Franklin Algorithm:

We indicate how the number of possible comparisons of polygons grows as the square of the number of polygons in the scene. Many of the hidden-surface algorithms exhibit this behaviour and have serious performance problems on difficult scenes. Franklin developed an approach that gives linear time behaviour for most scenes. It is done by overlaying a grid of cells on the scene (similar to Warnocks approach, only these cells are not subdivided). The size of the cells is on the order of the size of an edge in the scene. At each of cell the algorithm looks for a covering face and find out which edges are in front of this face. It then computes the intersections of these edges and find out their visibility. The idea is that as objects are added to the scene and the number of polygons enhance, the new objects shall either be hidden by objects already in the scene or shall hide other objects in the scene. Whereas the number of objects enhance, the complexity of the final scene (after hidden portions are removed) does not enhance. By considering only the edges in front of the covering face for a cell, the algorithm considers only the edges likely to be in the final image. Although the total number of edges may increase, this enhance occurs, for the most part, behind the covering faces, and the number of edges in front shall remain small.