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282:(Voronoi) polygon generation can only be performed on Delaunay conforming triangulations. A constrained Delaunay triangulation can be considered when you need to explicitly define certain edges that are guaranteed not to be modified (that is, split into multiple edges) by the triangulator. Constrained Delaunay triangulations are also useful for minimizing the size of a TIN, since they have fewer nodes and triangles where breaklines are not densified.
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Delaunay. Delaunay conforming triangulations are recommended over constrained triangulations. This is because the resulting TINs are likely to contain fewer long, skinny triangles, which are undesirable for surface analysis. Additionally, natural neighbor interpolation and Thiessen
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that determines which points are most necessary to create an accurate representation of the terrain. Data input is therefore flexible and fewer points need to be stored than in a raster DEM, with regularly distributed points. While a TIN may be considered less suited than a raster DEM for certain
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The TIN model was developed in the early 1970s as a simple way to build a surface from a set of irregularly spaced points. The first triangulated irregular network program for GIS was written by W. Randolph
Franklin, under the direction of David Douglas and Thomas Peucker (Poiker), at Canada's
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The vertices of these triangles are created from field recorded spot elevations through a variety of means including surveying through conventional techniques, Global
Positioning System Real-Time Kinematic (GPS RTK),
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A TIN comprises a triangular network of vertices, known as mass points, with associated
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A variety of different file formats exist for saving TIN information, including
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Representation of a surface as a triangle mesh with elevated vertices
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Franklin, W. R. (1973). Triangulated irregular network program.
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that are arranged in a network of non-overlapping triangles.
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kinds of GIS applications, such as analysis of a surface's
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219:{\displaystyle (x,y,z)}
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