On 21 April 2010 12:56, R.E. Boss <[email protected]> wrote:
>
> The basic idea of winding number is brilliant .........

The winding number method does have certain beauty in the abstract
mathematical sense but is computationally awful and for this reason
not much used.  Due to the complicated nature of the involved
operations (angular computations) and the resulting computational
inaccuracies, it is much less stable than the even/odd intersection
counting method.

> I estimate that this solution performs better than others.

Better than what?  Measured on what?  I find your statement doubtful
in view of the complexity of the above mentioned numeric operations
that it is based upon (apart from them making the method less stable).

Note also that, by its nature, the even/odd intersection counting
method can work with only integer arithmetic, provided that all given
coordinates are integers.  This should both ensure maximum accuracy
and improve performance.  The winding number method does not
have this feature.

> Apart from that it works for a large(r) collection of polygons.

‘Works’ would depend on how you would want to treat islands –
polygons entirely within polygons, and islands' islands etc.
Are they holes (and holes within holes) or are they just internal
areas – preferences vary.  Similar for intersecting polygons.
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