## Information

- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: December 1994
- Number: TR-186-2-94-19
- Keywords: L-Systems, CSG-graphs, Ray Tracing, Natural Phenomena, Fractals

## 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.

## Additional Files and Images

## Weblinks

No further information available.

## BibTeX

@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.",
month = dec,
number = "TR-186-2-94-19",
address = "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
institution = "Institute of Computer Graphics and Algorithms, Vienna
University of Technology ",
note = "human contact: technical-report@cg.tuwien.ac.at",
keywords = "L-Systems, CSG-graphs, Ray Tracing, Natural Phenomena,
Fractals",
URL = "https://www.cg.tuwien.ac.at/research/publications/1994/Traxler-1994-RRR/",
}