Offsetting spherical curves in vector and raster form

Alderson, Troy; Mahdavi-Amiri, Ali; Samavati, Faramarz

doi:10.1007/s00371-018-1525-7

Cited by 8 publications

(2 citation statements)

References 17 publications

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“…While traditional GIS still makes heavy use of projection for analysis and visualization of geographic and geospatial data, there have been many works on developing algorithms and techniques for performing spatial analysis directly on the sphere. Some recent examples include better representations of rational points [23], multiresolution representations of B-spline [24] and NURBS [25] curves, and methods for offsetting curves in both vector and raster form [26].…”

Section: Related Workmentioning

confidence: 99%

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: Related Workmentioning

confidence: 99%

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

Self Cite

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“…Results are shown in Figure 12. After generating discrete lines, spatial operations such as buffer generation [23] and overlay analysis can be performed, providing a reference for solving practical problems.…”

Section: Application Of Our Algorithm In Dggsmentioning

confidence: 99%

Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid

Ben

Wang

et al. 2018

IJGI

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Vectors are a key type of geospatial data, and their discretization, which involves solving the problem of generating a discrete line, is particularly important. In this study, we propose a method for constructing a discrete line mathematical model for a triangular grid based on a “weak duality” hexagonal grid, to overcome the drawbacks of existing discrete line generation algorithms for a triangular grid. First, a weak duality relationship between triangular and hexagonal grids is explored. Second, an equivalent triangular grid model is established based on the hexagonal grid, using this weak duality relationship. Third, the two-dimensional discrete line model is solved by transforming it into a one-dimensional optimal wandering path model. Finally, we design and implement the dimensionality reduction generation algorithm for a discrete line in a triangular grid. The results of our comparative experiment indicate that the proposed algorithm has a computation speed that is approximately 10 times that of similar existing algorithms; in addition, it has better fitting effectiveness. Our proposed algorithm has broad applications, and it can be used for real-time grid transformation of vector data, discrete global grid system (DGGS), and other similar applications.

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Toward volume preserving spheroid degenerated-octree grid

Ulmer

Samavati

2020

Geoinformatica

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Offsetting spherical curves in vector and raster form

Cited by 8 publications

References 17 publications

General Method for Extending Discrete Global Grid Systems to Three Dimensions

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid

Toward volume preserving spheroid degenerated-octree grid

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