Abstract: A method for accurately calculating the movement of a vertex in a three-dimensional (3-D) topography simulator. The method is particularly suited for calculating vertex movement for cases in which etch/deposition rate depends on the angle between the surface normal and the vertical direction. A workpiece is represented as a collection of material solids. Each of the material solids has a boundary model representation. The method of the present invention is comprised primarily of the steps of: advancing edges and surface planes adjacent to the vertex, creating a set of 2-D solutions by clipping with pairs of adjacent surface planes; creating a set of combined 2-D solutions by clipping invalid sections of combined 2-D solutions; construct an arbitrary vertical plane that intersects the surface at the vertex point; constructing vertex trajectories for the vertex to be moved; and clipping constructed vertex trajectories at intersections of created surface and the constructed vertical plane.