Spacetime Ray Tracing for Animation

Abstract

Techniques for the efficient ray tracing of animated scenes are presented. They are based on two central concepts: spacetime ray tracing, and a hybrid adaptive space subdivision/boundary volume technique for generating efficient, nonoverlapping hierarchies of bounding volumes. In spacetime ray tracing, static objects are rendered in 4-D space-time using 4-D analogs to 3-D techniques. The bounding volume hierarchy combines elements of adaptive space subdivision and bounding volume techniques. The quality of hierarchy and its nonoverlapping character make it an improvement over previous algorithms, because both attributes reduce the number of ray/object intersections that must be computed. These savings are amplified in animation because of the much higher cost of computing ray/object intersections for motion-blurred animation. It is shown that it is possible to ray trace large animations more quickly with space-time ray tracing using this hierarchy than with straightforward frame-by-frame rendering.

References

1. 1. A. Appel, "Some Techniques for Shading Machine Renderings of Solids," Proc. AFIPS Conf., Vol. 32, 1968, pp. 37-45.
2. 2. W. Bouknight and K. Kelley, "An Algorithm for Producing Half-Tone Computer Graphics Presentations with Shadows and Movable Light Sources," Proc. AFIPS Conf., Vol. 36, 1970, pp. 1-10.
3. 3. D. Kay, "Transparency, Refraction, and Ray Tracing for Computer Synthesized Images," master's thesis, Cornell University, Ithaca, NY, 1979.
4. 4. T. Whitted, "An Improved Illumination Model for Shaded Display," CACM, June 1980, pp. 343-349.
5. 5. R.L. Cook, T. Porter, and L. Carpenter, "Distributed Ray Tracing," Computer Graphics (Proc. SIGGRAPH), July 1984, pp. 137-145.
6. 6. M.E. Lee, R.A. Redner, and S.P. Uselton, "Statistically Optimized Sampling for Distributed Ray Tracing," Computer Graphics (Proc. SIGGRAPH), July 1985, pp. 61-67.
7. 7. J.T. Kajiya, "The Rendering Equation," Computer Graphics (Proc. SIGGRAPH), July 1986, pp. 143-150.
8. 8. E.A. Haines and D.P. Greenberg, "The Light Buffer: A Shadow-Testing Accelerator," CG&A, Sept. 1986, pp. 6-16.
9. 9. T. Kay and J.T. Kajiya, "Ray Tracing Complex Scenes," Computer Graphics (Proc. SIGGRAPH), July 1986, pp. 269-278.
10. 10. H. Weghorst, G. Hooper, and D. Greenberg, "Improved Computational Methods for Ray Tracing," ACM Trans. on Graphics, Jan. 1984, pp. 52-69.
11. 11. J.T. Kajiya, "New Techniques for Ray Tracing Procedurally Defined Objects," Computer Graphics (Proc. SIGGRAPH), July 1982, pp. 245-254.
12. 12. S. Roth, "Ray Casting for Modelling Solids," Computer Graphics and Image Processing, Vol. 18., 1982, pp. 109-144.
13. 13. S.M. Rubin and T. Whitted, "A 3-Dimensional Representation for Fast Rendering of Complex Scenes," Computer Graphics (Proc. SIGGRAPH), July 1980, pp. 110-116.
14. 14. J. Goldsmith and J. Salmon, "Automatic Creation of Object Hierarchies for Ray Tracing," CG&A, May 1987, pp. 14-20.
15. 15. A.S. Glassner, "Space Subdivision for Fast Ray Tracing," CG&A, Oct. 1984, pp. 15-22.
16. 16. M. Dippe and J. Swenson, "An Adaptive Subdivision Algorithm and Parallel Architecture for Realistic Image Synthesis," Computer Graphics (Proc. SIGGRAPH), July 1984, pp. 149-158.
17. 17. M. Kaplan, "Space Tracing: A Constant Time Ray Tracer," SIGGRAPH 85 Tutorial on the State of the Art in Image Synthesis, July 1985.
18. 18. A. Fujimoto, T. Tanaka, and K. Iwata, "ARTS: Accelerated Ray-Tracing System," CG&A, Apr. 1986, pp. 16-27.
19. 19. P. Heckbert, "Color Image Quantization for Frame Buffer Display," Computer Graphics (Proc. SIGGRAPH), July 1982, pp. 297-307.
20. 20. A.S. Glassner, "Spacetime Ray Tracing for Animation," Introduction to Ray Tracing, course notes #13 (SIGGRAPH), ACM, New York, 1987.
21. 21. J.T. Kajiya, "New Techniques for Ray Tracing Procedurally Defined Objects," Computer Graphics (Proc. SIGGRAPH) July 1983, pp. 91-102.
22. 22. R. Rucker, The Fourth Dimension, Houghton Mifflin, Boston, 1984.
23. 23. A. Abbott, Flatland, Dover Publications, Mineola, N.Y., 1952 (original copyright 1884).
24. 24. P. Bergmann, Introduction to the Theory of Relativity, Dover Publications, Mineola, N.Y., 1975.
25. 25. A.S. Glassner, "Supporting Animation in Rendering Systems, Proc. CHI+GI, Canadian Information Processing Soc., Toronto, 1987.
26. 26. P. Amburn, E. Grant, and T. Whitted, "Managing Geometric Complexity with Enhanced Procedural Models," Computer Graphics (Proc. SIGGRAPH), July 1986, pp. 189-195.
27. 27. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes, Cambridge University Press, N.Y., 1986.
28. 28 J. Arvo and D. Kirk, "Fast Ray Tracing by Ray Classification, Computer Graphics (Proc. SIGGRAPH), July 1987, pp. 55-64.

Index Terms

• Computing methodologies

  • Computer graphics

    • Rendering

      • Ray tracing