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@article{yoshida2004application,
title={Application of the {Yin-Yang} Grid to a Thermal Convection of a Boussinesq Fluid with Infinite {Prandtl} Number in a Three-Dimensional Spherical Shell},
author={Yoshida, Masaki and Kageyama, Akira},
journal={Geophysical research letters},
volume={31},
number={12},
year={2004},
publisher={Wiley Online Library}
}
@article{tackley2008modelling,
title={Modelling Compressible Mantle Convection with Large Viscosity Contrasts in a Three-Dimensional Spherical Shell using the {Yin-Yang} Grid},
author={Tackley, Paul J},
journal={Physics of the Earth and Planetary Interiors},
volume={171},
number={1},
pages={7--18},
year={2008},
publisher={Elsevier}
}
@inproceedings{harrison2011optimization,
title={Optimization of Inverse {Snyder} Polyhedral Projection},
author={Harrison, Erika and Mahdavi-Amiri, Ali and Samavati, Faramarz},
booktitle={Cyberworlds (CW), 2011 International Conference on},
pages={136--143},
year={2011},
organization={IEEE}
}
@inproceedings{mahdavi2013one,
title={One-to-two Digital {Earth}},
author={Mahdavi-Amiri, Ali and Bhojani, Faraz and Samavati, Faramarz},
booktitle={International Symposium on Visual Computing},
pages={681--692},
year={2013},
organization={Springer}
}
@article{mahdavi2015hexagonal,
title={Hexagonal Connectivity Maps for Digital {Earth}},
author={Mahdavi-Amiri, Ali and Harrison, Erika and Samavati, Faramarz},
journal={International Journal of Digital Earth},
volume={8},
number={9},
pages={750--769},
year={2015},
publisher={Taylor \& Francis}
}
@article{mahdavi2015survey,
title={A Survey of Digital {Earth}},
author={Mahdavi-Amiri, Ali and Alderson, Troy and Samavati, Faramarz},
journal={Computers \& Graphics},
volume={53},
pages={95--117},
year={2015},
publisher={Elsevier}
}
@inproceedings{ketabchi20153d,
title={{3D} Maquetter: Sketch-Based {3D} Content Modeling for Digital {Earth}},
author={Ketabchi, Kaveh and Runions, Adam and Samavati, Faramarz F},
booktitle={Cyberworlds (CW), 2015 International Conference on},
pages={98--106},
year={2015},
organization={IEEE}
}
@article{samavati2016interactive,
title={Interactive {3D} Content Modeling for Digital {Earth}},
author={Samavati, Faramarz and Runions, Adam},
journal={The Visual Computer},
volume={32},
number={10},
pages={1293--1309},
year={2016},
publisher={Springer}
}
@article{djavaherpour2017physical,
title={Physical Visualization of Geospatial Datasets},
author={Djavaherpour, Hessam and Mahdavi-Amiri, Ali and Samavati, Faramarz F},
journal={IEEE Computer Graphics and Applications},
volume={38},
number={3},
pages={61--69},
year={2017},
publisher={IEEE}
}
@inproceedings{brown2017real,
title={Real-Time Panorama Maps},
author={Brown, S Alex and Samavati, Faramarz},
booktitle={Proceedings of the Symposium on Non-Photorealistic Animation and Rendering},
pages={6},
year={2017},
organization={ACM}
}
@inproceedings{kageyama2005geodynamo,
title={Geodynamo and Mantle Convection Simulations on the {Earth} Simulator using the {Yin-Yang} Grid},
author={Kageyama, Akira and Yoshida, Masaki},
booktitle={Journal of Physics: Conference Series},
volume={16},
number={1},
pages={325},
year={2005},
organization={IOP Publishing}
}
@article{lee2017quasi,
title={Quasi-Equal Area Subdivision Algorithm for Uniform Points on a Sphere with Application to any Geographical Data Distribution},
author={Lee, Sanghyun and Mortari, Daniele},
journal={Computers \& Geosciences},
volume={103},
pages={142--151},
year={2017},
publisher={Elsevier}
}
@article{yu2012lithosphere,
title={{SDOG}-Based Multi-Scale {3D} Modeling and Visualization on Global Lithosphere},
author={Yu, JieQing and Wu, LiXin and Zi, GuoJie and Guo, ZengZhang},
journal={Science China. Earth Sciences},
volume={55},
number={6},
pages={1012},
year={2012},
publisher={Springer Science \& Business Media}
}
@article{yu2012large-scale,
