Discrete evaluation of Stokes?s integral by means of Voronoi and Delaunay structures

Santos, Newton Pereira dos; Escobar, Iris Pereira

doi:10.1007/s00190-004-0402-5

Cited by 12 publications

(5 citation statements)

References 21 publications

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“…As remarked in an earlier paper (Santos and Escobar, 2004), the schemes presented similar results with each other, as well as in comparison with a classical point-wise numerical integration. In this work, Voronoi scheme does not close the convex hull to ensure that the border cells were exactly those produced by Voronoi tesselation.…”

Section: Discussionsupporting

confidence: 79%

“…In addition, Voronoi and Delaunay schemes were used to compute the geoid, now considering the gridded data alone, that is, after removing the "observed" irregularly distributed points. This procedure nearly corresponds to the classical method issue by point-wise numerical integration (Santos and Escobar, 2004). This gridded data include 2881 evenly spaced 5-arcmin resolution Helmert anomalies, that were derived from Bouguer data according to Eq.(12).…”

Section: 1 V O R O N O I / D E L a U N A Y P A R T I T I O N Smentioning

confidence: 99%

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Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro, Brazil: A case study with Voronoi/Delaunay discretisations

Santos

Escobar

2010

Stud Geophys Geod

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The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes, target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones, as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m, respectively, for Voronoi, Delaunay, computed between 32 GPS/leveling points. K e y w o r d s : Gravimetric geoid, Earth gravitational model, high resolution DTE, Voronoi and Delaunay tesselations

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Section: Discussionsupporting

confidence: 79%

Section: 1 V O R O N O I / D E L a U N A Y P A R T I T I O N Smentioning

confidence: 99%

Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro, Brazil: A case study with Voronoi/Delaunay discretisations

Santos

Escobar

2010

Stud Geophys Geod

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“…This is because the non-homogeneity of space requires, for cognitive reasons, that it is divided into elements with an identical structure, clearly distinguishable from the other parts of the area under study [11]. The most significant characteristic of this method is the possibility of preserving the original data despite their processing, and, primarily, for surviving the unavoidable smoothing in connection with the spatial distribution of data and avoiding additional smoothing due to interpolation of the analyzed values [24].…”

Section: Research Methodology-voronoi Diagramsmentioning

confidence: 99%

3D Modeling of Discontinuity in the Spatial Distribution of Apartment Prices Using Voronoi Diagrams

Bełej

Figurska

2020

Remote Sensing

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An immanent feature of the housing market is a large spatial dispersion of real estate prices along with their simultaneous high stratification. Application of classic methods of data interpolation results in an excessive simplification of the outcome because of a conversion of the dispersed data sets into areas of spatial continuity by reducing the above-average real estate prices. The main aim of the article was to search for spatial discontinuities of real estate prices’ distribution with 3D modeling using Voronoi diagrams as a method of irregular division of this space. Used methods of geospatial analyses with GIS tools enabled to identify clusters of high housing market activity and to avoid an excessive generalization of data resulting from the reduction of the above-average real estate prices. The research was conducted for over 7000 real estate transactions in years 2010–2017 in Olsztyn, the capital city of Warmia and Mazury in Poland, resulting in a 3D visualization of real estate prices for the chosen market, including the discontinuity in their spatial distribution.

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“…As a result, the spatial aspects of the studied phenomena can be visualized in a manner that accounts for their heterogeneous character, particularly when data are dispersed or in short supply [ 35 ]. In addition, data are not over-smoothed by interpolation, and their original form is preserved during processing [ 48 ].…”

Section: Literature Reviewmentioning

confidence: 99%

Voronoi Diagrams for Senior-Friendly Cities

Figurska

Dawidowicz

Zysk

2022

IJERPH

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Motives: Active aging places (AAP) should be identified during the COVID-19 pandemic to ensure the sanitary safety of seniors, prevent older adults from feeling excluded, and eliminate health threats that discourage seniors from being active. Aim: The aim of this study was to apply a new analytical approach with the use of Voronoi diagrams in GIS tools to spatially identify the AAP in the context of apparent social dynamics. Methods: An empirical study was conducted with the use of qualitative (literature review, questionnaire survey, AAP classification, visualization of AAP location with GIS tools) and quantitative methods (AAP ranking based on a statistical analysis of survey responses). Results: Voronoi diagrams were used to determine the accessibility of selected objects in the city of Olsztyn and identify spaces that belong to the social logic of space.

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Discrete evaluation of Stokes?s integral by means of Voronoi and Delaunay structures

Cited by 12 publications

References 21 publications

Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro, Brazil: A case study with Voronoi/Delaunay discretisations

Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro, Brazil: A case study with Voronoi/Delaunay discretisations

3D Modeling of Discontinuity in the Spatial Distribution of Apartment Prices Using Voronoi Diagrams

Voronoi Diagrams for Senior-Friendly Cities

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