuine limitation, in which case, could you
explain why you don't, given that many computational geometry problems
are given in terms of some floating point format? I have some guesses
but figure I should just ask outright.

Also, I have a question (or multiple...) concerning the line-sweeping
algorithm, which I don't fully understand. To begin with, I don't fully
understand what you mean by the "derivative of a polygon", despite
several paragraphs devoted to this. I understand this is a novel
concept you've invented, so I don't expect to find anything useful in
the references. It seems you're implicitly using a 2-dimensional as
well as a 1-dimensional representation of a polygon...? Section 5.1
begins by viewing the polygon as a characteristic function of the plane.
That's reasonable. And it is indeed a "mathematical function of two
variables". What's a jump in derivation to me is going from the "usual"
partial derivatives of these characteristic functions (which amounts to
a vectorized-delta distribution on the boundary of the polygon...right?)
to these vertex-support quantities. What's adding to my confusion is
that "magnitudes" of the impulses that compose the derivative may be +1
or -1, indicating that an impulse with magnitude +1 is different from an
impulse in the opposite direction of magnitude -1. So I'm not really
sure why you pick the specific arrow directions and signs in Figure 3.
Would it be possible to explain this in more detail, or provide another
reference?

Thanks,

- Jeff