title={An {SDOG}-Based Intrinsic Method for Three-Dimensional Modelling of Large-Scale Spatial Objects},
author={Yu, Jieqing and Wu, Lixin and Li, Zhifeng and Li, Xiaojing},
journal={Annals of GIS},
volume={18},
number={4},
pages={267--278},
year={2012},
publisher={Taylor \& Francis}
}
@inproceedings{yu2009sdog,
title={Spatial Subdivision and Coding of a Global Three-Dimensional Grid: Spheoid Degenerated-Octree Grid},
author={Yu, Jie-qing and Wu, Li-xin},
booktitle={Geoscience and Remote Sensing Symposium, 2009 IEEE International, IGARSS 2009},
volume={2},
pages={II--361},
year={2009},
organization={IEEE}
}
@article{kageyama2004yin-yang,
title={{``Yin-Yang grid''}: An Overset Grid in Spherical Geometry},
author={Kageyama, Akira and Sato, Tetsuya},
journal={Geochemistry, Geophysics, Geosystems},
volume={5},
number={9},
year={2004},
publisher={Wiley Online Library}
}
@article{calhoun2008rectangluar,
title={Logically Rectangular Grids and Finite Volume Methods for {PDEs} in Circular and Spherical Domains},
author={Calhoun, Donna A and Helzel, Christiane and LeVeque, Randall J},
journal={SIAM review},
volume={50},
number={4},
pages={723--752},
year={2008},
publisher={SIAM}
}
@article{jupp1989unified,
title={A Unified View of the Theory of Directional Statistics, 1975-1988},
author={Jupp, PE and Mardia, KV},
journal={International Statistical Review/Revue Internationale de Statistique},
pages={261--294},
year={1989},
publisher={JSTOR}
}
@article{raskin1994spatial,
title={Spatial Analysis on the Sphere: A Review (94-7)},
author={Raskin, Robert G},
year={1994},
publisher={UC Santa Barbara: National Center for Geographic Information and Analysis}
}
@book{snyder1987map,
title={Map Projections--A Working Manual},
author={Snyder, John Parr},
volume={1395},
year={1987},
publisher={US Government Printing Office, Washington, D.C., USA}
}
@book{snyder1997flattening,
title={Flattening the {Earth}: Two Thousand Years of Map Projections},
author={Snyder, John P},
year={1997},
publisher={University of Chicago Press}
}
@article{braun2008douar,
title={{DOUAR:} A New Three-Dimensional Creeping Flow Numerical Model for the Solution of Geological Problems},
author={Braun, Jean and Thieulot, C{\'e}dric and Fullsack, Philippe and DeKool, Marthijn and Beaumont, Christopher and Huismans, Ritske},
journal={Physics of the Earth and Planetary Interiors},
volume={171},
number={1-4},
pages={76--91},
year={2008},
publisher={Elsevier}
}
@article{bassin2000current,
title={The Current Limits of Resolution for Surface Wave Tomography in {North America}},
author={Bassin, C},
journal={EOS Trans. AGU. 81: Fall Meet. Suppl., Abstract},
volume={81},
pages={F897},
year={2000}
}
@article{zhao2004global,
title={Global Tomographic Images of Mantle Plumes and Subducting Slabs: Insight into Deep {Earth} Dynamics},
author={Zhao, Dapeng},
journal={Physics of the Earth and Planetary Interiors},
volume={146},
number={1-2},
pages={3--34},
year={2004},
publisher={Elsevier}
}
@article{wadell1935volume,
title={Volume, Shape, and Roundness of Quartz Particles},
author={Wadell, Hakon},
journal={The Journal of Geology},
volume={43},
number={3},
pages={250--280},
year={1935},
publisher={University of Chicago Press}
}
@article{mahdavi2015categorization,
title={Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems},
author={Mahdavi-Amiri, Ali and Samavati, Faramarz and Peterson, Perry},
journal={ISPRS International Journal of Geo-Information},
volume={4},
number={1},
pages={320--336},
year={2015},
publisher={Multidisciplinary Digital Publishing Institute}
}
@article{goodchild2018reimagining,
title={Reimagining the History of {GIS}},
author={Goodchild, Michael F},
journal={Annals of GIS},
volume={24},
number={1},
pages={1--8},
year={2018},
publisher={Taylor \& Francis}
}
@misc{ogcDGGS,
title={Discrete Global Grid Systems Abstract Specification},
author="{OGC (2017a)}",
howpublished={\url{http://docs.opengeospatial.org/as/15-104r5/15-104r5.html}},
