REPRESENTATION AND REALISTIC RENDERING OF NATURAL PHENOMENA WITH CYCLIC CSG GRAPHS

A method for ray tracing recursive objects defined by parametric rewri ting systems using constructive solid geometry (CSG) as the underlying method of object representation is introduced. Thus, the formal langu ages of our rewriting systems are subsets of the infinite set of CSG e xpressions. 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 pu rpose the CSG concept is extended by three new nodes. Selection nodes join all the rules for one grammar symbol, control flow by selecting p roper 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 fl ow control and transformations. The CSG graphs introduced here are a v ery compact data structure, much like the describing data set. This pr operty meets our intention to avoid both restrictions of the complexit y of the scenes by computer memory and the approximation accuracy of o bjects.