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# Triangulation

Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks.

Delanuy
A process to derive TINs. Delaunay : by definition, 3 points form a Delaunay triangle if and only if the circle which passes through them contains no other point.

Triangulation of a point set is an important method with many applications including finite element simulations.

Delaunay
Delaunay - [3D analysis] A technique for creating a mesh of contiguous, nonoverlapping triangles from a dataset of points.

Delaunay triangulation

3-3. During special surveys when the need to locate the position of a point that cannot be occupied arises, is necessary. This technique places special demands on the recon party.

Triangulation Station
A point on the Earth, the position of which is determined by triangulation. Also called trig point.
Triangulation Station in the Santa Monica Mountains, California.

In the past it was difficult to accurately measure very long distances, but it was possible to accurately measure the angles between points many kilometres apart, limited only by being able to see the distant beacon.

triangulation A method of surveying in the location of an object may be calculated from the known locations of two other objects.

A method of determining the location of an unknown point, as in GPS navigation, by using the laws of plane trigonometry.
TRK
See Track.

Aerial Triangulation - (a.k.a. aerotriangulation) The mathematical process of establishing precise and accurate relationships between the individual photographic film coordinate systems and a defined datum and projection.

A land surveying process, using simple trigonometry, in which the length of a line between two points and the angle or bearing from these two points to a third point is used to calculate the distance to that point.
True North ...

Triangulation - (1) The process of subdividing a 2-D geographic space into triangular-shaped units in digital terrain modeling. (2) The geodetic surveying process that establishes a network of horizontal control points for mapping purposes.

The method does the transformation quite differently. It divide the image space into many small triangles based on your selected control points and generates a formula for each triangle.

Delaunay triangulation and Voronoi diagram example:
Delaunay Triangulation (left pane), Voronoi diagram (center pane), and both (right pane)
EXAMPLE
Commands used with the Spearfish dataset to create the above figure.

With the method, one first needs to know the horizontal distance to the object. If this is not known or cannot be measured directly, it is determined as explained in the article.

Small area triangulation
SAW
Spill analysis workstation; Surface acoustic wave ...

- Method of extending horizontal position on the surface of the Earth by measuring the angles of triangles and the included sides of selected triangles.

The first step in triangulation is to pick three topographic features that you can see and can identify on your map (mountains are ideal). Start with the first feature you have chosen and determine the bearing between you and it, as outlined above.

Brunson Electronic System
BEV
Bundesamt fur Eich- und Vermessungswesen (Austria) ...

Delaunay triangulation p. 153 a network that connects each point in a set of points to its nearest neighbors; topological 'dual' of the Voronoi network. DEM p.

The second application, the Delone , is directly related to our topic. First we should consider that three points determine a plane.

In the 17th century there is the development of surveying equipment and triangulation methods, including the logarithms, theodolite, pendulum clock, and barometric level.

These discrepancies are the differences in coordinate (x and y) values derived by comparing the data being tested with values determined during aero or by an independent survey of higher accuracy. All remaining inputs and processes (e.g.

A GPS based solution might be simpler and more economical than alternative techniques such as radio tower triangulation, leading to lower consumer costs.

The work consists in capturing topographic features in 3D based on photographs in the aero database, according to ...

Surface models are formed using proven and tested triangulation methods and may represent existing topography, design, or a combination thereof.

Another popular use of R is for doing Voronoi diagrams using the R Delaunay and Dirichlet (Voronoi) Tesselation (deldir) Comprehensive R Archive Network (CRAN) package.

Careful 'mission planning' is essential to avoid times when the satellites offer a poor configuration for triangulation or when a reduced number of satellites are visible from the observation site.

This is a high-tech version of (see Figure 2.14), called trilateration. The first satellite locates you somewhere on a sphere (top left of Figure 2.14).

It contains several different interpolation techniques including Inverse Distance, Kriging, Minimum Curvature, Polynomial Regression, Triangulation, Nearest Neighbor, Shepard's Method, Radial Basis Functions, Natural Neighbor, Moving Average, ...

The network itself contains a series of triangles, which is constructed by connected the points within a group of triangles called a Delaunay . There are two separate ways to construct a TIN.

When satellites are spread across the sky far from each other, the triangulation calculations result in precise locations. When satellites are bunched closely together, the location obtained is imprecise. DOP includes specific sources of imprecision: ...