Fast Ray Tracing of Unevaluated Constructive Solid Geometry Models

  • P. Getto


We present a refinement of the ray tracing algorithm, for use with unevaluated constructive solid geometry models. Bounding enclosures around the children of a part are combined into a tree with nearly optimal minimum expected number of extent-ray intersections. An approximate evaluation of the expression represented by the part can be evaluated on the enclosure-ray intersections to find the subset of children that might be hit by a ray. These candidate children are then used to evaluate the expression exactly. Several criteria are suggested which allow early termination of the exact expression evaluation.


Union Operator Expression Tree Constructive Solid Geometry Auxiliary Tree Random Ball 
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.


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  1. Amaldi B, Priol T, Bouatouch K (1987) A new space subdivision method for ray tracing CSG modelled scenes. Visual Computer 3:98–108.CrossRefGoogle Scholar
  2. Bronsvoort W, van Wijk JJ, Jansen FW (1984) Two methods for improving the efficiency of ray casting in solid modelling. CAD 16(1):51–55.Google Scholar
  3. Fujimoto A, Perrot CG, Iwata K (1986) Environment for Fast Elaboration of Constructive Solid Geometry. In: Kunii TL (ed) Advanced Computer Graphics. Springer-Verlag, Tokyo, pp 20–33.CrossRefGoogle Scholar
  4. Goldsmith J, Salmon J (1987) Automatic creation of object hierarchies for ray tracing. IEEE CG & A 7(5): 14–20.Google Scholar
  5. Kay TL, Kajiya JT (1986) Ray Tracing Complex Scenes. Computer Graphics 20(4):269–278.CrossRefGoogle Scholar
  6. Roth SD (1984) Ray Casting for Modeling Solids. CG & IP 18:109–144.Google Scholar
  7. Warnock JE (1969) A Hidden-Surface Algorithm for Computer-Generated Halftone Pictures. Computer Science Department, University of Utah, TR 4–15, UT, 1969.Google Scholar
  8. Watkins JS (1970) A Real-Time Visible Surface Algorithm. Computer Science Department, University of Utah, UTECH-CSC-70-101, 1970.Google Scholar
  9. Weghorst H, Hooper G, Greenberg DP (1984) Improved Computational Methods for Ray Tracing. ACM TOG 3 (1):52–69.CrossRefGoogle Scholar
  10. Whitted T (1980) An Improved Illumination Model for Shaded Display. Comm. ACM 23(6):343–349.CrossRefGoogle Scholar
  11. Woodwark JR, Quinlan KM (1982) Reducing the effect of complexity on volume model evaluation. CAD 14 (2): 89–95.Google Scholar
  12. Wyvil G, Kunii TL, Shirai Y (1986) Space Division for Ray Tracing in CSG. IEEE CG & A 6(4):28–34.Google Scholar

Copyright information

© Springer-Verlag Tokyo 1989

Authors and Affiliations

  • P. Getto
    • 1
  1. 1.Rensselaer Design Research Center, Rensselaer Polytechnic InstituteG. M. Low Center for Industrial InovationTroyUSA

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