The edge-based optical proximity correction (OPC) has been serving the industry for more than 20 years with few changes the mask geometry. In the past 10 years, ILT pioneers created the curvilinear mask using alternate algorithms. The two approaches differ so much that the experiences in conventional OPC do not easily translate to the use of ILT, and vice versa. We report a new approach to curvilinear masks that follows the conventional OPC workflow. It creates and manipulates the curvilinear shapes by generalizing the edge-based OPC to vertices. Conventional OPC techniques, including dissection, classification, target point placement, etc., remain as central roles. Full-chip correction results are included to demonstrate the good performance of the curvilinear mask for both contact and line/space patterns. The analysis of critical patterns shows that the curvilinear OPC lifts the mask rule check restriction to the mask shape that limits Manhattan OPC. The turnaround time of creating the curvilinear mask is around two times than that of the Manhattan mask.