Three-dimensional Clipping

Abstract

In chapter 5 we considered the clipping of lines and facets in two-dimensional space, determining which parts lay within a rectangular window with dimensions horiz × vert. These methods are also sufficient for dealing with orthographic projections of three-dimensional scenes since the whole of space can be projected onto the view plane and clipped in two dimensions. Dealing with perspective projections is rather more complex. Once again we assume that we have a view plane some distance from the eye along the negative z-axis of the right-handed OBSERVER system. A rectangular (horiz × vert) window on this plane is to be identified with the graphics viewport. In previous chapters we have assumed that the eye is positioned in such a way that each vertex has a strictly negative OBSERVED z co-ordinate. This ensures that every vertex can be projected onto the view plane by a standard perspective projection as defined in chapter 11, whence two-dimensional clipping ascertains which parts of the image lie totally within the window. Suppose, however, that we wish to depict a scene as viewed from a position within the model, such as a point lying in a landscape with a large ground plane. Clearly, parts of the model will lie behind the eye and consequently cannot be projected onto the view plane. Such problems cannot be resolved by two-dimensional clipping and so extended methods must be developed. Three-dimensional clipping must determine which parts of a line or facet can be projected onto the window before the projection occurs.