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

Year 2020, , 26 - 32, 01.02.2020

Hüseyin İnce Nuri Erdem

https://doi.org/10.26833/ijeg.580373

Cited By: 1

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.

Keywords

Circle Center Coordinate Calculation, Radius Calculation, Polar Coordinates, Coordinates Calculation, Polar Measurements, Circle Center Coordinate Calculation, Radius Calculation

References

• Allan, A.L., Hollwey, J.R., and Maynes, J.H.B. 1968. Practical Field Surveying and Computations. Heinnemann, London.
• Anderson, J.M. and Mikhail, E.M., 1998. Surveying theory and practice. 7th ed. Boston, MA: Mc Graw Hill.
• Bannister, A., Baker, R., and Raymond, S., 1992. Surveying. John Willey & Sons. Inc., New York, pp. 186–188.
• Bannister, A., Raymond, S. and Baker, R., 1998. Surveying. 7th ed. Harlow, UK: Addison Wesley Longman Limited Edinburg Gate, 81–82.
• Coope, I. D. , 1993. Circle fitting by linear and nonlinear least squares. Journal of Optimization Theory and Applications, 76(2), 381-388.
• Erdem, N., and İnce, H., 2016. The Proposal Of The Building Application For More Benefiting From Solar Light, International Journal of Engineering and Geosciences, 1 (1), 7-14. DOI: 10.26833/ijeg.285215
• İnce, H, Erdem, N., 2019. Positioning Buildings on a Zoning Island to Provide Maximum Shading: A Case Study. International Journal of Engineering and Geosciences, 4 (3), 129-140. DOI: 10.26833/ijeg.525020
• Kåsa, I., 1976. A circle fitting procedure and its error analysis. IEEE Transactions on instrumentation and measurement, (1), 8-14.
• Kavanagh, F. B., 2003. Geomatics. Pearson Education˙Inc. Prentice Hall, Upper Saddle River, NJ pp. 159–160.
• Kavanagh, F. B., and Bird, S.J.G., 2000. Surveying Principles and Applications. Pearson Education ˙Inc. Prentice Hall, Upper Saddle River, NJ
• Kavanagh, F.B., 2009. Surveying principles and application. 8th ed. Columbus: Pearson Education Inc., 525-526.
• Ulvi, A , Toprak, A., 2016. Investigation of ThreeDimensional Modelling Availability Taken Photograph of the Unmanned Aerial Vehicle; Sample of Kanlidivane Church. International Journal of Engineering and Geosciences, 1 (1), 1-7. DOI: 10.26833/ijeg.285216
• Wilfred, S., 2001. Engineering surveying. 5th ed. Oxford, UK: Butterworth Heinemann, 395-397.
• Wolf, P. R., and Ghilani, C. D., 2008. Elementary Surveying an Introduction to Geomatics. 12th Edition, Upper Saddle River, New Jersey: Pearson Prentice-Hall. pp 271-274, 716-717, 720-721