Uniform spherical grids via equal area projection from the cube to the sphere

Rosca, Daniela; Plonka, Gerlind

doi:10.1016/j.cam.2011.07.009

Cited by 30 publications

(21 citation statements)

References 5 publications

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“…In addition to Snyder's projection, other types of equal-area projection have also been used in DGGSs. For instance, Roşca and Plonka's projection (Roşca and Plonka 2011) was used in the one-to-two Digital Earth, which is a cube-based Digital Earth (Mahdavi-Amiri et al 2013), and extended to the octahedron in (Roşca and Plonka 2012). This equal-area projection describes a mapping from a cubic domain to a spherical domain .…”

Section: Projection For Polyhedral Globesmentioning

confidence: 99%

Digital Earth Platforms

Alderson

Purss

et al. 2019

Manual of Digital Earth

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In this chapter, we provide a thorough discussion on Digital Earth with particular focus on Discrete Global Grid Systems (DGGS), which are a standardized representation of the Earth. We describe the necessary components of a DGGS, such as the underlying 2D representation, indexing system, projection, and cell types. We also discuss a selection of well-known public and commercial DGGSs followed by current DGGS standards. Keywords Discrete Global Grid • OGC Standard • Digital Earth 2.1 Introduction Digital Earth is a framework for geospatial data management. In this model, data are assigned to locations on a 3D model of the Earth and analyzed at multiple resolutions, each representing data at a specific level of detail. To locate and retrieve data sets associated with the Earth, mechanisms are needed for data representation, region addressing, and the assignment and retrieval of data for a region of interest. Digital Earth provides a reference model that can handle all of these queries.

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Section: Projection For Polyhedral Globesmentioning

confidence: 99%

Digital Earth Platforms

Alderson

Purss

et al. 2019

Manual of Digital Earth

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“…In the frameworks proposed in [2,6,22], Snyder equal area projection has been used, which is a popular projection due to its low angular distortion and the mapping of edges of the polyhedron to great circle arcs [27]. However, other types of equal area projection have also been used due to their own desirable properties, such as providing closed forms for both projection and inverse projection [10,28].…”

Section: Projectionmentioning

confidence: 99%

Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems

Amiri

Samavati

Peterson

2015

IJGI

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Digital Earth frameworks provide a tool to receive, send and interact with large location-based datasets, organized usually according to Discrete Global Grid Systems (DGGS). In DGGS, an indexing method is used to assign a unique index to each cell of a global grid, and the datasets corresponding to these cells are retrieved or allocated using this unique index. There exist many methods to index cells of DGGS. Toward facility, interoperability and also defining a "standard" for DGGS, a conversion is needed to translate a dataset from one DGGS to another. In this paper, we first propose a categorization of indexing methods of DGGS and then define a general conversion method from one indexing to another. Several examples are presented to describe the method.

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“…This idea can also be generalized to construct uniform and refinable grids on elliptic domains and on some surfaces of revolution, see [6]. In [7], the authors have recently constructed an equal area projection from the cube to the sphere.…”

Section: Roşca and G Plonkamentioning

confidence: 99%

An Area Preserving Projection from the Regular Octahedron to the Sphere

Rosca

Plonka

2012

Results. Math.

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Abstract. In this paper, we propose an area preserving bijective map from the regular octahedron to the unit sphere S 2 , both centered at the origin. The construction scheme consists of two steps. First, each face Fi of the octahedron is mapped to a curved planar triangle Ti of the same area. Afterwards, each Ti is mapped onto the sphere using the inverse Lambert azimuthal equal area projection with respect to a certain point of S 2 . The proposed map is then used to construct uniform and refinable grids on a sphere, starting from any triangular uniform and refinable grid on the triangular faces of the octahedron. Mathematics Subject Classification (2000). Primary 86A30; Secondary 85-08, 86-08.

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Uniform spherical grids via equal area projection from the cube to the sphere

Cited by 30 publications

References 5 publications

Digital Earth Platforms

Digital Earth Platforms

Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems

An Area Preserving Projection from the Regular Octahedron to the Sphere

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