Efficiency Structures

Homework 5

Simon Premoze 

1. Introduction

Ray tracing is known to be very slow. It has been often considered too computationally expensive to be useful. Therefore, efficiency is a critical issue that has been addressed in research from the beginning.
The most fundamental ray tracing acceleration technique is to find object/ray intersection as fast as possible. There are many different methods that address this problem. In this assignment I have tried two  familis of efficiency structures: bounding volume hierarchy and spatial subdivision (ie uniform grid).

The following scenes were used to test this structure: For testing purposes, N spheres were created centered at ( drand48()*2-1,drand48()*2-1,drand48()*2-1) and a radius of 0.1/(N^0.3333 ). I think that ths scene does not reflect the performance of individual efficiency schemes, so be careful interpreting the results. In addition, shading and lighting were turned off to speed up the raytracing time.

I ran the test program on R8000 with dual FP unit and 128 Mb of RAM. As it turned out, my raytracer was not particulary suited for these tests, because some features I have implemented slow it down (bigger memory consumption due: each object has name, transformation matrix, inverse transformation matrix, ray ID, etc. ).

2. Grid
 
 I implemented adaptive grid as described by Jevans and Wyvill (ie if number of objects in a voxel exceeds some threshold, subdivide the voxel). Adaptive grid option was not used due to the bug in my code. There is more room for improvement  especially in voxel traversal scheme.
 

Num Spheres Preprocess time Trace time Total time
1 small 10.34 s 10.34 s
10 small 13.15 s 13.15 s
100 small 17.76 s 17.76 s
1000 small 24.92 s 24.92 s
10000 0.2 s 32.73 s 32.93 s
100000 3.12 s 44.59 s 47.71 s
1000000 16.43 s 119.1 s 135.53 s
 

3. Bounding Volume Hierarchy
 
 I implemented automiatic bounding volume hierarchy creation scheme as described by Goldsmith and Salmon. Whene there were large number of objects in the scene, I was unable to experiment with the number of tries hierarchy was generated due to poor implmentation on my part (ie I ran out of memory, because I kept too many object lists around).
 
 

Num Spheres Preprocess time Trace time Total time
1 0 s 8.3 s 8.3 s
10 0.8 s 12.53 s 13.33 s
100 1.4 s 14.2 s 15.6 s
1000 7.4 s 21.21 s 28.61 s
10000 20.3 s 38.2 s 58.5 s
100000 164.6 s 49.69 s 214.29 s
1000000 613 s 107.4 s 720.4 s
 

4. BSP Tree
 
BSP tree is another space subdivision acceleration scheme. I have implemented hybrid method: build hierarchical bounding volume structure to some degree then partition it and build a BSP tree.

I have not been able to test this method yet.
 

5. Conclusion
 
Efficiency structures reduce the ray tracing time dramatically.
Grid efficiency scheme was the fastest for THIS PARTICULAR SCENE, using my own implementation. It does not mean that it will outperform other schemes for different scenes and different raytracers. I need to run more experiements on more realistic scenes to determine the performance.
 

6. References

1. Glassner A., An Introduction To Ray Tracing, pp. 202-262, 1989
2. Goldsmith, J., and Salmon, J., Automatic creation of object hierarchies for ray tracing, IEEE Comput. Graph. Appl. 7(5), 14-20, May 1987
3. Snyder, J.M. and Barr, A.H., Ray tracing complex models containing surface tesselations, Siggraph Proceedings 1987, 45-54, July 1987
4. Fujimoto, A. et al., ARTS: Accelerated Ray-Tracing System. IEEE Comput. Graph Appl. 6(4), 16-26, April 1986
5. Jevans, D. and Wyvill, B., Adaptive Voxel Subdivision for Ray Tracing, Graphics Interface '89, 164-172, 1989
6. Woo, A. and Amanatides, J., Voxel Occlussion Testing: A Shadow Determination Accelerator for Ray Tracing, Graphics Interface 1990, 213-220, 1990
 
 

Simon Premoze

premoze@cs.utah.edu