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Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Also, this formula is the tape sag correction to be added to the measured distance, so the negative sign in front can be removed and the tape sag correction can be made instead by subtracting the absolute value as is done in the preceding section.
In surveying, free stationing (also known as resection) is a method of determining a location of one unknown point in relation to known points. [1] There is a zero point of reference called a total station. The instrument can be freely positioned so that all survey points are at a suitable sight from the instrument.
In surveying work, [16] the most common methods of computing the coordinates of a point by angular resection are the Collin's "Q" point method (after 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 ...
A surveyor using a total station A student using a theodolite in field. Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them.
Over the next century this work was extended most notably by the Cassini family: between 1683 and 1718 Jean-Dominique Cassini and his son Jacques Cassini surveyed the whole of the Paris meridian from Dunkirk to Perpignan; and between 1733 and 1740 Jacques and his son César Cassini undertook the first triangulation of the whole country ...
J. M. Tienstra [] (1895-1951) was a professor of the Delft university of Technology where he taught the use of barycentric coordinates in solving the resection problem. It seems most probable that his name became attached to the procedure for this reason, though when, and by whom, the formula was first proposed is unknown.
Wild brand subtense bar. Another device used in tacheometry to measure distance between the measuring station and a desired point is the subtense bar. [2] This is a rigid rod, usually of a material insensitive to change in temperature such as invar, of fixed length (typically 2 metres (6.6 ft)).