Optimization of Inverse Snyder Polyhedral Projection

2011 ◽  
Author(s):  
Erika Harrison ◽  
Ali Mahdavi-Amiri ◽  
Faramarz Samavati
Keyword(s):  
Polyhedral Projection

scholarly journals General Method for Extending Discrete Global Grid Systems to Three Dimensions

2020 ◽  
Vol 9 (4) ◽  
pp. 233 ◽  
Author(s):  
Benjamin Ulmer ◽  
John Hall ◽  
Faramarz Samavati
Keyword(s):  
Three Dimensional ◽  
Use Cases ◽  
Three Dimensions ◽  
Grid Systems ◽  
3D Data ◽  
Third Dimension ◽  
2D And 3D ◽  
Polyhedral Projection ◽  
Global Grid ◽  
General Method

Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.

scholarly journals On Polyhedral Projection and Parametric Programming

2008 ◽  
Vol 138 (2) ◽  
pp. 207-220 ◽  
Author(s):  
C. N. Jones ◽  
E. C. Kerrigan ◽  
J. M. Maciejowski
Keyword(s):  
Parametric Programming ◽  
Polyhedral Projection

scholarly journals Image of the World on polyhedral maps and globes

2016 ◽  
Vol 48 (4) ◽  
pp. 197-210 ◽  
Author(s):  
Paweł Pędzich
Keyword(s):  
19Th Century ◽  
Continuous Image ◽  
Tectonic Plates ◽  
Regular Octahedron ◽  
Truncated Octahedron ◽  
Polyhedral Map ◽  
The Earth ◽  
The World ◽  
The 19Th Century ◽  
Polyhedral Projection

Abstract Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries. The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.

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