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Interactive Rendering of Natural Phenomena with Directed Cyclic Graphs Dieter Schmalstieg, Christoph Traxler, Michael Gervautz
Vienna University of Technology, Austria
Introduction. Display of natural phenomena is still a significant problem for interactive rendering systems and virtual reality applications. A large amount of detail is required to be convincing, and the modeling effort can be enormous. Many systems that aim to show outdoor scenes such as flight simulators try to overcome this restriction by use of textures and satellite imagery for terrain. However, such a solution still lacks real details and works only well for distant views, or it requires extensive storage, which is in conflict with the tight resource budget of low cost systems. Bandwidth restrictions have also precluded the use of very complex models in distributed virtual reality systems. Other areas where interactive rendering of natural phenomena is important, are landscape architecture and city reconstruction.

Methodology. Many natural phenomena, such as plants, trees, mountains, and even buildings, have an inherently repetitive structure. Parametric Lindenmayer-Systems (PL-Systems) are a well-established technique to define such phenomena [Prus90]. Models defined by PL-systems do not suffer from degraded quality at close-ups, since they can be arbitrarily complex. However, the standard production-based representation must be interpreted in order to be displayed. To combine PL-systems with conventional geometric models, often an explicit representation of the model is built from the definition [Prus94, Webe95].

We propose a simple extension to existing modeling and rendering toolkits that is capable of direct representation of PL-systems: Adding the possibility of cyclic references turns a directed acyclic graph (DAG), which is the standard data structure for interactive graphics and virtual reality, into a directed cyclic graph (DCG), which can also represent arbitrary PL-systems. Such a DCG can directly be rendered with existing tools, because only the graph traversal works differently. Thus, conventional modeling toolkits can easily be extended to represent PL-systems.

Use of deterministic (reproducible) random numbers as parameters for models allows the creation of many different individuals from a single model, that can be used to populate a scene without to much explicit modeling of detail (e.g., a forest) [Reev85]. Exact modeling is unhindered where precise control of details is desired. Using a procedural language (e.g., Java) for procedural modeling might have similar benefits, but lacks a unified structure for procedural and conventional geometric models; also procedural models cannot be rendered directly.

Interactive design of natural phenomena. While ray tracing of natural phenomena, as described in [Gerv95], produces beautiful images, the process of designing the models is tedious because of the lack of