Triangulated irregular network
Encyclopedia
A triangulated irregular network (TIN) is a digital data structure
used in a geographic information system
(GIS) for the representation of a surface
. A TIN is a vector
-based representation of the physical land surface or sea bottom, made up of irregularly distributed nodes
and lines with three-dimensional
coordinates (x, y, and z) that are arranged in a network of nonoverlapping triangles. TINs are often derived from the elevation data of a rasterized
digital elevation model
(DEM). An advantage of using a TIN over a raster DEM in mapping and analysis is that the points of a TIN are distributed variably based on an algorithm
that determines which points are most necessary to 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. A TIN may be less suited than a raster DEM for certain kinds of GIS applications, such as analysis of a surface's slope
and aspect
.
A TIN comprises a triangular network of vertices, known as mass points, with associated coordinates in three dimensions
connected by edges to form a triangular tessellation
. Three-dimensional visualizations are readily created by rendering of the triangular facets. In regions where there is little variation in surface height, the points may be widely spaced whereas in areas of more intense variation in height the point density is increased.
A TIN is typically based on a Delaunay triangulation
but its utility will be limited by the selection of input data points: well-chosen points will be located so as to capture significant changes in surface form, such as topographical summits, breaks of slope, ridges, valley floors, pits and cols.
Although usually associated with 3-dimensional data (x, y, and z) and topography, TINs are also useful for the description and analysis of general horizontal (x and y) distributions and relationships.
The first triangulated irregular network program for GIS was written by Randolph Franklin at Simon Fraser University
in 1973.
Data structure
In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks...
used in a geographic information system
Geographic Information System
A geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...
(GIS) for the representation of a surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
. A TIN is a vector
Array
In computer science, an array data structure or simply array is a data structure consisting of a collection of elements , each identified by at least one index...
-based representation of the physical land surface or sea bottom, made up of irregularly distributed nodes
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
and lines with three-dimensional
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
coordinates (x, y, and z) that are arranged in a network of nonoverlapping triangles. TINs are often derived from the elevation data of a rasterized
Rasterisation
Rasterisation is the task of taking an image described in a vector graphics format and converting it into a raster image for output on a video display or printer, or for storage in a bitmap file format....
digital elevation model
Digital elevation model
A digital elevation model is a digital model or 3-D representation of a terrain's surface — commonly for a planet , moon, or asteroid — created from terrain elevation data....
(DEM). An advantage of using a TIN over a raster DEM in mapping and analysis is that the points of a TIN are distributed variably based on an algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
that determines which points are most necessary to 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. A TIN may be less suited than a raster DEM for certain kinds of GIS applications, such as analysis of a surface's slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
and aspect
Aspect (geography)
In physical geography, aspect generally refers to the horizontal direction to which a mountain slope faces. For example, a slope on the eastern edge of the Rockies toward the Great Plains is described as having an easterly aspect...
.
A TIN comprises a triangular network of vertices, known as mass points, with associated coordinates in three dimensions
Dimensions
Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....
connected by edges to form a triangular tessellation
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
. Three-dimensional visualizations are readily created by rendering of the triangular facets. In regions where there is little variation in surface height, the points may be widely spaced whereas in areas of more intense variation in height the point density is increased.
A TIN is typically based on a Delaunay triangulation
Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT such that no point in P is inside the circumcircle of any triangle in DT. Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the...
but its utility will be limited by the selection of input data points: well-chosen points will be located so as to capture significant changes in surface form, such as topographical summits, breaks of slope, ridges, valley floors, pits and cols.
Although usually associated with 3-dimensional data (x, y, and z) and topography, TINs are also useful for the description and analysis of general horizontal (x and y) distributions and relationships.
The first triangulated irregular network program for GIS was written by Randolph Franklin at Simon Fraser University
Simon Fraser University
Simon Fraser University is a Canadian public research university in British Columbia with its main campus on Burnaby Mountain in Burnaby, and satellite campuses in Vancouver and Surrey. The main campus in Burnaby, located from downtown Vancouver, was established in 1965 and has more than 34,000...
in 1973.