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Within this triangle, the distance between the sensors is the base b and must be known. By determining the angles between the projection rays of the sensors and the basis, the intersection point, and thus the 3D coordinate, is calculated from the triangular relations.
Triangulation of Kodiak Island in Alaska in 1929. 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 by using trigonometry, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as ...
In Japan, there are five classes of triangulation stations (三角点, sankakuten, lit. 'three corner points'): Class 1 (一等三角点, ittō sankakuten) They are installed approximately every 40 kilometres (25 mi), with smaller ones (as necessary) about every 25 kilometres (16 mi). [3] There are about 1000 throughout Japan.
There is no accepted or widely-used general term for what is termed true-range multilateration here . That name is selected because it: (a) is an accurate description and partially familiar terminology (multilateration is often used in this context); (b) avoids specifying the number of ranges involved (as does, e.g., range-range; (c) avoids implying an application (as do, e.g., DME/DME ...
[2] [3] Moreover, different fields of endeavor may employ different terms. In geometry , trilateration is defined as the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles , spheres or triangles .
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 packed together.
A triangulation of a set of points in the Euclidean space is a simplicial complex that covers the convex hull of , and whose vertices belong to . [1] In the plane (when P {\displaystyle {\mathcal {P}}} is a set of points in R 2 {\displaystyle \mathbb {R} ^{2}} ), triangulations are made up of triangles, together with their edges and vertices.
To triangulate an implicit surface (defined by one or more equations) is more difficult. There exist essentially two methods. There exist essentially two methods. One method divides the 3D region of consideration into cubes and determines the intersections of the surface with the edges of the cubes in order to get polygons on the surface, which ...