Browsing by Author "Alderson, Troy"
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- ItemOpen AccessData Management Possibilities for Aperture 3 Hexagonal Discrete Global Grid Systems(2016-08-22) Mahdavi-Amiri, Ali; Alderson, Troy; Samavati, FaramarzIn a Digital Earth framework, data sets are gathered from different sources in three main forms: imagery/elevation, vector, and quantitative data sets. In order to efficiently work with these data sets in a Digital Earth framework, effective methods to represent and transmit these data sets are required. While these representations may be different for each type of data set, they must all preserve the actual data as much as possible in order to accurately address queries. Furthermore, they also need to be compatible with the underlying structure of the Digital Earth framework. In this paper, we describe several data representations for an Aperture 3 Hexagonal Discrete Global Grid System which is a common approach to build a Digital Earth framework. We also discuss how they can be used to transmit data sets or address specific queries.
- ItemOpen AccessMultiresolution on Spherical Curves(2014-11-03) Alderson, Troy; Mahdavi Amiri, Ali; Samavati, FaramarzIn this paper, we present a simple multiresolution framework for curves on the surface of a sphere. Multiresolution by subdivision and reverse subdivision allows one to decrease and restore the resolution of a curve, and is typically defined by affine combinations of points in Euclidean space. However, translating such combinations to spherical space is challenging. Several works perform such operations in an intermediate Euclidean space instead using some mapping (e.g. the exponential map), but such mappings cause distortions and are often complicated. We use a simple geometric construction for a multiresolution scheme on the sphere that does not require the use of an intermediate space, which is based on a modified Lane-Riesenfeld algorithm (point duplication followed by repeated averaging) that features an invertible averaging step. Such a multiresolution scheme allows one to simplify/compress and reconstruct curves on the surface of a sphere-like object — such as the Earth — simply, efficiently, and without distortion.
- ItemOpen AccessRegularity-Preserving Terrain Simplification For Faster Line-of-Sight(2014-04-28) Alderson, Troy; Samavati, FaramarzThree-dimensional terrain models play a key role in many applications. Line-of-sight queries, which are important operations in some applications (e.g. battlefield simulations), test whether or not two entities can see each other over the terrain. Given enough entities and a large enough terrain, computing these queries can be expensive. Terrain simplification can be used to speed up the queries, with a penalty to accuracy. To take advantage of the especially fast algorithms that exist for regular terrain models, we introduce regularity-preserving terrain simplification methods based on reverse subdivision and examine their effect on query accuracy. Furthermore, we develop a novel feature preserving reverse subdivision scheme that attempts to improve query accuracy over the pre-existing methods. Additionally, we have examined the problem of where entities should be located after terrain simplification to maximize accuracy. Using iterative methods that attempt to maximize accuracy, we show that room for improvement exists over the standard projection method. Then, we develop practical relocation methods designed to maximize accuracy over regular simplified terrain models, the first taking a hybrid approach between projection and no relocation and the second using residual vectors to map entities onto the simplified terrain. Accuracy improvements over these basic methods can be achieved by making use of the iterative methods in a pseudo-optimization pre-processing step. Finally, we introduce a practical line-of-sight algorithm based on hierarchies of simplified terrains that is both fast and accurate. Our approach combines two existing algorithms, using each of their strengths to achieve highly efficient line-of-sight queries in local areas.
- ItemOpen AccessA Survey of Digital Earth Representation and Visualization(2015-04-07) Mahdavi-Amiri, Ali; Alderson, Troy; Samavati, FaramarzThe creation of a digital representation of the Earth and its associated data is a complex and difficult task. The incredible size of geospatial data and differences between data sets pose challenges related to big data, data creation, and data integration. Advances in globe representation and visualization have made use of Discrete Global Grid Systems (DGGSs) that discretize the globe into a set of cells to which data are assigned. DGGSs are well studied and important in GIS, OGC, and Digital Earth communities. However, DGGSs have not been introduced very well to computer graphics community. In addition, there are many advanced techniques related to geospatial data creation and representation that might be very useful to Digital Earth community. In this paper, we provide an overview of DGGSs and their use in digitally representing the Earth as well as the list of current Digital Earths and their method of Earth representation. In addition, we present key research areas and related papers in computer graphics that are useful for a Digital Earth framework. Moreover, we list a number of applications of Digital Earths and their related works.