APPLICATIONS OF VORONOI AND DELAUNAY DIAGRAMS IN THE SOLUTION OF THE GEODETIC BOUNDARY VALUE PROBLEM

Autores

  • C. A. B. QUINTERO Observatório Nacional, Ministério da Ciência e Tecnologia
  • I. P. ESCOBAR Departamento de Engenharia Cartográfica, Universidade do Estado do Rio de Janeiro
  • C. F. Ponte-NETO Observatório Nacional, Ministério da Ciência e Tecnologia

DOI:

https://doi.org/10.5380/bcg.v18i3.29182

Palavras-chave:

2-D tessellation, Delaunay Triangulation, Voronoi Cells, Geodesy, Stokes’ Integral

Resumo

Voronoi and Delaunay structures are presented as discretization tools to be used innumerical surface integration aiming the computation of geodetic problemssolutions, when under the integral there is a non-analytical function (e. g., gravityanomaly and height). In the Voronoi approach, the target area is partitioned intopolygons which contain the observed point and no interpolation is necessary, onlythe original data is used. In the Delaunay approach, the observed points are verticesof triangular cells and the value for a cell is interpolated for its barycenter. If theamount and distribution of the observed points are adequate, gridding operation isnot required and the numerical surface integration is carried out by point-wise. Evenwhen the amount and distribution of the observed points are not enough, thestructures of Voronoi and Delaunay can combine grid with observed points in orderto preserve the integrity of the original information. Both schemes are applied to thecomputation of the Stokes’ integral, the terrain correction, the indirect effect and thegradient of the gravity anomaly, in the State of Rio de Janeiro, Brazil area.

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Publicado

2012-09-26

Como Citar

QUINTERO, C. A. B., ESCOBAR, I. P., & Ponte-NETO, C. F. (2012). APPLICATIONS OF VORONOI AND DELAUNAY DIAGRAMS IN THE SOLUTION OF THE GEODETIC BOUNDARY VALUE PROBLEM. Boletim De Ciências Geodésicas, 18(3). https://doi.org/10.5380/bcg.v18i3.29182

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