Bibliography for Global Grids (compiled by Denis White of the EPA)

Updated 1/9/2000

Ahuja N. 1983. On approaches to polygonal decomposition for hierarchical image representation. Computer Vision, Graphics, and Image Processing 24:200-214.

Arlinghaus SL. 1993. Central place fractals: theoretical geography in an urban setting. Fractals in geography. Lam NS-N, De Cola L, eds. Prentice Hall, Englewood Cliffs, NJ. pp. 213-227.

Bailey HP. 1956. Two grid systems that divide the entire surface of the earth into quadrilaterals of equal area. Transactions, American Geophysical Union 37(5):628-635.

Barrett P. 1995. Application of the linear quadtree to astronomical databases. Proceedings of Astronomical Data Analysis Software and Systems IV. Shaw RA, Payne HE, Hayes JJE, eds. ASP Conference Series, Vol. 77, Astronomical Society of the Pacific. pp. 472-478.

Bauer MA. 1985. Set operations on linear quadtrees. Computer Vision, Graphics, and Image Processing 29:248-258.

Baumgardner JR, Frederickson PO. 1985. Icosahedral discretization of the two-sphere. SIAM Journal on Numerical Analysis 22(6):1107-1115.

Bell SBM, Diaz BM, Holroyd F, Jackson MJ. 1983. Spatially referenced methods of processing raster and vector data. Image and Vision Computing 1(4):211-220.

Bell SBM, Holroyd FC. 1996. Lattice rings: coordinates for self-similar hierarchies and their relevance to geographic information systems. International Journal of Geographical Information Systems 10(2):147-177.

Bradley AD. 1946. Equal-area projection on the icosahedron. Geographical Review 36(1):101-104.

Brooks DR. 1981. Grid systems for earth radiation budget experiment applications. NASA Technical Memorandum 83233. National Aeronautics and Space Administration, Hampton, VA. 42 pp.

Brown JJ. (Unpublished). Sampling plans for an isotropic random sphere. University of North Carolina, Chapel Hill. 16 pp.

Brown JJ. 1995. A bootstrap algorithm for the isotropic random sphere. Advances in Applied Probability (Stochastic Geometry and Statistical Applications) 27:627-641.

Brown JJ. 1995. A central limit theorem for an isotropic random sphere. Advances in Applied Probability (Stochastic Geometry and Statistical Applications) 27:642-651.

Burt PJ. 1980. Tree and pyramid structures for coding hexagonally sampled binary images. Computer Graphics and Image Processing 14:271-280.

Carr DB, Olsen AR, White D. 1992. Variations of hexagon mosaic maps for display of univariate and bivariate geographical data. Cartography and Geographic Information Systems 19(3):228-236.

Carr D, Kahn R, Sahr K, Olsen T. 1998. ISEA discrete global grids. Statistical Computing & Statistical Graphics Newsletter 8(2/3):31-39.

Ceulemans A, Fowler PW. 1991. Extension of Euler's theorem to symmetry properties of polyhedra. Nature 353:52-54.

Christaller W. 1966. The central places of southern Germany. Baskin CW, trans. Prentice Hall, Englewood Cliffs, NJ. 230 pp.

Chung F, Sternberg S. 1993. Mathematics and the Buckyball. American Scientist 81(1):56-71.

Clarke KC, Mulcahy KA. 1995. Distortion on the Interrupted Modified Collignon projection. Proceedings of GIS/LIS '95. American Society for Photogrammetry and Remote Sensing, Nashville, TN. pp. 175-181.

Colombo, O.,1979, "Optimal Estimation from Data Regularly Sampled on a Sphere….", Department of Geodetic Science, Report #291, Ohio State University, Columbus.

Conway JH, Sloane NJA. 1999. Sphere packings, lattices and groups. 3rd edition. Springer-Verlag, New York. 777 pp.