note={Accessed on 2018-08-02}
}
@misc{rohlf2014system,
title={System and Method for Storing and Retrieving Geospatial Data},
author={Rohlf, John H and Hancher, Matthew Dexter},
year={2014},
month=feb # "~11",
publisher={Google Patents},
note={US Patent 8,650,220}
}
@article{gang2013sphere,
author={Gang, W.A.N. and Xuefeng, C.A.O. and Feng, L.I. and Ke, L.I.},
year={2013},
month={10},
pages={77-82},
title={Sphere Shell Space {3D} Grid},
volume={40},
journal={International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives},
doi={10.5194/isprsarchives-XL-4-W2-77-2013}
}
@article{yu2009coding,
title={On Coding and Decoding for Sphere Degenerated-Octree Grid},
author={Yu, Jieqing and Wu, Lixin},
journal={Geography and Geo-Information Science},
volume={25},
pages={5--9},
year={2009}
}
@inproceedings{bahrdt2017rational,
title={Rational Points on the Unit Sphere: Approximation Complexity and Practical Constructions},
author={Bahrdt, Daniel and Seybold, Martin P},
booktitle={Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation},
pages={29--36},
year={2017},
organization={ACM}
}
@article{alderson2019multiscale,
title={Multiscale {NURBS} Curves on the Sphere and Ellipsoid},
author={Alderson, Troy and Samavati, Faramarz},
journal={Computers \& Graphics},
volume={82},
pages={243--249},
year={2019},
publisher={Elsevier}
}
@article{alderson2016multiresolution,
title={Multiresolution on Spherical Curves},
author={Alderson, Troy and Mahdavi-Amiri, Ali and Samavati, Faramarz},
journal={Graphical Models},
volume={86},
pages={13--24},
year={2016},
publisher={Elsevier}
}
@article{alderson2018offsetting,
title={Offsetting Spherical Curves in Vector and Raster Form},
author={Alderson, Troy and Mahdavi-Amiri, Ali and Samavati, Faramarz},
journal={The Visual Computer},
volume={34},
number={6-8},
pages={973--984},
year={2018},
publisher={Springer}
}
@article{sahr2003geodesic,
title={Geodesic Discrete Global Grid Systems},
author={Sahr, Kevin and White, Denis and Kimerling, A Jon},
journal={Cartography and Geographic Information Science},
volume={30},
number={2},
pages={121--134},
year={2003},
publisher={Taylor \& Francis}
}
@article{bellman1963differential,
title={Differential-Difference Equations},
author={Bellman, Richard Ernest and Cooke, Kenneth L},
year={1963},
publisher={Rand Corporation}
}
@article{morton1966computer,
title={A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing},
author={Morton, Guy M},
year={1966},
publisher={International Business Machines Company New York}
}
@misc{era5,
title={{Copernicus Climate Change Service (C3S)} (2017): {ERA5}: Fifth Generation of {ECMWF} Atmospheric Reanalyses of the Global Climate},
author="{Copernicus Climate Change Service Climate Data Store (CDS)}",
howpublished={\url{https://cds.climate.copernicus.eu/cdsapp}},
note={Accessed on 2019-10-04}
}
@inproceedings{sun20153d,
title={{3D} Integrated Representation Model and Visualization Based on the Global Discrete Voxel—{GeoSOT3D}},
author={Sun, Zhongqiu and Cheng, Chengqi},
booktitle={2015 23rd International Conference on Geoinformatics},
pages={1--5},
year={2015},
organization={IEEE}
}
@article{miao2019low,
title={A Low-Altitude Flight Conflict Detection Algorithm Based on a Multilevel Grid Spatiotemporal Index},
author={Miao, Shuangxi and Cheng, Chengqi and Zhai, Weixin and Ren, Fuhu and Zhang, Bo and Li, Shuang and Zhang, Junxiao and Zhang, Huangchuang},
journal={ISPRS International Journal of Geo-Information},
volume={8},
number={6},
pages={289},
year={2019},
publisher={Multidisciplinary Digital Publishing Institute}
}
@article{zhai2019collision,
title={Collision Detection for {UAVs} Based on {GeoSOT-3D} Grids},
author={Zhai, Weixin and Tong, Xiaochong and Miao, Shuangxi and Cheng, Chengqi and Ren, Fuhu},
journal={ISPRS International Journal of Geo-Information},
volume={8},
number={7},
pages={299},
year={2019},
publisher={Multidisciplinary Digital Publishing Institute}
