[R] integrate over polygon

[Paul Lynch]

Oops.  I just re-read your message and saw you were trying to
integrate a function over a polygon, not calculate its area.  I'm
sorry I didn't read more carefully.
         --Paul

On 2/15/07, Paul Lynch <plynchnlm at gmail.com> wrote:
> I'm still pretty ignorant about R, but I think it might be possible to
> work out an algorithm using  cross products.  First you would want to
> subdivide the polygon into convex polygons.  I haven't tried to do
> that before, but it looks like it might be possible by looking at the
> sign of cross products of vectors between vertices.  (In other words,
> pick a vertex, and then start working your way around the polygon and
> pay attention to the sign of cross products of vectors from the
> starting vertex to successive vertices.)  Once you have convex
> polygons, you can calculate the area using cross products of vectors
> from some point (e.g. the origin) to adjacent vertices of the polygon.
>  I think that probably most computer graphics texts would have such an
> algorithm.
>
> How to implement that in R is not something I can answer, but it
> doesn't sound hard.
>        --Paul
>
> On 2/14/07, Haiyong Xu <xuhy at ucla.edu> wrote:
> > Hi there,
> >
> > I want to integrate a function over an irregular polygon. Is there
> > any function which can implement this easily? Otherwise, I am
> > thinking of divide the polygon into very small rectangles and use
> > "adapt" to approximate it. Do you have any suggestions to get the
> > fine division? Any advice is appreciated.
> >
> > Haiyong
> >
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