Dear All,
I have convex polygon (expressed by points in cartesian coordinate system). I am looking for a solution to splitting into two congruent pieces. Is there any way to to estimate the points that lead cut?
Dear All, I have convex polygon (expressed by points in cartesian coordinate system). I am looking for a solution to splitting into two congruent pieces. Is there any way to to estimate the points that lead cut? 


There exist convex quadrilaterals which have no such splitting.
And there is an $O(n^3)$ algorithm to decide if such a splitting exists for a (nonconvex) $n$gon.
See the paper by
Dania ElKhechen, Thomas Fevens, John Iacono, and Günter Rote,
"Partitioning a polygon into two mirror congruent pieces."
In Proc. 20th Canad. Conf. Comput. Geom., pages 131134, August 2008
(PDF download link).


