Optimization of Inverse Snyder Polyhedral Projection
Erika Harrison, Ali Mahdavi-Amiri and Faramarz Samavati
CyberWorlds 2011
Abstract
Modern techniques in area preserving projections used by cartographers and other geospatial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder's inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided.
Bibtex
\@inproceedings{harrison11,
author = "Erika Harrison and Ali Mahdavi-Amiri and Faramarz Samavati",
title = "Optimization of Inverse Snyder Polyhedral Projection",
year = "2011"
}
Optimization of Inverse Snyder Polyhedral Projection
Erika Harrison, Ali Mahdavi-Amiri and Faramarz Samavati
CyberWorlds 2011
Abstract
Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions - from the planar map to the spherical approximation of the Earth - are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been fairly successful, however the work herein improves it further by adjusting the approximating polynomial. An evaluation against the original and improved optimizations is provided, along with a previously unexplored real-time analysis.
Bibtex
\@incollection{harrison12,
author={Harrison, Erika and Mahdavi-Amiri, Ali and Samavati, Faramarz},
title={Analysis of Inverse Snyder Optimizations},
booktitle={Transactions on Computational Science XVI},
year={2012},
isbn={978-3-642-32662-2},
volume={7380},
series={Lecture Notes in Computer Science},
editor={Gavrilova, MarinaL. and Tan, C.J.Kenneth},
doi={10.1007/978-3-642-32663-9_8},
url={http://dx.doi.org/10.1007/978-3-642-32663-9_8},
publisher={Springer Berlin Heidelberg},
keywords={equal area; projection; optimization; Snyder projection},
pages={134-148}
}
Hexagonal Connectivity Maps for Digital Earth
Ali Mahdavi-Amiri, Erika Harrison and Faramarz Samavati
International Journal of Digital Earth 2014
Abstract
Geospatial data is gathered through a variety of different methods. The integration and handling of such data-sets within a Digital Earth framework are very important is to use a Discrete Global Grid System and map points of the Earth's surface to cells. An indexing mechanism is needed to access the data and handle data queries within these cells.. In this paper, we present a general hierarchical indexing mechanism for hexagonal cells resulting from the refinement of triangular spherical polyhedra representing the Earth. In this work, we establish a 2D hexagonal coordinate system and diamond-based hierarchies for hexagonal cells that enables entirely efficient determination of hierarchical relationships for various hexagonal refinements, and demonstrate its usefulness in Digital Earth frameworks.
Bibtex
\@article{mahdaviamiri14,
author = {Ali Mahdavi-Amiri and Erika Harrison and Faramarz Samavati},
title = {Hexagonal Connectivity Maps for Digital Earth},
journal = {International Journal of Digital Earth},
publisher = {Taylor & Francis},
year = {2014},
note = {To Appear}
}