🚀 go-pugleaf

On 22 Oct 1998 11:30:46 GMT, einhardschule@t-online.de (Rudolf Polzer)
wrote:

> Rich Pasco <pasco@best.com> schrieb im Beitrag <362C91A2.7F40@best.com>...
> > If you define the area as a polygon, then the point is "in" the area
> > if it is on the correct side of each of the sides of the polygon, e.g.
 
> Then the polygon has to be convex.
 
> Example: a concav (or concave?) polygon
 
> +++++    +++++
> +   +    +   +
> +   +    + p +
> +   xxxxxx   +
> +            +
> ++++++++++++++
 
> Now we check if the point p is on the correct side of xxxxxx.
> It isn't, is it?
 
> The point is that your rule doesn't work in a concav polygon, but only in
> convex ones.
 
Just a remark: There is no concave polygon. A polygon is either convex
or not convex.  Concave is not the contrary of convex.

The function x^2 is (srictly) convex. The function -x^2 is concave.
The function sin(x) is neither convex nor concave.

(Yes, we may say that there are concave polygons if we define the
"outside" of a convex polygon to be a polygon, too... but that's not
what you meant)


Regards
Horst