A displacement field can be defined by a vector field and a height field on an orientable surfaceS, describing the direction and the amount of displacement to be applied toSin order to get a surface represented by the displacement field.Stogether with the vector field can also be considered as a representation of a volume by a ``surface crust''. The crust allows the application of sculpturing operations for designing detailed structure. For conventional height fields over the plane, sculpturing can be reduced to the task of finding the minimum or maximum of the height values of a surface and the height values stored. Over the plane, depth-buffering with parallel projection has been used for calculation. For displacement fields over curved surfaces the projection is more complicated. In this contribution, an efficient solution is presented for displacement fields over triangular meshes. The central task is to insert a triangle in space into the curved depth-buffer represented by the displacement field. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations