Accelerated Ray Tracing

  • Akira Fujimoto
  • Kansei Iwata


This paper proposes algorithms for dealing with two essential problems encountered in generating continuous-tone images by the ray tracing method: speed and aliasing. These two factors are considered an Achilles’ heel of the method and have been the main cause preventing the method from being widely used. The paper examines previous approaches to the problem and finally proposes a scheme based on the coherency of an auxiliary data structure imposed on the original object domain. Both simple spatial enumeration and a hybrid octree approach were investigated. 3DDDA (3D line generator) was developed for efficient traversing of both structures. It constitutes the essential factor providing a dramatic improvement (order of magnitude) in processing speed in comparison to other known ray tracing methods. In particular, processing time is found to be virtually independent of the number of objects involved in the scene. For a larger number of objects (around 1500), this method actually becomes faster than scan-line methods. In order to remove jags from edges, a scheme for identifying the edge orientation and the distance from a pixel center to the true edge has been implemented. The additional time required for antialiasing depends on the total length of the edges encountered in the scene, but is normally only a fractional addition to the time required to produce such a scene without antialiasing.


Computer Graphic Cell Decomposition Control Term Overhead Time Constructive Solid Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Steven M. Rubin, Turner Whitted, A 3-Dimensional Representation for Fast Rendering of Complex Scenes 1980 ACM 0-89791-021-4/80/0700-0110Google Scholar
  2. 2.
    Turner Whitted, An Improved Illumination Model for Shaded Display, Communications of the ACM, June 1980, Vol.23, No.6Google Scholar
  3. 3.
    Peter R. Atherton, A Method of Interactive Visualization of CAD Surface Models on a Color Video Display, Computer Graphics, Vol.15, No.3, August 1981Google Scholar
  4. 4.
    Roy A. Hall and Donald P. Greenberg, A Testbed for Realistic Image Synthesis, IEEE CG&A, Nov, 1983Google Scholar
  5. 5.
    John Amanatides, Ray Tracing with Cones, Computer Graphics, Vol.18, No.3, July 1983Google Scholar
  6. 6.
    Hank Weghorst, Gary Hooper, and Donald P. Greenberg, Improved Computational Methods for Ray Tracing, ACM Transactions on Graphics, Vol.3, No.1, January 1984Google Scholar
  7. 7.
    Paul S. Heckbert, Pat Hanrahan, Beam Tracing Polygonal Objects, Computer Graphics Vol.18, No.3, July 1984Google Scholar
  8. 8.
    Robert L. Cook, Thomas Porte, Loren Carpenter, Distributed Ray Tracing Computer Graphics Vol.18, No.3, July 1984Google Scholar
  9. 9.
    Mark Dippe, John Swensen, An Adaptive Subdivision Algorithm and Parallel Architecture for Realistic Image Synthesis, Computer Graphics Vol.18, No.3, July 1984Google Scholar
  10. 10.
    C.B. Jones A New Approach to the ‘Hidden Line’ Problem, The Computer Journal Vol.14, No.3Google Scholar
  11. 11.
    Louis J. Doctor, John G. Torborg, Display Techniques for Octree-Encoded Objects, IEEE CG&A, July 1981Google Scholar
  12. 12.
    Chris L. Jackins and Steven L. Tanimoto, Oct-Trees and Their Use in Representing Three-dimensional Objects, Computer Graphics and Image Processing 14, 249–270 (1980)CrossRefGoogle Scholar
  13. 13.
    Donald Meagher, Geometric Modelling Using Octree Encoding, Computer Graphics and Image Processing 19, 129–147 (1982)CrossRefGoogle Scholar
  14. 14.
    K. Yamaguchi, T.L. Kunii, K. Fujimura, H. Toriya Octree-Related Data Structures and Algorythms IEEE CG&A, January 1984Google Scholar
  15. 15.
    Mark A. Yerry and Mark S. Shephard, A Modified Quadtree Approach to Finite Element Mesh Generation, IEEE CG&A, January/February 1983Google Scholar
  16. 16.
    K. Fujimura, H. Toriya, K. Yamaguchi, and T. L. Kunii, An Enhanced Oct-tree Data Structure and Operations for Solid Modelling, Technical Report 83-01, Dept. of Information Science, University of TokyoGoogle Scholar
  17. 17.
