Calculation of Tight Bounding Volumes for Cyclic CSG- Graphs*

Cyclic CSG graphs are a memory safe representation of objects with a very complex, recursive structure. This class of objects are defined by CSG-PL-Systems, an adaption of the well known Parametric Lindenmayer Systems (PL-Systems) to the CSG concept. They are a powerful tool to model natural phenomena like plants, clouds or fractal terrain but also linear fractals or any objects with a repetitive structure. CSG-PL-Systems are directly translated into CSG graphs, which are a proper object representation for ray tracing. A derivation and geometric interpretation of strings is no longer necessary. Because CSG graphs are as compact as the CSG-PL-Systems the memory usage is low, so that restrictions of the complexity of the scene are avoided. To be efficient as well it is very important to adapt conventional optimization techniques to CSG graphs. For CSG trees a hierarchy of bounding volumes is buildt up by a simple recursive algorithm. A straight forward transition of this algorithm to CSG graphs yields to very huge and thus useless bounding volumes. In this paper we introduce an algorithm which calculates tight bounding volumes for the nodes of cyclic CSG graphs. This method can also be applied to CSG trees with explicit transformation nodes or CSG dags.