Triangulation in three dimensions: Difference between revisions

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In [[vector analysis]], [[triangulation]] is a method of finding points in [[three dimensional]] spaces using distances, angles and vector functions such as [[magnitude]], [[dot product]] and [[cross product]]. Among its uses are in [[surveying]], [[navigation]], and [[astronomy]].

'''Triangulation in three dimensions''' is a method of finding the ___location of a point in [[three dimensional|three dimensions]] based on other known coordinates and distances, it is commonly used in [[surveying]] and [[astronomy]].

This article describes a method for determining the [[coordinates]] of the point where three lines meet, given the [[scalar]] lengths of the lines and the coordinates of their bases. First treat these three lines as if they are the [[Radius|radii]] of three [[sphere]]s of known centers (these known centres being the coordinates of the known end of each line), this method can then be used to calculate the intersection of the three spheres ''if they intersect''. In the event that the three spheres don't intersect, this method obtains the closest solution to the [[axis of symmetry]] between three spheres.

[[Triangulation]] is also used in 2 dimensions to find the ___location of a point on a [[Plane_(geometry)|plane]], this is commonly used in [[navigation]] to plot positions on a map.

===One method to triangulate a ___location in 3D===

This articlemethod describesuses a[[vector methodanalysis]] forto determiningdetermine the [[coordinates]] of the point where three lines meet, given the [[scalar]] lengths of the lines and the coordinates of their bases. First treat these three lines as if they are the [[Radius|radii]] of three [[sphere]]s of known centers (these known centres being the coordinates of the known end of each line), this method can then be used to calculate the intersection of the three spheres ''if they intersect''. In the event that the three spheres don't intersect, this method obtains the closest solution to the [[axis of symmetry]] between three spheres.

== Development ==