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Sweephull [21] is a hybrid technique for 2D Delaunay triangulation that uses a radially propagating sweep-hull, and a flipping algorithm. The sweep-hull is created sequentially by iterating a radially-sorted set of 2D points, and connecting triangles to the visible part of the convex hull, which gives a non-overlapping triangulation.
Jump-and-Walk is an algorithm for point location in triangulations (though most of the theoretical analysis were performed in 2D and 3D random Delaunay triangulations). Surprisingly, the algorithm does not need any preprocessing or complex data structures except some simple representation of the triangulation itself.
The Bowyer–Watson algorithm is an incremental algorithm. It works by adding points, one at a time, to a valid Delaunay triangulation of a subset of the desired points. After every insertion, any triangles whose circumcircles contain the new point are deleted, leaving a star-shaped polygonal hole which is then re-triangulated using the new point.
By triangulation, the location of a radio source can be determined by measuring its direction from two or more locations. Radio direction finding is used in radio navigation for ships and aircraft, to locate emergency transmitters for search and rescue , for tracking wildlife, and to locate illegal or interfering transmitters.
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity.
Bowyer–Watson algorithm, an O(n log(n)) to O(n 2) algorithm for generating a Delaunay triangulation in any number of dimensions, can be used in an indirect algorithm for the Voronoi diagram. The Jump Flooding Algorithm can generate approximate Voronoi diagrams in constant time and is suited for use on commodity graphics hardware. [42] [43]
A simpler randomized algorithm with linear expected time is also known. [13] Seidel's decomposition algorithm [10] and Chazelle's triangulation method are discussed in detail in Li & Klette (2011). [14] The time complexity of triangulation of an n-vertex polygon with holes has an Ω(n log n) lower bound, in algebraic computation tree models of ...
Acoustic location is a method of determining the position of an object or sound source by using sound waves. Location can take place in gases (such as the atmosphere), liquids (such as water), and in solids (such as in the earth).