1. A method for execution by a data processor to prepare an object for display on a display means wherein the object is represented by a plurality of vertices and planar faces each having boundaries defined in terms of the plurality of vertices, the method comprising the steps of: generating a first model of the object that represents the object's original geometry by partitioning the planar faces of the object into a plurality of non-overlapping planar sub-faces each having boundaries defined in terms of the plurality of vertices of the object; partitioning space enclosing the first model into a first plurality of grid cells; generating a first simplified model by, for each grid cell of the first plurality of grid cells containing more than one vertex of the first model, combining the vertices of the first model within the grid cell into at least one first representative vertex; and storing the first simplified model for subsequent use.