Results

Now we look at the cumulative effects for shadow rays of the three main optimizations described in the paper. First we speed up bounding box tests. Next we speed up the traversal using the different methods from Section 4.3. We then treat shadow rays differently from intersection rays and lastly we add a shadow cache. In all of the experiments 1,000,000 rays are generated by choosing random pairs of points from within a bounding box 20% larger than the bounding box of the environment. In the last experiment, 500,000 rays are generated, each generated ray is cast twice, resulting in 1,000,000 rays being cast overall. The first two test cases are real environments, the rest are composed of randomly oriented and positioned unit right triangles. The number gives the number of triangles. Small, mid, and big refer to the space the triangles fill. Small environments are 20 units cubed, mid are 100 units cubed, and big are 200 units cubed. The theater model has 46502 polygons. The science center model has 4045 polygons. The code was run on an SGI O2 with a 180 MHz R5000 using the SGI compiler with full optimization turned on². No shading or other computation was done and time to build the hierarchies was not included.

The experiments reported in Table 1 are explained in more detail below:

1.

Bounding box test computes intersection point, traversal uses recursion, and shadow rays are treated as intersection rays.

2.

Bounding box test replaced by slab version from Section 4.1.

3.

Recursive traversal replaced by iterative traversal using left child, right sibling, and parent pointers as in Section 4.3.

4.

Skip pointer used to speed up traversal as in Section 4.3.

5.

Tree traversal replaced by array traversal as in Section 4.3.

6.

Intersection rays replaced by shadow rays as in Section 4.2.

7.

Shadow caching used as in Section 4.4.

8.

Shadow caching used, but each ray checked twice before generating a new ray. The same number of checks were performed.

Table 1: Results of the different experiments described in the text on different environments. Times rounded to the nearest second.

	1	2	3	4	5	6	7	8
theater	64	36	30	21	22	11	10	6
lab	79	41	32	22	20	12	12	7
10,000 small	415	223	191	142	110	48	50	27
10,000 mid	392	185	154	103	81	77	79	65
10,000 big	381	179	152	104	82	79	77	69
100,000 small	995	620	550	449	351	62	63	33
100,000 mid	932	473	424	324	230	146	148	89
100,000 big	1024	508	442	332	240	210	212	156
300,000 mid	1093	597	536	421	312	120	121	64

The first thing to notice is that real models require much less work than random polygons. This is because the polygons are distributed very unevenly and vary greatly in size. The theater has a lot more open space and even more variation in polygon size than the lab, resulting in many inexpensive rays and a faster average time. In spite of this, the results show very similar trends for all models. In the first 5 experiments we haven't used any model-specific knowledge, we have just reduced the amount of work done. Special shadow rays and caching are more model specific. Shadow rays are more effective when there are many intersections along the ray and are almost the same when there is zero or one intersection. Shadow caching is based on ray coherence and the likelihood of having an intersection. In experiment 7 there is an unrealistically low amount of coherence (none). In experiment 8 we guaranteed that there would be significant coherence by casting each ray twice.