Rendering volumes using path tracing can produce stunning images, but the process is notoriously expensive. For some volumes such as clouds, there are cases where the volume has no interaction with other objects in the scene. For these cases, combined with an isotropic phase function, unidirectional path tracing from the camera computes many similar paths regardless of camera position. Computing these light paths beforehand to determine the full radiance transport through the volume speeds up the rendering stage drastically, with the result still being physically accurate.

In this thesis, we present a two-stage method designed for the aforementioned cases. The first stage is a precomputation stage, in which light paths are traced through the volume and stored in a space-efficient manner using a graph structure. Through this graph, radiance transport is then computed. In the rendering stage, the graph structure with radiance values can then be used to render the volume. The results show that our method can produce renders with negligible bias. They also show that the method is heavily constrained by space requirements as volume size increases, which results in an increase in bias for larger volumes. The main advantage of the method is its efficiency in rendering multiple images of the same object.

Virtual robot soccer competitions have been rising in popularity in recent years, due to their easier accessibility than physical robot soccer. This is also the reason these virtual competitions were created. The goal is to compete in the AI world cup, one of the virtual soccer competitions. A coach-based framework has already been built, and the aim is to create strong defensive capabilities for the robot team. This paper in particular focuses on covering opponents without the ball. The marking strategy and specific opponent covering that have been devised for this are explained. Both are completely rule-based, and opponent covering has been thoroughly tested with an in-house developed batch-runner. In short, opponent covering consists of standing at the optimal position between the passer and receiver, and when the ball is passed going to the closest intercept point. This optimal position is learned with the batch-runner. Opponent covering performs well in the generated test cases. Some specific algorithms counter attacking strategies which have not been implemented yet, therefore it was not possible to evaluate those algorithms. They are theoretically optimal however.