Engineering Art Galleries

The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive experiment. Furthermore, we show what core algorithmic ingredients have led to recent successes

09111 Abstracts Collection -- Computational Geometry

From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

On IO-efficient viewshed algorithms and their accuracy

Given a terrain T and a point v, the viewshed or visibility map of v is the set of points in T that are visible from v. To decide whether a point p is visible one needs to interpolate the elevation of the terrain along the line-of-sight (LOS) vp. Existing viewshed algorithms differ widely in which and how many points they chose to interpolate, how many lines-of-sight they consider, and how they interpolate the terrain. These choices crucially affect the running time and accuracy of the algorithms. In this paper our goal was to obtain an IO-efficient algorithm that computes the viewshed on a grid terrain with as much accuracy as possible given the resolution of the data. We describe two algorithms which are based on computing and merging horizons, and we prove that the complexity of horizons on a grid of n points is O(n), improving on the general O(na(n)) bound on triangulated terrains. Our finding is that, in practice, horizons on grids are significantly smaller than their theoretical worst case bound, which makes horizon-based approaches very fast. To measure the differences between viewsheds computed with various algorithms we implement an error metric that averages differences over a large number of viewsheds computed from a set of viewpoints with topological significance, like valleys and ridges. Using this metric we compare our current approach, Van Kreveld's model used in our previous work [7], the algorithm of Ferreira et al. [6], and the viewshed module r.los in the open source GIS GRASS

A Framework for Dynamic Terrain with Application in Off-road Ground Vehicle Simulations

The dissertation develops a framework for the visualization of dynamic terrains for use in interactive real-time 3D systems. Terrain visualization techniques may be classified as either static or dynamic. Static terrain solutions simulate rigid surface types exclusively; whereas dynamic solutions can also represent non-rigid surfaces. Systems that employ a static terrain approach lack realism due to their rigid nature. Disregarding the accurate representation of terrain surface interaction is rationalized because of the inherent difficulties associated with providing runtime dynamism. Nonetheless, dynamic terrain systems are a more correct solution because they allow the terrain database to be modified at run-time for the purpose of deforming the surface. Many established techniques in terrain visualization rely on invalid assumptions and weak computational models that hinder the use of dynamic terrain. Moreover, many existing techniques do not exploit the capabilities offered by current computer hardware. In this research, we present a component framework for terrain visualization that is useful in research, entertainment, and simulation systems. In addition, we present a novel method for deforming the terrain that can be used in real-time, interactive systems. The development of a component framework unifies disparate works under a single architecture. The high-level nature of the framework makes it flexible and adaptable for developing a variety of systems, independent of the static or dynamic nature of the solution. Currently, there are only a handful of documented deformation techniques and, in particular, none make explicit use of graphics hardware. The approach developed by this research offloads extra work to the graphics processing unit; in an effort to alleviate the overhead associated with deforming the terrain. Off-road ground vehicle simulation is used as an application domain to demonstrate the practical nature of the framework and the deformation technique. In order to realistically simulate terrain surface interactivity with the vehicle, the solution balances visual fidelity and speed. Accurately depicting terrain surface interactivity in off-road ground vehicle simulations improves visual realism; thereby, increasing the significance and worth of the application. Systems in academia, government, and commercial institutes can make use of the research findings to achieve the real-time display of interactive terrain surfaces

Engineering Art Galleries

The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive experiment. Furthermore, we show what core algorithmic ingredients have led to recent successes