Simple Solution to the Three Point Resection Problem
Publication: Journal of Surveying Engineering
Volume 139, Issue 3
Abstract
The paper presents a simple method of finding the solution to the planar three point resection problem. The main concept leading to the solution is based on an idea of two intersecting circles (which is not new in the literature). The points of intersection of two circles (of which one solves the problem) are obtained by solving a quadratic equation. As a result of the fact that one root of the quadratic equation is known, Vieta’s formula is applied to find the other. When one of the measured angles is equal to 0 or 180°, the problem reduces to the intersection of a straight line and a circle. This also leads to a quadratic equation which is solved by Vieta’s formula. The derivation of the method is very simple (purely analytic) and free from any intermediate parameters, for example, angles, distances, or azimuths.
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Acknowledgments
The paper is the result of research on geospatial methods carried out within the statutory research no. 11.11.150.006 in the Department of Geomatics, AGH University of Science and Technology, Krakow, Poland.
References
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Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 139 • Issue 3 • August 2013
Pages: 120 - 125
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 24, 2012
Accepted: Jan 30, 2013
Published online: Feb 1, 2013
Published in print: Aug 1, 2013
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