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'''Position resection and intersection''' are methods 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.
==Resection versus intersection==
Resection and its related method, ''intersection'', are used in [[surveying]] as well as in general land navigation (including inshore marine navigation using shore-based landmarks). Both methods involve taking [[azimuth]]s or [[bearing (navigation)|bearings]] to two or more objects, then drawing ''lines of position'' along those recorded bearings or azimuths.
When intersecting, lines of position are used to fix the position of an unmapped feature or point by fixing its position relative to two (or more) mapped or known points, the method is known as ''intersection''.<ref>Mooers, pp. 129–132</ref> At each known point (hill, lighthouse, etc.), the navigator measures the bearing to the same unmapped target, drawing a line on the map from each known position to the target. The target is located where the lines intersect on the map. In earlier times, the ''intersection'' method was used by forest agencies and others using specialized [[Osborne Fire Finder|alidades]] to plot the (unknown) ___location of an observed forest fire from two or more mapped (known) locations, such as forest fire observer towers.<ref>Mooers, pp. 130–131</ref>
The reverse of the ''intersection'' technique is appropriately termed ''resection''. Resection simply reverses the intersection process by using ''crossed back bearings'', where the navigator's position is the unknown.<ref>Mooers, p. 132–133</ref> Two or more bearings to mapped, known points are taken; their resultant lines of position drawn from those points to where they intersect will reveal the navigator's ___location.<ref>Mooers, p. 132–133</ref>
==In navigation==
When resecting or
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. 129–134</ref><ref>Kals, pp. 43–49</ref><ref>Touche, pp. 60–67</ref>
==In surveying==
{{
In surveying work, the most common methods of computing the [[coordinate]]s of a point by resection are [[Giovanni Domenico Cassini|Cassini's]] Method 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.▼
In surveying work,<ref>Glossary of the Mapping Sciences, American Society of Civil Engineers, page 451. [https://books.google.com/books?id=jPVxSDzVRP0C&q=resection&pg=PA450]</ref> the most common methods of computing the [[coordinate]]s of a point by '''angular resection''' are the '''Collin's "Q" point method''' (after [[John Collins (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]]).
▲
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==
* [[Hand compass]]
* [[Hansen's problem]]▼
* [[Intersection (aeronautics)]]
* [[Orienteering]]▼
* [[Orienteering compass]]
* [[
* [[Real time locating]]
▲* [[Orienteering]]
▲* [[Hansen's problem]]
▲* [[Position fixing]]
* [[Solving triangles]]
* [[True-range trilateration]]
==Notes==
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==References==
* Mooers Jr., Robert L., ''Finding Your Way In The Outdoors'', Outdoor Life Press (1972), {{ISBN
* Kals, W.S., Practical Navigation, New York: Doubleday & Co. (1972), {{ISBN
* Seidman, David, and Cleveland, Paul, ''The Essential Wilderness Navigator'', Ragged Mountain Press (2001), {{ISBN
==External links==
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[[Category:Navigation]]
[[Category:Trigonometry]]
[[Category:Geopositioning]]
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