Investigation of the center coordinates of a circle with unknown radius using polar measurements

Abstract

Circular pools or buildings may be encountered in production of maps for making development plans, in the first facility cadaster and on land. Geodetic measurements may be made on at least three different points of the circleshaped pool or building to obtain positions in a coordinate system of measurement points with a geodetic ground-based electronic tachometer after connection to another polygon. It is possible to get a circle from these three points where the coordinates can be calculated, the coordinates of the center of the circle and the radius of the circle with the help of drawing programs (Netcad, Carto CAD, GEOCAD ...). In drawing programs related to cartography, the details of passing the circle from three points, the coordinates of the center of the circle and the radius of the circle cannot be accessed because the details are kept proprietary by software companies. We have been curious about how the coordinates of the center of the circle or the radius of the circle in question are calculated by using the subprograms on a computer. Apart from the information hidden by software companies, two studies which are indirectly close to the subject mentioned in the application have been identified with respect to the solution of the problem on the computer. However, it was found that these studies did not directly illuminate our research topic, so, this issue should be investigated. This study presents theoretical solutions for the topic, makes numerical implementations and provides findings and interpretations.

Automatic Creation of 3D Documentation in CAD/BIM Based on Topology

“…Some CAD systems have a limited set of drawing functions and users have to program the necessary procedures themselves. In [26], an algorithm for finding the center and radius of a circle based on three geodetically oriented points is proposed. The script is stored in the module and is used to automatically draw arcs and circles from given points.…”