🚀 go-pugleaf

In article <91604@netnews.upenn.edu> jim@heart.seas.upenn.edu (Jim Streicher) writes:
>
>I have a question concerning the determination of
>planar symmetry from two irregular "concentric" shapes.
>
...



Wouldn't some kind of Monte Carlo approach be nice?

(i)   Pick a number of random points in the plane with some
      distribution (for example uniform). Store the points
      that lies between the two shapes. (The cytoplasm? ;-)

(ii)  Pick a random line orientation and find its location
      so that it has half the points on each of its sides.

If the distribution is uniform the line should divide the area
into two equally big areas. If this is not enough you could also
use some kind of momentum criterion to find a good line in (ii).
For example you could specify the variance to be equal:

              sum  x(i)^2      =          sum  x(i)^2
       i: x(i) in area 1           i: x(i) in area 2

where x(i) is the distance from the line to point i, and area 1
and 2 are the areas on the two sides of the line.

(The exact criterions depends on what you're looking for, but
Monte Carlo should be a fast method, probably faster than doing
some other kind of area estimation, especially if you want to do
some weighted integration in your criterion.)

Good Luck!

Mattias