Compared to the nineties where fast 3D graphics was the domain of expensive workstations, in the last few years the development of ever faster 3D graphics hardware was mainly driven by the gaming industry. The upcoming of programmable PC graphics hardware has opened the field for new graphics algorithms which allow unprecedented realism in real time applications. Nevertheless, one area of application is persistently resisting most efforts to achieve sufficient rendering performance: This is the area of volume rendering. Because of the huge amounts of data that have to be processed to obtain a three-dimensional visualization, it is very challenging to achieve real time performance for large volumetric data sets.

In this thesis we try to tackle this problem in one specific application field. We devise algorithms that are suitable for the real time display of natural gaseous phenomena. In particular our goal is to render clouds and fog in real time. In principle, the problem reduces to solving the so called ray integral. A common technique for solving this ray integral is ray casting which collects the incoming light on each viewing ray by sampling the volume. On the one hand ray casting achieves very good rendering quality, but on the other hand it becomes very slow at high screen resolutions. Many improvements have been presented to accelerate the original approach, but despite all efforts ray casting is still only beginning to be an option for high-quality real-time rendering. Very recent advances in graphics hardware have lead to the implementation of hardware-accelerated ray casters, but this approach still suffers from a variety of limitations of the graphics hardware.

The main technique developed in this thesis is the so called pre-integrated cell-projection method which offloads as much computation of the ray integral as possible into a preprocessing step. This is the first step toward real-time rendering of natural gaseous phenomena. In a second step we develop a hierarchical approximation scheme which decimates the huge amount of data in a view-dependent way. For this purpose we borrow ideas from the area of terrain rendering and apply the so-called continuous level of detail method to the three-dimensional case, that is fog and cloud volumes. In combination with the pre-integrated cell-projection method this permits real-time flights through natural looking clouds and ground fog. In comparison to previous methods image quality is also improved significantly.