Volume rendering continues to be a critical method for analyzing large-scale scalar fields, in disciplines as diverse as biomedical engineering and computational fluid dynamics. Commodity desktop hardware has struggled to keep pace with data size increases, challenging modern visualization software to deliver responsive interactions for O(N3) algorithms such as volume rendering. We target the data type common in these domains: regularly-structured data. In this work, we demonstrate that the major limitation of most volume rendering approaches is their inability to switch the data sampling rate (and thus data size) quickly. Using a volume renderer inspired by recent work, we demonstrate that the actual amount of visualizable data for a scene is typically bound considerably lower than the memory available on a commodity GPU. Our instrumented renderer is used to investigate design decisions typically swept under the rug in volume rendering literature. The renderer is freely available, with binaries for all major platforms as well as full source code, to encourage reproduction and comparison with future research.

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In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger's best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a systemoptimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples.

Figure 1: Basic object manipulation techniques such as translation (a) and rotation (b) are illustrated in long exposure photographs. Augmentation can be projector-based (a-c) or via video-see-through (d). These application examples show basic augmentations of building structures (a,b,d), distance measurements (c) and material-color simulations (c).

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