Implementação e desenvolvimento de uma metodologia aplicada ao cálculo de áreas em Geodésia

Abstract

The calculation of ellipsoidal areas in Geodesy is a not trivial task. By this motive, is common the calculation of plane areas, whose difficulty degree is enough small. For short areas, the simple abstraction of the real format of the Land is sufficient. For bigger areas, however, the Cartography uses the equivalent projections that, for being indirect forms, present a minor reliability in relation the direct numerical methods. More grave still it is the case of Brazil, where the areas send for certification together the Instituto Nacional de Colonização e Reforma Agrária (INCRA), second to the Brazilian Law 10267 of Cadastro Nacional de Imóveis Rurais (CNIR), are calculated as function of the coordinates of the projection system Universal Transverse Mercator (UTM). This projection system is conformal, that is, presenting distortions in relation to the ellipsoidal. The majority of the used commercial programs does not present more efficient forms of calculation. The present work of research is directed in this direction. We searchs a executable program that incorporates fundamental characteristics to the calculation of areas and to programming, generating a product that can present effective results consumer market. A methodology was chosen that considers solution for the calculation of any areas or polygon form that they desires to calculate. The methodology was codified in different forms and was generated an executable in C language. The results had been compared with the same integration carried through in environment of calculator HP42S and in the Spring system through the Albers Equivalent Conical Projection. The research shows that the proposal methodology possess ample potential to computational employment, having presented great efficiency in the calculation of ellipsoidais areas.