Toward volume preserving spheroid degenerated-octree grid

Ulmer, Benjamin; Samavati, Faramarz

doi:10.1007/s10707-019-00391-w

Cited by 7 publications

(6 citation statements)

References 22 publications

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“…Below we describe three different radial maps that are used for varying degrees of volume preservation between layers in the grid. The first two-which are identical to ones provided in [22]-are special cases of the more general third. Volume preservation between cells is also dependent on the projection and refinement of the input DGGS, and is therefore not discussed in general for our 3D DGGSs.…”

Section: Radial Mappingmentioning

confidence: 61%

“…This type of grid system has been used for the modelling of large-scale geospatial objects [43] and multi-scale visualization of the lithosphere [44]. Furthermore, there are extensions of the method that improve the volume preservation of the grid without significantly sacrificing the efficiency of indexing [22]. Another approach similar to SDOG is the Sphere Shell Space 3D Grid [14], which uses a similar octree based refinement of cells, but is based on multiple sphere shells as opposed to a single sphere.…”

Section: Related Workmentioning

confidence: 99%

“…To accomplish this, we can define a radial mapping that maps radial splits in the grid to corresponding radial splits that result in the appropriate volume. We summarize the method below, with more details available in [22]. The volume shell n represents is proportional to c 3n − c 3(n+1) .…”

Section: Shell-volume Preserving Mappingmentioning

confidence: 99%

“…We accomplish this by splitting encoding and decoding into a surface and radial component, which are handled by the input DGGS and our methods, respectively. As a part of these operations, we extend the radial mappings introduced in [22] for use with our 3D DGGSs. These mappings serve a similar purpose as projection in a conventional DGGS and use a single parameter to blend between volume and shape preservation.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

Self Cite

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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: 61%

Section: Related Workmentioning

confidence: 99%

Section: Shell-volume Preserving Mappingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another interesting active branch of DGGS research is 3D DGGSs. There exist some works that aim to build a 3D DGGS or extend current 2D DGGSs to 3D DGGS [34,35]. For this work, we have assumed a 2D DGGS, but the same idea might be able to be reimplemented for a 3D DGGS.…”

Section: Discussionmentioning

confidence: 99%

Efficient Calculation of Distance Transform on Discrete Global Grid Systems

Kazemi

Wecker

Samavati

2022

IJGI

Self Cite

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Geospatial data analysis often requires the computing of a distance transform for a given vector feature. For instance, in wildfire management, it is helpful to find the distance of all points in an area from the wildfire’s boundary. Computing a distance transform on traditional Geographic Information Systems (GIS) is usually adopted from image processing methods, albeit prone to distortion resulting from flat maps. Discrete Global Grid Systems (DGGS) are relatively new low-distortion globe-based GIS that discretize the Earth into highly regular cells using multiresolution grids. In this paper, we introduce an efficient distance transform algorithm for DGGS. Our novel algorithm heavily exploits the hierarchy of a DGGS and its mathematical properties and applies to many different DGGSs. We evaluate our method by comparing its speed and distortion with the distance transform methods used in traditional GIS and general 3D meshes. We demonstrate that our method is efficient and has minimal distortion.

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GIScience and remote sensing in natural resource and environmental research: Status quo and future perspectives

Pei

Liu

et al. 2021

Geography and Sustainability

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Toward volume preserving spheroid degenerated-octree grid

Cited by 7 publications

References 22 publications

General Method for Extending Discrete Global Grid Systems to Three Dimensions

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Efficient Calculation of Distance Transform on Discrete Global Grid Systems

GIScience and remote sensing in natural resource and environmental research: Status quo and future perspectives

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