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

, 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 Types of mesh, type of polygon mesh. It comprises a set of triangles (typically in three dimensions) that are connected by their common Edge (geometry), edges or Vertex (geometry), vertices. Many gra ...

), used mainly as Discrete Global Grid 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 Photogrammetry is the science and technology of obtaining reliable information about physical objects and the environment through the process of recording, measuring and interpreting photographic images and patterns of electromagnetic radiant ima ...

, 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 landforms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary sci ...

, TINs are useful for the description and analysis of general horizontal distributions and relationships. Digital TIN

data structures In computer science, a data structure is a data organization and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functi ...

are used in a variety of applications, including

geographic information systems A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database; however, this is not ...

(GIS), and

computer aided design Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...

(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 * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

-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 geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the Position (geometry), position of the Point (geometry), points or other geometric elements on a manifold such as ...

in three dimensions 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 ...

. 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 (), alternatively relief or topographical relief, is the dimension and shape of a given surface of land. In physical geography, terrain is the lay of the land. This is usually expressed in terms of the elevation, slope, and orientati ...

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, Natural satellite, moon, or asteroid. A "global DEM" refer ...

(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

(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 Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

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 (mathematics), line is a number that describes the direction (geometry), direction of the line on a plane (geometry), plane. Often denoted by the letter ''m'', slope is calculated as the ratio of t ...

and aspect, 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 computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles whose circumcircles do not contain any of the points; that is, each circumcircle has its gen ...

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 Canada's

Simon Fraser University Simon Fraser University (SFU) is a Public university, public research university in British Columbia, Canada. It maintains three campuses in Greater Vancouver, respectively located in Burnaby (main campus), Surrey, British Columbia, Surrey, and ...

, in 1973.

File formats

A variety of different file formats exist for saving TIN information, including Esri TIN, along with others such as AquaVeo and ICEM CFD.

References

External links

UBC GeographyPSU Education
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irregular network Geometric data structures Geographic data and information