Position resection and intersection: Difference between revisions

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'''ResectionPosition resection and intersection''' isare a methodmethods for determining an unknown [[geographic position]] ([[geopositioning|position finding]]) by measuring angles with respect to known positions.
In ''resection'', the one point with unknown coordinates is occupied and sightings are taken to the known points;
in ''intersection'', the two points with known coordinates are occupied and sightings are taken to the unknown point.

Measurements can be made with a [[compass]] and [[topographic map]] (or [[nautical chart]]),<ref>Mooers Jr., Robert L., ''Finding Your Way In The Outdoors'', Outdoor Life Press (1972), {{ISBN|0-943822-41-6}}, pp. 129&ndash;134</ref><ref>Kals, W.S., ''Practical Navigation'', New York: Doubleday & Co. (1972), {{ISBN|0-385-00246-7}}, pp. 43&ndash;49</ref> [[Theodolitetheodolite]] or with a [[total station]] using known points of a [[Geodeticgeodetic network]] or landmarks of a map.

==Resection versus intersection==

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==In navigation==

{{broader|Position fixing}}

When resecting or fixing a position, the geometric strength (angular disparity) of the mapped points affects the precision and accuracy of the outcome. Accuracy increases as the angle between the two position lines approaches 90 degrees.<ref>Seidman, David, and Cleveland, Paul, ''The Essential Wilderness Navigator'', Ragged Mountain Press (2001), {{ISBN|0-07-136110-3}}, p. 100</ref> Magnetic bearings are observed on the ground from the point under ___location to two or more features shown on a map of the area.<ref>Mooers, pp. 129&ndash;134</ref><ref>Kals, pp. 43&ndash;49</ref> Lines of reverse bearings, or ''lines of position'', are then drawn on the map from the known features; two and more lines provide the resection point (the navigator's ___location).<ref>Mooers, pp. 129&ndash;134</ref> When three or more lines of position are utilized, the method is often popularly (though erroneously) referred to as [[triangulation]] (in precise terms, using three or more lines of position is still correctly called ''resection'', as angular [[law of tangents]] ([[cotangent|cot]]) calculations are not performed).<ref>Touche, Fred, ''Wilderness Navigation Handbook'', Fred Touche (2004), {{ISBN|978-0-9732527-0-5}}, {{ISBN|0-9732527-0-7}}, pp. 60&ndash;67</ref> When using a map and compass to perform resection, it is important to allow for the difference between the magnetic bearings observed and grid north (or true north) bearings ([[magnetic north|magnetic declination]]) of the map or chart.<ref>Mooers, p. 133</ref>

Resection continues to be employed in land and inshore navigation today, as it is a simple and quick method requiring only an inexpensive magnetic compass and map/chart.<ref>Mooers, pp. 129&ndash;134</ref><ref>Kals, pp. 43&ndash;49</ref><ref>Touche, pp. 60&ndash;67</ref>

==In surveying==

{{distinguish-redirect|Resection (surveying)|Free stationing}}

{{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&fpg=falsePA450]</ref> the most common methods of computing the [[coordinate]]s of a point by ('''angular) resection''' are the '''Collin's "Q" point method''' (after [[GiovanniJohn DomenicoCollins Cassini(mathematician)|John Collins]]) as well as the '''Cassini's]] Method''' (after [[Giovanni Domenico Cassini]]) and the ''[[Tienstra formula]]'', though the first known solution was given by [[Willebrord 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.

===Vs. free stationing===

{{excerpt|Free stationing#Comparison of methods}}

==See also==

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* [[Hansen's problem]]

* [[Intersection (aeronautics)]]

* [[Orienteering]]

* [[Orienteering compass]]

* [[Position line]]

* [[Orienteering]]

* [[Real time locating]]

* [[Solving triangles]]

* [[True-range trilateration]]

==Notes==