}
@inproceedings{yoo2019concept,
title={Concept and Framework of {3D} Geo-Spatial Grid System},
author={Yoo, Ji Song and Min, Kyung Ju and Ahn, Jong Wook},
booktitle={International Symposium on Web and Wireless Geographical Information Systems},
pages={136--149},
year={2019},
organization={Springer}
}
@article{du2018duality,
title={Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid},
author={Du, Lingyu and Ma, Qiuhe and Ben, Jin and Wang, Rui and Li, Jiahao},
journal={ISPRS International Journal of Geo-Information},
volume={7},
number={10},
pages={391},
year={2018},
publisher={Multidisciplinary Digital Publishing Institute}
}
@article{sirdeshmukh2019utilizing,
title={Utilizing a Discrete Global Grid System for Handling Point Clouds with Varying Locations, Times, and Levels of Detail},
author={Sirdeshmukh, Neeraj and Verbree, Edward and Oosterom, Peter Van and Psomadaki, Stella and Kodde, Martin},
journal={Cartographica: The International Journal for Geographic Information and Geovisualization},
volume={54},
number={1},
pages={4--15},
year={2019},
publisher={University of Toronto Press}
}
@article{sahr1998discrete,
title={Discrete Global Grid Systems},
author={Sahr, Kevin and White, Denis},
journal={Computing Science and Statistics},
pages={269--278},
year={1998},
publisher={Citeseer}
}
@article{gorski2005healpix,
title={HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere},
author={Gorski, Krzysztof M and Hivon, Eric and Banday, Anthony J and Wandelt, Benjamin D and Hansen, Frode K and Reinecke, Mstvos and Bartelmann, Matthia},
journal={The Astrophysical Journal},
volume={622},
number={2},
pages={759},
year={2005},
publisher={IOP Publishing}
}
@article{sahr2008location,
title={Location Coding on Icosahedral Aperture 3 Hexagon Discrete Global Grids},
author={Sahr, Kevin},
journal={Computers, Environment and Urban Systems},
volume={32},
number={3},
pages={174--187},
year={2008},
publisher={Elsevier}
}
@article{tong2013efficient,
title={Efficient Encoding and Spatial Operation Scheme for Aperture 4 Hexagonal Discrete Global Grid System},
author={Tong, Xiaochong and Ben, Jin and Wang, Ying and Zhang, Yongsheng and Pei, Tao},
journal={International Journal of Geographical Information Science},
volume={27},
number={5},
pages={898--921},
year={2013},
publisher={Taylor \& Francis}
}
@article{gregory2008comparison,
title={A Comparison of Intercell Metrics on Discrete Global Grid Systems},
author={Gregory, Matthew J and Kimerling, A Jon and White, Denis and Sahr, Kevin},
journal={Computers, Environment and Urban Systems},
volume={32},
number={3},
pages={188--203},
year={2008},
publisher={Elsevier}
}
@article{holhocs2014octahedral,
title={An Octahedral Equal Area Partition of the Sphere and Near Optimal Configurations of Points},
author={Holho{\c{s}}, Adrian and Ro{\c{s}}ca, Daniela},
journal={Computers \& Mathematics with Applications},
volume={67},
number={5},
pages={1092--1107},
year={2014},
publisher={Elsevier}
}
@inproceedings{dutton1996encoding,
title={Encoding and Handling Geospatial Data with Hierarchical Triangular Meshes},
author={Dutton, Geoffrey},
booktitle={In Proceedings of the 7th Symposium on Spatial Data Handling},
year={1996},
volume={43},
pages={505--518},
organization={Taylor \& Francis}
}
@inproceedings{fekete1990sphere,
title={Sphere Quadtrees: A New Data Structure to Support the Visualization of Spherically Distributed Data},
author={Fekete, Gyorgy and Treinish, Lloyd A},
booktitle={Extracting Meaning from Complex Data: Processing, Display, Interaction},
volume={1259},
pages={242--253},
year={1990},
organization={International Society for Optics and Photonics}
}
@article{vince2006indexing,
title={Indexing the Aperture 3 Hexagonal Discrete Global Grid},
author={Vince, Andrew},
journal={Journal of Visual Communication and Image Representation},
volume={17},
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