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Abstract

A method for ray tracing of recursive objects defined by parametric rewriting systems is introduced. Constructive Solid Geometry (CSG) is used as underlying object representation. Thus the formal languages of our rewriting systems are subsets of the infinite set of CSG expressions. Instead of deriving such expressions to build up large CSG trees we translate the systems into cyclic CSG graphs, which can be used directly as an object representation for ray tracing. For this purpose the CSG concept is extended by three new nodes. Selection nodes join all the rules for one grammar symbol, control the flow by selecting proper rules, and are end-points of cyclic edges. Transformation nodes map the rays in affine space. Calculation nodes evaluate a finite set of arithmetic expressions to modify global parameters, which effect flow control and transformations. The CSG graphs introduced here are a very compact data structure, much like the describing data set. This property meets our intention to avoid both restrictions of the complexity of the scenes by computer memory and the approximation accuracy of objects.

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@techreport{Traxler-1994-RRR,
  title =      "Representation and Realistic Rendering of Natural Phenomena
                with Cyclic CSG-graphs",
  author =     "Michael Gervautz and Christoph Traxler",
  year =       "1994",
  abstract =   "A method for ray tracing of recursive objects defined by
               parametric rewriting systems is introduced. Constructive
               Solid Geometry (CSG) is used as underlying object
               representation. Thus the formal languages of our rewriting
               systems are subsets of the infinite set of CSG expressions.
               Instead of deriving such expressions to build up large CSG
               trees we translate the systems into cyclic CSG graphs, which
               can be used directly as an object representation for ray
               tracing. For this purpose the CSG concept is extended by
               three new nodes. Selection nodes join all the rules for one
               grammar symbol, control the flow by selecting proper rules,
               and are end-points of cyclic edges. Transformation nodes map
               the rays in affine space. Calculation nodes evaluate a
               finite set of arithmetic expressions to modify global
               parameters, which effect flow control and transformations.
               The CSG graphs introduced here are a very compact data
               structure, much like the describing data set. This property
               meets our intention to avoid both restrictions of the
               complexity of the scenes by computer memory and the
               approximation accuracy 		of objects.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      dec,
  number =     "TR-186-2-94-19",
  keywords =   "L-Systems, CSG-graphs, Ray Tracing, Natural Phenomena,
               Fractals",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1994/Traxler-1994-RRR/",
}