Coxeter HSM. 1991. Regular complex polytopes. 2nd edition. Cambridge University Press, Cambridge. 210 pp.

Dacey MF. 1964. A note on some number properties of a hexagonal hierarchical plane lattice. Journal of Regional Science 5(2):63-67.

Deile M-L. (Unpublished). Could the disarming generation claim a liberated cartography? (Provided by Waldo Tobler). Morges, Switzerland.

Deile M-L. (Unpublished). Hexagonal pilot world map. (Provided by Waldo Tobler). Morges, Switzerland.

Dutton G. (Unpublished, 1994). Area inequalities in a quaternary triangular mesh. Watertown, MA. 17 pp.

Dutton G. 1984. Geodesic modelling of planetary relief. Cartographica 21(2&3, Monograph 32-33):188-207.

Dutton G. 1988. Modeling locational uncertainty via hierarchicall tessellation. Accuracy of spatial databases. Goodchild M, Gopal S, eds. Taylor & Francis, London. pp. 123-140.

Dutton G. 1989. Planetary modelling via hierarchical tessellation. Proceedings of the Eleventh International Conference on Computer-Assisted Cartography (Auto-Carto 9). Anderson E, ed. American Congress on Surveying and Mapping, Baltimore, MD. pp. 462-471.

Dutton G. 1991. Zenithial orthotriangular projection. Proceedings of the Tenth International Conference on Computer-Assisted Cartography (Auto-Carto 10). American Congress on Surveying and Mapping, Baltimore, MD. pp. 77-95.

Dutton G. 1996. Improving locational specificity of map data--a multi-resolution, metadata-driven approach and notation. International Journal of Geographical Information Systems 10(3):253-268.

Dutton G. 1998. A hierarchical coordinate system for geoprocessing and cartography. Lecture Notes in Earth Science 78. Springer-Verlag, Berlin. 231 pp.

Fekete G. 1990. Rendering and managing spherical data with sphere quadtrees. Proceedings of Visualization '90. IEEE Computer Society, Los Alamitos, CA. pp. 176-186.

Fekete G, Treinish L. 1990. Sphere quadtrees: a new data structure to support the visualization of spherically distributed data. Proceedings of the SPIE, Extracting Meaning from Complex Data: Processing, Display, Interaction, Vol. 1259. Farrell EJ, ed. International Society for Optical Engineering. pp. 242-253.

Frisch U, Hasslacher B, Pomeau Y. 1986. Lattice-gas automata for the Navier-Stokes equations. Physics Review Letters 56:1505-1508.

Fuller RB. 1974. Remapping our world. Today's Education(November-December).

Fuller RB. 1979. Synergetics 2: explorations in the geometry of thinking. Macmillan, New York. 592 pp.

Gabrosek J, Cressie N, Huang H-C. 1999. Spatio-temporal prediction of Level 3 data for NASA's Earth Observing System. Proceedings of 3rd International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Quebec, Canada.

Gargantini I. 1982. An effective way to represent quadtrees. Communications of the Association for Computing Machinery 25(12):905-910.

Gasson PC. 1983. Geometry of spatial forms. Ellis Horwood, Chichester, West Sussex. 561 pp.

Giacaglia GEO, Lundquist CA. 1972. Sampling functions for geophysics. SAO Special Report No. 344. Smithsonian Institution Astrophysical Observatory, Cambridge, MA. 93 pp.

Gibson L, Lucas D. 1982. Vectorization of raster images using hierarchical methods. Computer Graphics and Image Processing 20:82-89.

Gibson L, Lucas D. 1982. Spatial data processing using generalized balanced ternary. Proceedings of the Conference on Pattern Recognition and Image Processing. IEEE Computer Society. pp. 566-571.

Golay MJE. 1969. Hexagonal parallel pattern transformations. IEEE Transactions on Computers 18(8):733-740.

