Typical ILT goes through a continuous tone mask to define a greyscale mask for the best process window, followed by a conversion into actual mask geometries, which are typically Manahttanized to be compatible with printing on existing mask writers. On mask, however, the features to be printed are not Manhattan, and we demonstrate that, by not taking into account the actual mask shapes, current Manhattan mask 3D (M3D) approximations using width, shape, and corner libraries, give rise to poor predictions for the final aerial image. Now that curvilinear ILT is possible to manufacture, we introduce a fully curvilinear mask 3D approximations, compatible with ILT masks, that predict the aerial image significantly better than before.