What is "triangulation"

Triangulation \Tri*an`gu*la"tion\, n. [Cf. F. triangulation.] (Surv.) The series or network of triangles into which the face of a country, or any portion of it, is divided in a trigonometrical survey; the operation of measuring the elements necessary to determine the triangles into which the country to be surveyed is supposed to be divided, and thus to fix the positions and distances of the several points connected by them.

1809, from French triangulation, from Medieval Latin triangulationem (mid-12c., nominative triangulatio), noun of action from Latin *triangulare, from triangulum (see triangle).

n. 1 (context uncountable English) A technique in surveying in which distances and directions are estimated from an accurately measured baseline and the principles of trigonometry 2 (context countable English) The network of triangles, so obtained, that are the basis of a map or chart 3 (context uncountable English) In navigation or seismology, a process by which an unknown location is found using three known distances from known locations. 4 (context chess English) A delaying move in which the king moves in a triangular path in order to force the advance of a pawn. 5 (context qualitative research English) The use of three (or more) researchers to interview the same people or to evaluate the same evidence to reduce the impact of individual bias.

1. n. a trigonometric method of determining the position of a fixed point from the angles to it from two fixed points a known distance apart; useful in navigation

2. a method of surveying; the area is divided into triangles and the length of one side and its angles with the other two are measured, then the lengths of the other sides can be calculated

In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.

Specifically in surveying, triangulation per se involves only angle measurements, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration.

Triangulation refers to measurement by using triangles (in surveying, using angles only). Triangulation may also refer to:

In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra ("pyramids" of various shapes and sizes) packed together.

In most instances, the triangles of a triangulation are required to meet edge-to-edge and vertex-to-vertex.

In mathematics, topology generalizes the notion of triangulation in a natural way as follows:

A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h : K → X.

Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories.

In politics, triangulation is the strategy in which a political candidate presents their ideology as being above or between the left and right sides (or "wings") of a traditional (e.g. American or British) democratic political spectrum. It involves adopting for oneself some of the ideas of one's political opponent. The logic behind it is that it both takes credit for the opponent's ideas, and insulates the triangulator from attacks on that particular issue.

In the social sciences, triangle is often used to indicate that two (or more) methods are used in a study in order to check the results of one and the same subject. "The concept of triangulation is borrowed from navigational and land surveying techniques that determine a single point in space with the convergence of measurements taken from two other distinct points." The idea is that one can be more confident with a result if different methods lead to the same result.

Triangulation is a powerful technique that facilitates validation of data through cross verification from two or more sources. In particular, it refers to the application and combination of several research methods in the study of the same phenomenon.

• It can be used in both quantitative (validation) and qualitative (inquiry) studies.
• It is a method-appropriate strategy of founding the credibility of qualitative analyses.
• It becomes an alternative to traditional criteria like reliability and validity.
• It is the preferred line in the social sciences.

By combining multiple observers, theories, methods, and empirical materials, researchers can hope to overcome the weakness or intrinsic biases and the problems that come from single method, single-observer and single-theory studies.

Triangulation is a tactic used in chess to put one's opponent in zugzwang. That is, it is a tactic, the goal of which is to return to the initial position in such a way that one's opponent is then forced to move first in the position, when it is a disadvantage for that player to move, e.g. he must abandon a blockade and let the other player penetrate his position. Triangulation is also called losing a tempo or losing a move.

Triangulation occurs most commonly in endgames with only kings and pawns when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares. Thus, if one king triangulates by using three moves to return to the original square and the opposing king cannot do the same, he has lost a crucial tempo and reached the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames .

Triangulation is a situation in which one family member will not communicate directly with another family member, but will communicate with a third family member, which can lead to the third family member becoming part of the triangle. The concept originated in the study of dysfunctional family systems, but can describe behaviors in other systems as well, including work.

Triangulation can also be a form of " splitting" in which one person plays the third family member against one that he or she is upset about. This is playing the two people against each other, but usually the person doing the splitting will also engage in character assassination, only with both parties.

In computer vision triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrices. Triangulation is sometimes also referred to as reconstruction.

The triangulation problem is in theory trivial. Since each point in an image corresponds to a line in 3D space, all points on the line are projected to the point in the image. If a pair of corresponding points in two, or more images, can be found it must be the case that they are the projection of a common 3D point x. The set of lines generated by the image points must intersect at x and the algebraic formulation of the coordinates of x can be computed in a variety of ways, as is presented below.

In practice, however, the coordinates of image points cannot be measured with arbitrary accuracy. Instead, various types of noise, such as geometric noise from lens distortion or interest point detection error, lead to inaccuracies in the measured image coordinates. As a consequence, the lines generated by the corresponding image points do not always intersect in 3D space. The problem, then, is to find a 3D point which optimally fits the measured image points. In the literature there are multiple proposals for how to define optimality and how to find the optimal 3D point. Since they are based on different optimality criteria, the various methods produce different estimates of the 3D point x when noise is involved.

In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side and two known angles.

Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of Willebrord Snell in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed points, a problem called resectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s.