🚀 go-pugleaf

I have a question concerning the determination of
planar symmetry from two irregular "concentric" shapes.

An example of the two shapes might be ...


                         -------
                       /         \
                      /    ____   \_
                      |   /    \     \
                      /  |    _/     |
                     /   |   |       |
                    /    |___/   x    \ 
                    |           ______/
                     \____     /
                          \___/


In general, the shapes will not have a line of symmetry
such that one half of the shape is the mirror image of the other.

I need to find the "best" line of symmetry and quantify the error
based on some numerical algorithm.

The symmetry must be based on the mass between the concentric
shapes, (ie the area indicated with an 'x').


By eyeballing these shapes, I guess the line of sym should be drawn
like this:



                         -------
                       /         \
                      /    ____   \_
                      |   /    \     \
          ------------/--|----_/-----|------------ 
                     /   |   |       |
                    /    |___/   x    \ 
                    |           ______/
                     \____     /
                          \___/


Obviously, this may be way off, and I don't know how far off it is.


Does anyone know of a algorithm to determine the best line of symmetry?
Any thoughts on this problem?

---
Jim Streicher                                         (215) 898-8099
jim@heart.seas.upenn.edu (best)                       Dept. of Bioengineering
jim@thrombus.seas.upenn.edu (forwarded to heart)      U. of Penn.
streiche@eniac.seas.upenn.edu (forwarded to heart)    Philadelphia, PA. 19104