    Akira Fujimoto and Kansei Iwata, Jag-Free Images on Raster Displays, IEEE CG&A, December 1983Google Scholar
  18. 18.
    Akira Fujimoto, Christopher G. Perrott and Kansei Iwata, A 3-D Graphics Display System with Depth Buffer and Pipeline Processor, IEEE CG&A, Vol.4, No.6, June 1984Google Scholar
  19. 19.
    Osaka University CG Group, LINKS-1, PIXEL ′83 5–6 No.12, page 73–92 (in Japanese)Google Scholar
  20. 20.
    Tsuyoshi Yamamoto Personal Computer Graphics (in Japanese) CQ Publishing Corporation 1983Google Scholar
  21. 21.
    Naoki Hashimoto, Edward Lau, TIPS-1 ′77 Version SYSTEM MANUAL, Computer Aided Manufacturing — International, Inc.Google Scholar
  22. 22.
    Paolo Sabella and Michael J. Wozny, Toward Fast Color-Shaded Images of CAD/CAM Geometry, IEEE CG&A, November 1983, page 65Google Scholar
  23. 23.
    Tomoyuki Nishita, Eihachiro Nakamae, Half-tone Representation of 3-D Objects Illuminated by Area Sources or Polyhedron Sources Proceedings of the IEEE Computer Society’s International Computer Software and Application Conference (Compsac), November 7–11, 1983Google Scholar
  24. 24.
    You-Dong Liang and Brian A. Barsky, A New Concept and Method for Line Clipping, ACM Transactions on Graphics, Vol.3, No.1, January 1984, page 1–22MATHCrossRefGoogle Scholar
  25. 25.
    Andrew S. Glassner, Space Subdivision for Fast Ray Tracing, IEEE CG&A, October 1984Google Scholar
  26. 26.
    Nelson L. Max, Computer Representation of Molecular Surfaces IEEE CG&A, August, 1983Google Scholar
  27. 27.
    Hitoshi Matsumoto, Kouichi Murakami, Ray-Tracing with Octree Data Structure (in Japanese) Proceedings of 28th Information Processing Conference 1983Google Scholar
  28. 28.
    David F. Rogers and Linda M. Ryback On an Efficient Line-Clipping Algorythm CG IEEE, January 1985Google Scholar
  29. 29.
    G. Hamlin, Jr., and C.W. Gear, Raster Scan Hidden Surface Algorythm Techniques Computer Graphics (Proc. Siggraph ′77), Vol.11, No.2 pp. 206–213Google Scholar
  30. 30.
    I.E. Sutherland, R.F. Sproull, and R.A. Schumacker, A Characterization of Ten Hidden Surface Algorythms”, Computing Surveys, Vol.6, No.1, Mar. 1974, pp.1–55MATHCrossRefGoogle Scholar
  31. 31.
    W. Jack Bouknight, A Procedure for Generation of Three-dimensional Half-toned Computer Graphics Representations, Communications of the ACM, September 1970Google Scholar
  32. 32.
    Henri Gouraud, Continous Shading of Curved Surfaces, IEEE Transactions on Computers, June 1971.Google Scholar
  33. 33.
    Bui Tuong Phong, Illumination for Computer Generated Pictures, Communications od the ACM, Vol.18, No.6, June 1975, pp. 311–317CrossRefGoogle Scholar
  34. 34.
    Kenetsu Hanabusa, Animation with CRAY-1 (Japanese) PIXEL 1983 7–8, No. 13Google Scholar
  35. 35.
    Jon Davis, Michael J. Bailey, David C. Anderson, Projecting Realistic Images of Geometric Solids, Computers in Mechanical Engineering /August 1982/Google Scholar
  36. 36.
    Peter R. Atherton, A Scan-line Hidden Surface Removal Procedure for Constructive Solid Geometry, ACM Computer Graphics, Vol.17, No.3, July 1983, pp. 73–83CrossRefGoogle Scholar
  37. 37.
    Ken H. Sears and Alan E. Middleditch, Set-Theoretic Volume Model Evaluation and Picture-Plane Coherence, IEEE CG&A March 1984, pp. 41–46Google Scholar
  38. 38.
    TIPS Working Group TIPS-1 (Technical Information Processing System for CAD/CAM) Program for Continuous Tone Image Generation (scan section shifting method) (in Japanese), Hokkaido University, Faculty of Mechanical Engineering, Precision Machinery Dpt., 17 January 1985Google Scholar
  39. 39.
    Roth, S.D., Ray Casting for Modelling Solids, Computer Graphics and Image Processing, No.18, 1982, pp. 109–104Google Scholar
  40. 40.
    Kouchi Murakami and Hitoshi Matsumoto, Method for Rendering CSG (Japanese), Proceedings of 27th Information Processing Conference 1983Google Scholar

Copyright information

© Springer-Verlag Tokyo 1985

Authors and Affiliations

  • Akira Fujimoto
    • 1
  • Kansei Iwata
    • 1
  1. 1.Graphica Computer CorporationTama, TokyoJapan

Personalised recommendations