TWO-PARTITION DISCRETE GLOBAL GRID SYSTEMS - A COMPARISON OF APPROACHES BASED ON ADJUSTED SPHERICAL CUBE AND CYLINDRICAL EQUIDISTANT PROJECTION

Aleksandar Dimitrijević

DOI Number
https://doi.org/10.22190/FUACR230322002D
First page
015
Last page
028

Abstract


The enormous volumes of geospatial data and the need to process and distribute them cry out for a unified framework that enables their efficient storage, analysis, and a high degree of interoperability. Discrete global grid systems provide such a framework by hierarchically tessellating cells to seamlessly partition and address the globe. Since they are usually based on a regular polyhedron, they partition the entire world into as many discrete data sets as the given polyhedron has sides. In this paper, we try to reduce the number of partitions to two, which is a minimum if we want to obtain spatially convex partitions without interruptions. Two approaches are presented, based on an adjusted spherical cube and an equidistant cylindrical projection. The distortions resulting from the application of these projections are compared and guidelines are presented to improve the quality of their implementation by reducing the distortion of the continental plates and making a better mapping to the WGS84 ellipsoid.

Keywords

Geospatial reference, discrete global grid system, map projection

Full Text:

PDF

References


E. H. Vestine, W. L. Sibley, J. W. Kern, and J. L. Carlstedt, “Integral and Spherical-Harmonic Analyses of the Geomagnetic Field for 1955.0, Part 2,” Journal of Geomagnetism and Geoelectricity, vol. 15, No. 2, pp.73–89, Aug. 1963.

A. J. Kimerling, K. Sahr, D. White, and L. Song, “Comparing Geometrical Properties of Global Grids”, Cartogr Geogr Inf Sci 26(4), pp.271–288, 1999

H. Alborzi, and H. Samet, “Augmenting SAND with a spherical data model”, In: Proc. First Int. Conf. on Discrete Global Grids, Santa Barbara, CA, USA, pp.26–28. Mar. 2000.

K. Sahr, D. White and A. J. Kimerling, “Geodesic Discrete Global Grid Systems”, Cartogr Geogr Inf Sci 30(2), pp.121–134, 2003.

Open Geospatial Consortium, “Topic 21: Discrete Global Grid Systems Abstract Specification”, Aug. 2017. URL: http://docs.ogc.org/as/15-104r5/15-104r5.html

ISO 19170-1:2021, "Geographic information — Discrete Global Grid Systems Specifications — Part 1: Core Reference System and Operations, and Equal Area Earth Reference System", May 2021. URL: https://www.iso.org/standard/32588.html

A. Dimitrijević and D. Rančić, "Ellipsoidal Clipmaps – A planet-sized terrain rendering algorithm", Computers & Graphics, Vol.52, pp.43–61, 2015. URL: https://www.sciencedirect.com/science/article/pii/ S0097849315000916. doi:10.1016/j.cag.2015.06.006.

D. White, A. J. Kimerling and S. W. Overton, "Cartographic and geometric components of a global sampling design for environmental monitoring", Cartography and Geographic Information Systems, Taylor & Francis, Vol.19, No.1, pp. 5–22, 1992.

R. Sadourney, “Conservative Finite-Difference Approximations of the Primitive Equations on Quasi-Uniform Spherical Grids”, Monthly Weather Review 100(2), pp. 136–144, Feb. 1972.

F. Chan and E. O’Neill, “Feasibility study of a quadrilateralized spherical cube earth data base”, Tech. Report EPRF 2-75 (CSC), Environmental Prediction Research Facility, Apr. 1975.

E. O’Neill and R. Laubscher, “Extended studies of a quadrilateralized spherical cube earth data base”, Tech. Report NEPRF 3–76 (CSC), Naval Environmental Prediction Research Facility, May 1976.

M. Calabretta and E. Greisen, “Representations of celestial coordinates in FITS”, Astronomy & Astrophysics, 395 (2002), pp. 1077–1122, 2002.

