An algorithm for displaying curved surfaces with hidden lines eliminated Is described. The surfaces are displayed as rectangular grids of straight segments which approximate those surfaces. The algorithm is essentially one of brute force. However, it divides the screen space into Enall 3D boxes to reduce the number of subpatches to be cheched to determine the visibility of each grid point. It turned out that this division process mode this algorithm about 10 times foster than the algorithm which had no use of the division.
Expanding the algorithm for mahing contour drawings is very easy. Some methods for drawing silhouette lines ore considered.
al#orithm, curved surfaces, hidden line elimination
Many display techniques have been developed for parametrically defined curved surfaces. Among these, one of the most common techniques is shading the picture with hidden surfaces removed. There is an abundance of literature on this technique 1-8. However, literature of hidden line elimination techniques for curved surfaces is very scarce. As far as the author knows, there are only two papers 9 and to Appel's algorithm 9and 11 is a complete brute force method; Griffith's 1Β° requires huge auxiliary storage and excessive page swapping between main and auxiliary storage.
In this report, another algorithm will be described. Curved surfaces are expressed as rectangular grids with straight grid lines in this method. Many hidden line algorithms that have been developed for polyhedra 12 could be used for such surfaces. However, this algorithm takes advantage of the simple structure of the 3D objects, that is, the objects to be displayed are restricted to rectangular arrays of quadrilaterals. The algorithm is essentially one of brute force, but it is an improvement over Appel's 9 in that it uses a projected quadrilateral pattern table and that it restricts quadrilaterals to be checked to determine visibility. We make no assumptions concerning the form of the expressions that define the surface patches, but the surface patches should be fairly smooth and continuous to get correct pictures.
The algorithm is implemented on the DEC-20 Systems of the College of Science of the University of Utah, USA and of the Keio University, Japan. The graphic terminals used are Tektronix storage-tube terminals.