Aplicação da transformação ortogonal no georreferenciamento com divisão de área

Abstract

The Geodesy methods and equipments progress brings with himself the growing need on geodetic surveys. Thereby, it is possible to make compatible any surveys with no extension boundary like from plane models and with no points overlap. These surveys are usually from geodetic satellites for that specific purpose. However, there are cases under precision restriction by nature of these systems, as well as physical conditions lack and equipments deficiency disables such operations. Thus, it becomes necessary to take place surveys from a topographical origin to a geocentric origin. To other cases, it is not enough just to know the geodetic coordinates but it is necessary to know its equivalent ones in the topographical plan, mostly to section and calculus of areas besides point locations. In these cases a solution of great use is the transformation of the geocentric coordinates to the UTM Projection plane cartographic coordinates, usually being ignored the deformations. Therefore it is a mistaken solution. Among the appropriate solutions to transform coordinates between surfaces from a topographical origin to a geocentric origin it is the Orthogonal Transformation. This method is more concise than the traditional Puissant´s methodology and to make possible the conversion of topographical coordinateds to geocentric coordinates and vice-versa. In this work the precision of Orthogonal Transformation method was compared initially with the Puissant´s method. Also were compared the differences among areas calculated from the UTM cartographic plan coordinates and topographical coordinates, besides having established the position discrepancy among boundary points calculated in a certain plan and implanted in other one without the true conversions. The results shows that the Orthogonal Transformation method precision is equivalent to Puissant´s method for observed ranges. It was possible to note that the values to areas calculated from coordinates related to models or different surfaces presents discrepancy. The areas section and estimation from the UTM cartographic projection plane coordinates, even with scale factor and elevation corrections, has been different to the area from the local topographical plan, although it was similar when under corrections. Points from section of geodetic areas can not to have implant in the topographical plane under use of UTM cartographic projection plane coordinates due to the position difference between it and the topographical coordinates. The more appropriate solution, due to good precision and easiness to section and estimate geodetic areas from geocentric coordinates, is the change to topographical ones using the Orthogonal Transformation. The Orthogonal Transformation of Coordinates is a practice and quick solution to make geodetic points from topographical surveys as well as to plot geodetic points in the topographical plan, and it is possible to implement it in the Electronic Total Stations in a easy way.