Goodchild MF, Shiren Y. 1989. A hierarchical spatial data structure for global geographic information systems. Technical Paper 89-5. National Center for Geographic Information and Analysis, University of California, Santa Barbara, CA. 25 pp.

Goodchild MF, Shiren Y, Dutton G. 1991. Spatial data representation and basic operations on triangular hierarchical data structure. Technical Paper 91-8. National Center for Geographical Information and Analysis, University of California, Santa Barbara, CA. 39 pp.

Goodchild MF, Shiren Y. 1992. A hierarchical spatial data structure for global geographic information systems. Computer Vision, Graphics, and Image Processing 54:31-44.

Gray RW. 1994. Fuller's Dymaxion(TradeMark) Map. Cartography and Geographic Information Systems 21(4):243-246.

Gray RW. 1995. Exact transformation equations for Fuller's world map. Cartographica 32(3):17-25.

Grimmett G. 1989. Percolation. Springer-Verlag, New York

Grünbaum B, Motzkin TS. 1963. The number of hexagons and the simplicity of geodesics on certain polyhedra. Canadian Journal of Mathematics 15(4):744-751.

Grünbaum B, Shephard GC. 1977. The eighty-one types of isohedral tilings in the plane. Mathematical Proceedings of the Cambridge Philosophical Society 82(2):177-196.

Grünbaum B, Shephard GC. 1981. Patterns on the 2-sphere. Mathematika 28(1):1-35.

Hales TC. 1999. The honeycomb conjecture. Department of Mathematics, University of Michigan, http://www.math.lsa.umich.edu/~hales/countdown/honey/. 22 pp.

Heikes R, Randall DA. 1995. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: basic design and results of tests. Monthly Weather Review 123(6):1862-1880.

Heikes R, Randall DA. 1995. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: a detailed description of the grid and an analysis of numerical accuracy. Monthly Weather Review 123(6):1881-1887.

Holroyd F, Bell SBM. 1992. Raster GIS: models of raster encoding. Computers & Geosciences 18(4):419-426.

Huang H-C, Cressie N. 1997. Multiscale spatial modeling. Proceedings of the Section on Statistics and the Environment. American Statistical Association, Alexandria, VA. pp. 49-54.

Hudson JC. 1967. An algebraic relation between the Lösch and Christaller central place networks. The Professional Geographer 19(3):133-135.

Kahn R, Haskins RD, Knighton JE, Pursch A, Granger-Gallegos S. 1991. Validating a large geophysical data set: experiences with satellite-derived cloud parameters. Proceedings of the 23rd Symposium on the Interface, Computing Science and Statistics 23:133-140.

Kahn R, Braverman A. 1999. What shall we do with the data we are expecting from upcoming earth observation satellites? Journal of Computational and Graphical Statistics 8(3):575-588.

Kant G. 1993. Hexagonal grid drawings. Proceedings of Graph-Theoretic Concepts in Computer Science, 18th International Workshop. Mayr EW, ed. Lecture Notes in Computer Science 657. Springer-Verlag, Wiesbaden-Naurod, Germany. pp. 263-276.

Kaula, W, 1967, "Theory of Statistical Analysis of Data Distributed over a sphere", Reviews of Geophysics, 1:83-107.

Keller JK, Heimbuch D, Richmond M. 1979. Optimization of grid cell shape for analysis of wildlife habitat. Proceedings of the Thirteenth International Symposium on Remote Sensing of the Environment, Vol. III. Environmental Research Institute of Michigan, Ann Arbor, MI. pp. 1419-1428.

Kimerling AJ, Sahr K, White D, Song L. (In press). Comparing geometric properties of discrete global grids. Cartography and Geographic Information Systems.

Kimerling AJ. 1984. Area computation from geodetic coordinates on the spheroid. Surveying and Mapping 44(4):343-351.

Kimerling AJ, Overton WS, White D. 1995. Statistical comparison of map projection distortions within irregular areas. Cartography and Geographic Information Systems 22(3):205-221.

