“General clipping on an oblique viewing frustrum” by Puk

An algorithm is presented which clips on a non-rotated viewport positioned anywhere on the viewport plane relative to the viewing vector. This is a generalization of the traditional three-dimensional clipping algorithm in which the viewing vector intersects the viewport at its center. This traditional algorithm is shown to be a special case of the general algorithm. Also shown is that both orthogonal box clipping and perspective pyramid clipping can be accomplished using the same algorithm with only a slight increase in complexity. Finally, the ability to perform switch-controlled hither and yon plane clipping is described. It should be noted that with this general clipping algorithm no separate clipping operation is required for two-dimensional operations since they can be handled as an orthogonal projection from an arbitrary default Z-plane onto the viewport plane.

1. Newman, W. M. and Sproull, R. F. Principles of Interactive Computer Graphics. McGraw-Hill Book Company, New York (1973). {N & S}
2. Puk, Richard F. Expanding the graphics compatibility system to three-dimensions. Computer Graphics and Art, Vol. I, No. 1 (Feb. 1976). {Puk}
3. Sutherland, I. E. and Hodgman, G. W. Reentrant polygon clipping. Communications of the ACM, Vol. XVII, No. 1 (Jan. 1974), pages 32-42.