Concise Proof of Tienstra’s Formula
Publication: Journal of Surveying Engineering
Volume 135, Issue 4
Abstract
The resection problem consists in finding the location of an observer by measuring the angles subtended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. Unfortunately, all available proofs for this remarkable formula are intricate. This paper shows how, by using barycentric coordinates for the observer in terms of the locations of the stations, a neat and short proof is straightforwardly derived.
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Acknowledgments
This work has been partially supported by the Spanish Ministry of Science and Innovation under Project No. UNSPECIFIEDDPI2007-60858 and by the “Comunitat de Treball dels Pirineus” under Project No. UNSPECIFIED2006ITT-10004.
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Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 135 • Issue 4 • November 2009
Pages: 170 - 172
Copyright
© 2009 ASCE.
History
Received: Mar 4, 2008
Accepted: Nov 25, 2008
Published online: Oct 15, 2009
Published in print: Nov 2009
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