FRONTAL GEOMETRIC MODEL OF THE DETERMINATION THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

Abstract

The present work analyses the geometric model of the determination of the inaccessible point of the object. The common issues and essential steps of their resolution are identified. A geometrical model of measurements is defined. This model connects measuring devices and object of research in certain system of co-ordinates with planes of projections using collimating rays and their projections. The problem essence is that a complicated procedure is needed for binding of model of measurements to the Cartesian system of coordinates. This contradicts to a requirement of simplification of a measurement technique, reduction of operations of processing of the obtained results, and decreasing the cost of the experiments. The purpose of the present research is to prove a rational way of a binding of geometrical model of measurements to the Cartesian system of coordinates. The objectives of the paper are: 1. To analyze the possible ways of binding of a two-dimensional geometrical model to the Cartesian system of coordinates using the criterion of minimization of the number of experimental measurements. 2. To define a rational variant of the geometrical model of experimental measurements including an analysis of its merits and drawbacks. Two hypotheses are formulated. Hypothesis 1 is that it is possible to define parameters of an inaccessible point of object using the parameters of four points accessible to measurement. Hypothesis 2 is that. the binding of geometrical model of measurements to the Cartesian system of coordinates defines the procedure of measurements, structure of a technique of processing measured results and, finally, the cost of geodetic works. A rational variant to the geometric model of experimental measurements and processing result is suggested. In the best variant (7) measurements of parameters of projections F₁ and A₁ of points F and A, coordinate measurement y for projection B₁ of point B and coordinate measurement x for projection D₁ of point D are excluded. Thus the coordinate x a directing vector directional ray BD has negative value.

Keywords: a building, a roof, the analysis, directional ray, collimating ray, measurement of coordinates of a point, geometrical model, a way of a binding of model to system of coordinates.