Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 008, 13 pages      arXiv:1410.7630      https://doi.org/10.3842/SIGMA.2015.008

Ambiguities in a Problem in Planar Geodesy

Josef Schicho and Matteo Gallet
Research Institute for Symbolic Computation, Johannes Kepler University, Altenberger Strasse 69, 4040 Linz, Austria

Received October 29, 2014, in final form January 16, 2015; Published online January 27, 2015

Abstract
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative position when the viewing angles between target points seen from measure points are known. In particular, we determine all situations in which there is more than one solution.

Key words: surveying; structure and motion problem; Gale duality.

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