Shadow generation Based on RE loops and their angular representations

The initial attempt was to find efficient technique to identify shadow plylgons in the shadow-volume based shadow generation algorithm. It was observed that shadows correspond to loops of ridge edges (REs). By identifying all the non-overlapping RE loops of a 3D object, one finds all the shadow polygons and, consequently, all the shadows it generates on other objects as well as shadows it generates on itself. This, however, requires extensive edge-edge intersection tests.It was subsequently realized that by storing the angular representations of the RE looks in a look up table, one can avoid the need of decomposing RE loops into non-overlapping loops and, consequently, the need of performation extensive edge-edge intersection tests. Actually, by building the look up table in a way similar to the bucket-sorted edge table of the standard scan-line method, one can use the table in the scan conversion process to mark the pixels that are in shadow directly, without the need of performing any ray-polygon intersection tests as required in the shadow-volume based shadow generation algorithm. Hence, one gets a new shadow generation technique without the need of performing expensive tests.