well-known type of puzzle in planar geometry requires to
find a cut of a given complex planar shape that divides the shape into two
identical parts
(up to translation and rotation). Not all shapes can be so dissected,
and for some shapes that can, the cutting curve may be quite surprising and
difficult to find.
In this paper we first analyse the inverse problem of assembling planar
shapes from two identical parts
having partially matching boundaries that allow self docking.  Then we show
how
one can use the insights gained from shape docking analysis to derive an
efficient algorithm
to solve dissection puzzles of this type, by mapping the problems into
string
structure detection problems.