Kimerling AJ, Sahr K, White D. 1997. Global scale data model comparison. Proceedings of the Thirteenth International Conference on Computer-Assisted Cartography (Auto-Carto 13). American Congress on Surveying and Mapping, Seattle, WA. pp. 357-366.

Lee M, Samet H. 1998. Traversing the triangle elements of an icosahedral spherical representation in constant time. Proceedings of the 8th International Symposium on Spatial Data Handling. Poiker TK, Chrisman N, eds. International Geographical Union, Burnaby, BC. pp. 22-33.

Lindgren CES. 1967. The geometry of mixed hexagonal hierarchies in the context of central place theory. Harvard Papers in Theoretical Geography No. 7. Laboratory for Computer Graphics and Spatial Analysis, Harvard University, Cambridge, MA.

Lösch A. 1954. The economics of location. 2nd edition. Woglom WH, Stolper WF, trans. Yale University Press, New Haven, CT. 520 pp.

Lugo JA, Clarke KC. 1995. Implementation of triangulated quadtree sequencing for a global relief data structure. Proceedings of the Twelfth International Conference on Computer-Assisted Cartography (Auto-Carto 12). American Congress on Surveying and Mapping, Charlotte, NC. pp. 147-156.

Lukatela H. 1987. Hipparchus geopositioning model: an overview. Proceedings of the Eighth International Conference on Computer-Assisted Cartography (Auto-Carto 8). American Congress on Surveying and Mapping. pp. 87-96.

Mark DM, Lauzon JP. 1985. Approaches for quadtree-based geographic information systems at continental or global scales. Proceedings of the Seventh International Conference on Computer-Assisted Cartography (Auto-Carto 7). American Congress on Surveying and Mapping. pp. 355-364.

Mark DM. 1990. Neighbor-based properties of some orderings of two-dimensional space. Geographical Analysis 22(2):145-157.

Matérn B. 1986. Spatial variation. 2nd edition. Lecture Notes in Statistics No. 36. Springer-Verlag, Berlin. 151 pp.

Murray BG, Jr. 1967. Dispersal in vertebrates. Ecology 48(6):975-978.
Olea RA. 1984. Sampling design optimization for spatial functions. Mathematical Geology 16(4):369-392.

Olea RA. 1984. Systematic sampling of spatial functions. Series on Spatial Analysis No. 7. Kansas Geological Survey, University of Kansas, Lawrence, KS. 57 pp.

Olsen AR, Stevens DL, Jr., White D. 1998. Application of global grids in environmental sampling. Proceedings of the 30th Symposium on the Interface, Computing Science and Statistics 30:279-284.

Otoo EJ, Zhu H. 1993. Indexing on spherical surfaces using semi-quadcodes. Proceedings of Third International Symposium on Advances in Spatial Databases. Abel DJ, Ooi BC, eds. Lecture Notes in Computer Science 692. Springer-Verlag, Singapore. pp. 510-529.

Ouyang Q, Swinney HL. 1991. Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352:610-612.

Paul MK. 1973. On computation of equal area blocks. Bulletin Geodésique 107:73-84.

Pearce P, Pearce S. 1978. Polyhedra primer. Van Nostrand Reinhold, New York. 134 pp.

Pequet DJ. 1984. A conceptual framework and comparison of spatial data models. Cartographica 21(4):66-113.

Popko E. 1968. Geodesics. University of Detroit Press, Detroit, MI. 124 pp.

Raskin R. 1994. Spatial analysis on the sphere: a review. Technical Paper 94-7. National Center for Geographic Information and Analysis, Santa Barbara, CA.

Saalfeld A. 1998. Sorting spatial data for sampling and other geographic applications. Geoinformatica 2:37-57.

Sadourny R, Arakawa A, Mintz Y. 1968. Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere. Monthly Weather Review 96(6):351-356.

