Hierarchical occlusion culling for arbitrarily-meshed height fields

Many graphics applications today have need for high-speed 3-D visualization of height fields. Most of these applications deal with the display of digital terrain models characterized by a simple, but vast, non-overlapping mesh of triangles. A great deal of research has been done to find methods of optimizing such systems. The goal of this work is to establish an algorithm to efficiently preprocess a hierarchical height field model that enables the real-time culling of occluded geometry while still allowing for classic terrain-rendering frameworks. By exploiting the planar-monotone characteristics of height fields, it is possible to create a unique and efficient occlusion culling method that is optimized for terrain rendering and similar applications. Previous work has shown that culling is possible with certain regularly-gridded height field models, but not until now has a system been shown to work with all height fields, regardless of how their meshes are constructed. By freeing the system of meshing restrictions, it is possible to incorporate a number of broader height field algorithms with widely-used applications such as flight simulators, GIS systems, and computer games

Efficient Hidden Surface Removal for Objects with Small Union Size

Let S be a set of n non-intersecting objects in space for which we want to determine the portions visible from some viewing point. We assume that the objects are ordered by depth from the viewing point (e.g., they are all horizontal and are viewed from infinity from above). In this paper we give an algorithm that computes the visible portions in time O((U(n)+ k)log 2 n), where U(n ) is a super-additive bound on the maximal complexity of the union of (the projections on a viewing plane of) any n objects from the family under consideration, and k is the complexity of the resulting visibility map. The algorithm uses O(U(n)logn) working storage. The algorithm is useful when the objects are "fat" in the sense that the union of the projection of any subset of them has small (i.e., subquadratic) complexity. We present three applications of this general technique: (i) For disks (or balls in space) we have U(n) = O(n), thus the visibility map can be computed in time O((n + k) log 2 n). (ii) For 'fat' triangles (where each internal angle is at least some fixed 0 degrees) we have U(n) = O(nloglogn) and the algorithm runs in time O((n log log n + k)log 2 n). (iii) The method also applies to computing the visibility map for a polyhedral terrain viewed from a fixed point, and yields an O((na(n)+ k)logn) algorithm

Sensor web geoprocessing on the grid

Recent standardisation initiatives in the fields of grid computing and geospatial sensor middleware provide an exciting opportunity for the composition of large scale geospatial monitoring and prediction systems from existing components. Sensor middleware standards are paving the way for the emerging sensor web which is envisioned to make millions of geospatial sensors and their data publicly accessible by providing discovery, task and query functionality over the internet. In a similar fashion, concurrent development is taking place in the field of grid computing whereby the virtualisation of computational and data storage resources using middleware abstraction provides a framework to share computing resources. Sensor web and grid computing share a common vision of world-wide connectivity and in their current form they are both realised using web services as the underlying technological framework. The integration of sensor web and grid computing middleware using open standards is expected to facilitate interoperability and scalability in near real-time geoprocessing systems. The aim of this thesis is to develop an appropriate conceptual and practical framework in which open standards in grid computing, sensor web and geospatial web services can be combined as a technological basis for the monitoring and prediction of geospatial phenomena in the earth systems domain, to facilitate real-time decision support. The primary topic of interest is how real-time sensor data can be processed on a grid computing architecture. This is addressed by creating a simple typology of real-time geoprocessing operations with respect to grid computing architectures. A geoprocessing system exemplar of each geoprocessing operation in the typology is implemented using contemporary tools and techniques which provides a basis from which to validate the standards frameworks and highlight issues of scalability and interoperability. It was found that it is possible to combine standardised web services from each of these aforementioned domains despite issues of interoperability resulting from differences in web service style and security between specifications. A novel integration method for the continuous processing of a sensor observation stream is suggested in which a perpetual processing job is submitted as a single continuous compute job. Although this method was found to be successful two key challenges remain; a mechanism for consistently scheduling real-time jobs within an acceptable time-frame must be devised and the tradeoff between efficient grid resource utilisation and processing latency must be balanced. The lack of actual implementations of distributed geoprocessing systems built using sensor web and grid computing has hindered the development of standards, tools and frameworks in this area. This work provides a contribution to the small number of existing implementations in this field by identifying potential workflow bottlenecks in such systems and gaps in the existing specifications. Furthermore it sets out a typology of real-time geoprocessing operations that are anticipated to facilitate the development of real-time geoprocessing software.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC) : School of Civil Engineering & Geosciences, Newcastle UniversityGBUnited Kingdo

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version