Hinged Kite Mirror Dissection

Abstract: Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open whether such a hinged dissection always exists. We solve a special case of this problem, by showing that any asymmetric polygon always has a hinged dissection to its mirror image. Our dissection forms a chain of kite-shaped pieces, found by a circle-packing algorithm for quadrilateral mesh generation. A hinged mirror dissection of a polygon with n sides can be formed with O(n) kites in O(n log n) time.