Geospatial data are gathered through a variety of different methods.The integration and handling of such datasets within a Digital Earth framework are very important in many aspects of science and engineering.One mean...Geospatial data are gathered through a variety of different methods.The integration and handling of such datasets within a Digital Earth framework are very important in many aspects of science and engineering.One means of addressing these tasks 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 efficient determination of hierarchical relationships for various hexagonal refinements and demonstrate its usefulness in Digital Earth frameworks.展开更多
Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one s...Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one special parameter;(2)a 2-parameter family of 2-layer earth map tilings with 2n tiles for each n≥3;(3)a 3-layer earth map tiling with 8n tiles for each n≥2,and two flip modifications for each odd n.The authors also describe the moduli of parameterized tilings and provide the full geometric data for all tilings.展开更多
基金This research was supported in part by PYXIS Innovation,the National Science and Engineering Research Council of Canada,and GRAND Net-work of Centre of Excellence of Canada.
文摘Geospatial data are gathered through a variety of different methods.The integration and handling of such datasets within a Digital Earth framework are very important in many aspects of science and engineering.One means of addressing these tasks 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 efficient determination of hierarchical relationships for various hexagonal refinements and demonstrate its usefulness in Digital Earth frameworks.
基金supported by the Key Projects of Zhejiang Natural Science Foundation(No.LZ22A010003)ZJNU Shuang-Long Distinguished Professorship Fund(No.YS304319159)。
文摘Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one special parameter;(2)a 2-parameter family of 2-layer earth map tilings with 2n tiles for each n≥3;(3)a 3-layer earth map tiling with 8n tiles for each n≥2,and two flip modifications for each odd n.The authors also describe the moduli of parameterized tilings and provide the full geometric data for all tilings.
