computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

, a triangulated irregular network (TIN) is a representation of a continuous

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

consisting entirely of triangular facets (a

triangle mesh In computer graphics, a triangle mesh is a type of polygon mesh. It comprises a set of triangles (typically in three dimensions) that are connected by their common edges or vertices. Many graphics software packages and hardware devices can ...

), used mainly as

Discrete Global Grid A discrete global grid (DGG) is a mosaic that covers the entire Earth's surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. In a usual grid-modeling strate ...

in primary elevation modeling. 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), photogrammetry, or some other means. Associated with three-dimensional data and

topography Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary sc ...

, TINs are useful for the description and analysis of general horizontal distributions and relationships. Digital TIN data structures are used in a variety of applications, including geographic information systems (GIS), and computer aided design (CAD) for the visual representation of a topographical surface. A TIN is a

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

-based representation of the physical land surface or sea bottom, made up of irregularly distributed nodes and lines with three-dimensional coordinates that are arranged in a network of non-overlapping triangles. A TIN comprises a triangular network of vertices, known as mass points, with associated coordinates in three

dimensions In physics and mathematics, the dimension of a mathematical 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 (1D) because only one coordin ...

connected by edges to form a triangular

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety o ...

. 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 used to represent

terrain Terrain or relief (also topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The Latin wo ...

is often called a

digital elevation model A digital elevation model (DEM) or digital surface model (DSM) is a 3D computer graphics representation of elevation data to represent terrain or overlaying objects, commonly of a planet, moon, or asteroid. A "global DEM" refers to a discrete g ...

(DEM), which can be further used to produce digital surface models (DSM) or digital terrain models (DTM). An advantage of using a TIN over a

rasterized In computer graphics, rasterisation (British English) or rasterization (American English) is the task of taking an image described in a vector graphics format (shapes) and converting it into a raster image (a series of pixels, dots or lines, whic ...

(DEM) in mapping and analysis is that the points of a TIN are distributed variably based on an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

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 kinds of GIS applications, such as analysis of a surface's

slope In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is use ...

and

aspect Aspect or Aspects may refer to: Entertainment * ''Aspect magazine'', a biannual DVD magazine showcasing new media art * Aspect Co., a Japanese video game company * Aspects (band), a hip hop group from Bristol, England * ''Aspects'' (Benny Carter ...

, it is often used in CAD to create contour lines. A DTM and DSM can be formed from a DEM. A DEM can be interpolated from a TIN. TIN are based on a

Delaunay triangulation In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle o ...

or constrained 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 (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. 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

Simon Fraser University Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located ...

in 1973.

File formats

A variety of different file formats exist for saving TIN information, including

Esri TIN The Esri TIN format is a popular yet proprietary geospatial vector data format for geographic information system (GIS) software for storing elevation data as a triangulated irregular network. It is developed and regulated by Esri, US. The Esri ...

, along with others such as AquaVeo and ICEM CFD.

References

External links

UBC GeographyPSU Education
{{DEFAULTSORT:Triangulated Irregular Network Triangulation (geometry) Geometric data structures Geographic data and information