Abstract: The layer representation (L-REP) is a triangle-based representation for polygons. It is simple and robust, and presents interesting properties for several applications. We extend this algorithm to curved-edge polygons and present CL-REP for Layer-based representation of curved-edge polygons. A formal mathematical model of it is defined and two representative algorithms to construct it are given. Several simple applications of this model are presented, with a special emphasis on the Boolean operations and point-in-polygon inclusion test, which can be easily and efficiently solved using the CL-REP.