| dc.description.abstract | For the transformation of the local coordinates in the global coordinates, and
contrariwise, it can be employed the traditional method of Puissant or the 3D
modelling. In this paper, both approaches were applied in the geodetic transport of
the coordinates of a topographic polygonal, framed in the geodetic base lines AB and
CD, considering the point B as the origin of the systems. The geodetic coordinates of
supporting points (A, B, C and D) which were determined with GPS (Glogal
Positioning System) and the observations which were obtained in topographic
search. From the local coordinates (v, u, w) the polygon was calculated: the
topographic components (Δv, Δu, Δw) and 3D modeling was transformed in geodesic
components (ΔX, ΔY, ΔZ); the geodetic cartesian coordenates (X, Y, Z) which were
subsequently transformed in geodetic coordenates (φ, λ, h). In the solution of the
Geodetic Direct Problem (PGD) were used the topographic observations, corrected
end reduced to the ellipsoid. The results comparison obtained by applying the two
methodologies, suggested here, shows a standard deviation (σ) of ± 7,31x10-4 for the
latitude (φ) and a standard deviation (σ) of ± 3,71x10-4 for the longitude (λ). This
result in an uncertainty of ± 0,080 meters, in 95% significance level between the
average position of a point determined by the 3D modeling and PGD. The change in
the origin of the system did not cause a relative error above the limit established by
the NBR 13.133 (Brasilian Norm 13.133), at the distances between the extreme
points of the polygon. These results allow, in this case, the replacement of the PGD
methodology for the 3D modeling and choose any point in the spatial database for
origin of the systems. The 3D function model performs the conversion of the
topographic coordindates in geodetic coordinates with equivalent accuracy to the
traditional method of Puissant, with fewer calculations and enables reverse process.
This methodology can be used for georeferencing and mapping work, rural and
urban cadastre, cartographic updating, among others, in which uncertainty found can
be accepted. The data suggest more evaluations of the functional model and the
introduction of the stochastic model, for evaluating the quality of data and system.
Keywords: Geodesy. Topography. Direct Geodetic Problem. 3D Modelling | |