M. Lambers and A. Kolb, “Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data”, in Proc. Pacific Graphics (Short Papers), pp. 5–10, 2012.

S2 Geometry Library, https://s2geometry.io

A. Dimitrijević, M. Lambers and D. Rančić, “Comparison of Spherical Cube Map Projections Used in Planet-Sized Terrain Rendering,” Facta Universitatis, Series: Mathematics and Informatics 31(2), 2016, pp.259–297.

M. Lambers, “Survey of Cube Mapping Methods in Interactive Computer Graphics”, The Visual Computer 36(5), pp. 1043–1051, 2020.

R. B. Fuller, "Synergetics - Explorations in the Geometry of Thinking", MacMillan Publishing, New York, 1975.

A. Dimitrijević, P. Strobl, M. Lambers, A. Milosavljević and D. Rančić, “Distortion Optimized Spherical Cube Mapping for Discrete Global Grid Systems”, In: Zdravković, M., Konjović, Z., Trajanović, M. (Eds.) ICIST 2020 Proceedings, pp. 109–113, 2020.

A. M. Amiri, F. Bhojani and F. Samavati, “One-to-two Digital Earth”, In: Bebis G. et al. (eds) Advances in Visual Computing, ISVC 2013, LNSC 8034, pp. 681–692, 2013.

A. M. Amiri, F. Samavati and P. Peterson, “Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems”, ISPRS Int. J. Geo-Inf. 4(1), pp. 320–336, 2015

M. B. J. Purss, P. R. Peterson, P. Strobl, C. Dow, Z. A. Sabeur, R. G. Gibb and J. Ben, “Datacubes: A Discrete Global Grid Systems Perspective”, Cartographica: The International Journal for Geographic Information and Geovisualization, 54(1), pp. 63–71, 2019. doi:10.3138/cart.54.1.2018-0017

T. Alderson, M. Purss, X. Du, A. M. Amiri and F. Samavati, “Digital Earth Platforms”, in: Manual of Digital Earth, edited by Guo, H., Goodchild, M. F., and Annoni, A., Springer, Singapore, 1 ed., pp. 25–55, 2020. doi: 10.1007/978-981-32-9915-3

European Commission, "Digital Earth", EU Science Hub, URL: https://joint-research-centre.ec.europa.eu/scientific-activities-z/digital-earth_en

A. M. Dimitrijević and P. A. Strobl, "Continuous 2D Maps Based on Spherical Cube Datasets," 2020 55th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST), Niš, Serbia, 2020, pp. 19-22, doi: 10.1109/ICEST49890.2020.9232678.

A. Kageyama, T. Sato, "Yin-Yang grid: An overset grid in spherical geometry", Geochemistry, Geophysics, Geosystems, 5(9), John Wiley & Sons Ltd, Sep. 2004. doi: 10.1029/2004GC000734

R. Lerbour, Adaptive streaming and rendering of large terrains, PhD thesis, Universite de Rennes 1, Dec. 2009.

R. Lerbour, J.-E. Marvie and P. Gautron, “Adaptive real-time rendering of planetary terrains”, in Full Paper Proc. Int. Conf. Computer Graphics, Visualization and Computer Vision (WSCG), pp. 89-96, 2010.

J. Snyder, "Map projections: A working manual" Professional Paper No.1395, US Geological Survey, 1987.

National Center for Geospatial Intelligence Standards (NCGIS) and National Geospatial-Intelligence Agency (NGA), "Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems", Version 1.0.0, July 2014. URL: https://nsgreg.nga.mil/doc/view?i=4085

O. Adams, “Latitude developments connected with geodesy and cartography: with tables including a table for Lambert equal-area meridional projection,” U.S. Coast and Geodetic Survey Spec. Pub. No. 67, 1921.




DOI: https://doi.org/10.22190/FUACR230322002D

Refbacks

  • There are currently no refbacks.


Print ISSN: 1820-6417
Online ISSN: 1820-6425