Triangulated Irregular Networks (TIN)

Advantages and Disadvantages

One of the main advantages of a TIN is that it can be used to approximate a terrain surface to a required accuracy with fewer polygons than a DEM. This is because the sample resolution can be varied across the terrain. For example, more samples can be used in areas of higher gradient, and, conversely, fewer samples are needed for relatively flat areas. Consequently, in practice, a TIN representation is often more compact than a DEM. For example, in the above figure, the DEM contains a regular grid of 65 × 65 height values, whereas the TIN representation contains 512 mass points. If we assume 4 bytes per coordinate, the DEM requires 16.5 KB to store (65 × 65 × 4/1024), whereas the TIN requires only 6.0 KB (512 × 3 × 4/1024). Therefore, in this example, the vertices for the TIN require just over a third of the storage space of the DEM vertices. In practice, there will be some overhead for the TIN structure, depending upon the particular data structure chosen, though this will be relatively small.

Further benefits of TINs include the range of geographic features that they can model, including topographical summits, valleys, saddle points, pits, and cols; linear features such as ridges and streams; and features that require multiple z-coordinates for the same (x, y) coordinate, such as overhangs, tunnels, and caves. TINs can also be sculpted to accommodate man-made features on the terrain, such as roads and buildings.

One of the disadvantages of the TIN representation over a regular grid is that it is less convenient for various types of terrain analysis, such as calculating elevation at an arbitrary (x, y) point. For complex GIS applications that manage large amounts of terrain data, a TIN model can also be more cumbersome for operations such as the paging of parts of the terrain model into and out of memory, performing collision detection, or deforming the terrain model in response to user input.

Creating a TIN

A common technique for creating a TIN terrain model is to produce a sampling of mass points over the surface based upon a specified vertical error tolerance, thus producing more mass points around areas of high gradient. These mass points are then typically connected together to form a triangle mesh using a mathematical process called Delaunay triangulation. This particular triangulation scheme guarantees that a circle drawn through the three mass points of a triangle will contain no other mass points. It is a popular method for creating TINs because it exhibits the following desirable

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