Simultaneous containment of several polygons: analysis of the contact configurations

The main concern of thi s paper i s t he det ect i on of double-cont act con gur at i ons f or s ome pol ygons movi ng i n t r ans l at i on i n a pol ygonal envi r onment . We r s t es t abl i s h s ome gener al pr oper t i es about s uch con gur at i ons , and gi ve condi t i ons of exi s t ence of doubl econt act s f or two or t hr ee object s . We deduce an al gor i t hm det ect i ng s uch a pos i t i on i n t i me O(n ) ( resp. O(n) ) f or two ( resp. t hr ee) convex pol ygons movi ng i n a non convex pol ygon.