Optimized Determination of 3d Coordinates in the Survey of Inaccessible Points of Buildings - Example of Application Implemented in Free Software

Abstract

The forward intersection method is already widely used in the geodetic survey of coordinates of inaccessible points, especially when only angle measurements are available, in this case, also called the triangulation method. However, the mathematical solution of the 3D forward intersection with the analytical definition of spatial lines, resolved by the Minimum Distances Method, is still not widespread in the academic and professional environment. This mathematical modeling determines the 3D coordinates of a point located in the middle of the minimum distance between two or more spatial lines, which spatially "intersect" towards the observation point. This solution is more accurate than others presented in the literature because it simultaneously solves the problem of 3D determination of a point by the method of least squares, in addition to providing an estimate of the coordinate precision, which are inherent to the adjustment. This work, therefore, has the objective of explaining the Minimum Distances Method for the spatial intersection of targeted measurements with a Total Station from two or more known observation points for the 3D determination of inaccessible points located in corners of buildings. For the analysis of the method, a Python tool was developed for QGIS that calculates the 3D coordinates and generates the adjustment processing report, being applied with real observations of the Geodetic survey of the SUDENE building, in Recife-PE. The methodology developed in this work proved to be suitable for measurements of large structures, achieving spherical precision better than ±1.0 cm, following the Brazilian standards for urban cadastre.