GEOG 486
Cartography and Visualization

Triangulated Irregular Network


A triangulated irregular network (TIN) is a vector-based representation of a surface. Although TINs are commonly used in applications that involve terrain, they can also be used for representing other variables that can be conceptualized as surfaces. TINs are composed of a series of contiguous, non-overlapping triangles that are known as faces. They are built from a series of points using a technique called Delaunay triangulation, in which a network that connects each point to its nearest neighbors is built to form the triangular faces (see Figure, below). TINs have some advantages over raster-based representations of surfaces in that they are much more efficient at storing data because the resolution of the representation can be matched to the scale of variability present in the surface by including more or fewer points. TINs are also used to construct Thiessen polygons, which form the basis for interpolating to areas (proximal interpolation; see Interpolation for more detail).

A series of drawings to illustrate Delaunay triangulation
Figure TINs are constructed from a series of irregularly spaced points that are in some way meaningful for the surface (i.e., peaks, valleys, places where slope changes abruptly, etc.) (upper left) by connecting each point with its nearest neighbors (upper right). Thiessen polygons are created by constructing a perpendicular bisector to each side of each of the Delaunay triangles (bottom).
Credit: Adrienne Gruver

Although TINs by themselves may be difficult to visually interpret (i.e., map readers who look at an unsymbolized TIN may have difficulty forming a mental image of what the terrain looks like, as in the example shown above in FIgure, we can use techniques such as hillshading (see Shaded Relief Terrain Visualization), hypsometric tints, and perspective views (see 3D-visualization) to enhance the reader's perception of the surface's shape.

A map made with a TIN and rotated for a perspective view.
Figure The image above (from the Sierra Nevada mountains on the west shore of Lake Tahoe, California) was created using a hypsometric tint draped over a TIN that was rotated to give a perspective view. Notice the triangular shapes of the terrain features, especially in the mountain peaks (compare this to the same area depicted in Shaded Relief).
Credit: StamenDesign