A "Slice-and-Dice" Approach to Area Equivalence in Polyhedral Map Projections

Leeuwen, Diederik van; Strebe, Daniel “daan”

doi:10.1559/152304006779500687

Cited by 13 publications

(14 citation statements)

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“…For many conventional DGGSs, area-preserving projections are used to ensure every cell in a certain resolution of the grid has the same area when mapped to the corresponding region of the Earth [19,21,48]. This property is important for applications where the area of cells is frequently used, as this can be expensive to compute.…”

Section: Radial Mappingmentioning

confidence: 99%

“…[49]. The input DGGS for this example uses a disdyakis triacontahedron as the initial polyhedron, a non-standard 1:4 triangle refinement, and the vertex oriented great circle slice and dice projection [48] to preserve area [50]. The 3D DGGS has a target aspect ratio of one, a radial mapping exponent of three to achieve perfect volume preservation (excluding the central layer), and a maximum radius of 1.33R (8495 km).…”

Section: Urban Planningmentioning

confidence: 99%

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General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

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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.

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Section: Radial Mappingmentioning

confidence: 99%

Section: Urban Planningmentioning

confidence: 99%

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

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“…19). Projection of the polyhedron's edge with a constant scale of distortion is an interesting aspect of this solution (D. van Leeuwen, D. Strebe 2006). This projection was described in the article titled Life presents Buckminster Fuller Dymaxion World; it also presents fragments of the Dymaxion …”

Section: Famous Polyhedral Mapsmentioning

confidence: 99%

Image of the World on polyhedral maps and globes

Pędzich

2016

Polish Cartographical Review

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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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“…Already in 1525 Albrecht Dürer proposed a projection of the sphere to the polyhedron, as an approximation of the surface of a globe. The polyhedral projections divide the spherical surface on a regular basis, and that is a significant problem for the presentation and data structure within the geographical databases (D. Van Leeuwen, D. Strebe 2006). Figure 12 shows an example of polyhedral projection.…”

Section: Polyhedral Map Projection and Projections For Constructing Tmentioning

confidence: 99%

From cartography of the Universe to molecular cartography – the use of map projections

Pędzich

2015

Polish Cartographical Review

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Map projections are very important in the compilation of various types of maps and spatial databases. Geographical information systems provide their users with the significant opportunities in the choice of map projections, coordinate systems, their definitions and transitions between them. The role of map projection can be considered depending on an objective, for which a map has to be used, user of this map and a form of its publication. The Internet, mobile devices and GIS caused that the map projections are used for two main purposes: data visualization and performing of calculations and analyses. The role of map projections is still important, despite the changes occurring in cartography. The rules for the applications of map projections developed over the centuries are still valid. However, the new rules resulting from the new functions of map projections are also created. The aim of this article, that is the author's overview of map projections, is to illustrate the broad spectrum of applications for the map projections.

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A "Slice-and-Dice" Approach to Area Equivalence in Polyhedral Map Projections

Cited by 13 publications

References 0 publications

General Method for Extending Discrete Global Grid Systems to Three Dimensions

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Image of the World on polyhedral maps and globes

From cartography of the Universe to molecular cartography – the use of map projections

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