Position resection and intersection: Difference between revisions

Revision as of 21:15, 15 March 2022

Revision as of 21:15, 15 March 2022

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{{see also|Triangulation (surveying)}}

In surveying work,<ref>Glossary of the Mapping Sciences, American Society of Civil Engineers, page 451. [https://books.google.com/books?id=jPVxSDzVRP0C&lpg=PA451&ots=n6eSezdwrn&dq=Cassini's%20resection&pg=PA450#v=onepage&q=resection&f=false]</ref> the most common methods of computing the [[coordinate]]s of a point by (angular) resection are the [[John Collins]] CollinsCollin's "Q" point Method as well as the [[Giovanni Domenico Cassini|Cassini's]] Method and the [[Tienstra formula]], though the first known solution was given by [[Willebrord van Snell aka "Snellius"]] (see [[Snellius–Pothenot problem]]). For the type of precision work involved in surveying, the unmapped point is located by measuring the angles subtended by lines of sight from it to a minimum of three mapped (coordinated) points. In [[geodesy|geodetic]] operations the observations are adjusted for [[spherical excess]] and [[projection variation]]s. Precise angular measurements between lines from the point under ___location using [[theodolite]]s provides more accurate results, with trig beacons erected on high points and hills to enable quick and unambiguous sights to known points.

When planning to perform a resection, the surveyor must first plot the locations of the known points along with the approximate unknown point of observation. If all points, including the unknown point, lie close to a circle that can be placed on all four points, then there is no solution or the high risk of an erroneous solution. This is known as observing on the "danger circle". The poor solution stems from the property of a chord subtending equal angles to any other point on the circle.