On Sat, Jul 7, 2012 at 8:45 PM, Tom Browder <tom.brow...@gmail.com> wrote:
>
> I believe that if you think of positive and negative areas it may
> work. Each "triangle" is formed by either clockwise or
> counterclockwise movement to the next vertex. If we consider
> counterclockwise movement as positive then the sum of all the fans, in
> the limit, should be the area.
>
> -Tom
>
Unless I'm misunderstanding what you've written (which I've been know to
do), I don't think this is generally true. Consider the following sketch:
mged> put sample_sketch sketch V {0 0 0} A {1 0 0} B {0 1 0} V {
{0 0}
{3 0}
{3 3}
{2 3}
{2 1}
{1 1}
{1 3}
{0 3}
} SL {
{line S 0 E 1}
{line S 1 E 2}
{line S 2 E 3}
{line S 3 E 4}
{line S 4 E 5}
{line S 5 E 6}
{line S 6 E 7}
{line S 7 E 0}
}
If we started the "fans" from vertex 0, I cannot see how simply looking at
the sign of the angular velocity term will be able to figure out the area
inside the contour.
In the meantime, I think this is the book I was thinking of:
http://perso.uclouvain.be/vincent.legat/teaching/data/meca2170-GmshCompanion.pdf
Looking at it now, this may or may not be it.
-Matt-
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