Saff EB, Kuijlaars A. 1997. Distributing many points on a sphere. Mathematical Intelligencer 19(1):5-11.

Sahr K, White D. 1998. Discrete global grid systems. Proceedings of the 30th Symposium on the Interface, Computing Science and Statistics 30:269-278.

Samet H. 1984. The quadtree and related hierarchical data structures. Computing Surveys 16(2):187-260.

Samet H, Tamminen M. 1985. Computing geometric properties of images represented by linear quadtrees. IEEE Transactions on Pattern Analysis and Machine Intelligence 7(2):229-240.

Schröder P, Sweldens W. 1995. Sperical wavelets: efficiently representing functions on the sphere. Industrial Mathematics Initiative Research Report 1995:01. Department of Mathematics, University of South Carolina, Columbia, SC. 27 pp.

Slade G. 1994. Self avoiding walks. Mathematical Intelligencer 16(1):29-35.

Snyder JP. 1992. An equal-area map projection for polyhedral globes. Cartographica 29(1):10-21.

Stauffer D, Aharony A. 1992. Introduction to percolation theory. 2nd edition. Taylor & Francis, London. 181 pp.

Stevens DL, Jr., Olsen AR. (In press). Spatially restricted surveys over time for aquatic resources. Journal of Agricultural, Biological, and Environmental Statistics.

Stevens DL, Jr. 1997. Variable density grid-based sampling designs for continuous spatial populations. Environmetrics 8:167-195.

Thuburn J. 1997. A PV-based shallow-water model on a hexagonal-icosahedral grid. Monthly Weather Review 125:2328-2347.

Tobler W, Chen Z-T. 1986. A quadtree for global information storage. Geographical Analysis 18(4):360-371.

Tobler, W.,1996, "Converting Administrative Data on a Sphere to a Continuous Surface",
Proceedings, 3rd International Conference on Integrating Geographic Information Systems and
Environmental Modeling, NCGIA (Santa Barbara), CD?ROM.

Tobler, W., 1992, "Preliminary Representation of World Population by Spherical Harmonics",
Proceedings, National Academy of Sciences, 89: 6262?6264.

Tobler, W.,1997, "Movement Modeling on the Sphere", Geographical & Environmental
Modeling, 1, 1: 97?103

Tobler, W., 1997, "World Population in a grid of Spherical Quadrangles", Int. J. Population
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van Roessel JW. 1988. Conversion of cartesian coordinates from an to generalized balanced ternary addresses. Photogrammetric Engineering and Remote Sensing 54(11):1565-1570.

Watson GS. 1983. Statistics on spheres. John Wiley & Sons, New York. 238 pp.

Watson DF. 1988. Natural neighbor sorting on the n-dimensional sphere. Pattern Recognition 21(1):63-67.

White D. (Accepted). Global grids from recursive diamond subdivisions of the surface of an octahedron or icosahedron. Environmental Monitoring and Assessment.

White D, Kimerling AJ, Overton WS. 1992. Cartographic and geometric components of a global sampling design for environmental monitoring. Cartography and Geographic Information Systems 19(1):5-22.

White D, Kimerling AJ, Sahr K, Song L. 1998. Comparing area and shape distortion on polyhedral-based recursive partitions of the sphere. International Journal of Geographical Information Science 12(8):805-827.

Wickman FE, Elvers E, Edvarson K. 1974. A system of domains for global sampling problems. Geografiska Annaler, Series A 56(3-4):201-212.

Woldenberg MJ. 1979. A periodic table of spatial hierarchies. Philosophy in geography. Gale S, Olsson G, eds. D. Reidel, Dordrecht, Netherlands. pp. 429-456.

Wolfram S. 1986. Cellular automaton fluids 1: basic theory. Journal of Statistical Physics 45:471-526.

Yfantis EA, Flatman GT, Behar JV. 1987. Efficiency of kriging estimation for square, triangular, and hexagonal grids. Mathematical Geology 19(3):183-205.