# Chapter 8. Terrain and elevation models

In this chapter we show the organization of the vertical data – used for geo-reference – into spatial models. We don’t aim to discuss the subject in depth of the extent literature of the terrain and elevation models. However, it is necessary to introduce the definition and model types at a level that is a good overview for the reader involved in GIS and especially in the geo-reference and the ortho-rectification of aerial images (Chapter 9).

## 8.1 Definition and types of the terrain models

In general, we call elevation model any procedure that is able to estimate the characteristic elevation of a surface at a point, defined by its horizontal coordinates. The quality of the model depends on the accuracy of this estimation. In this definition the surface can be any three-dimensional layer, however, in the GIS technology we usually model the terrain elevation, the relief, which is also displayed by the contour lines in the topographic maps. In this case, our model is called terrain model.

Fig. 46. The Voronoi diagram (red): connects the centers of the circumcircles of the original triangles (Wikipedia).

The terrain model can be of two kinds: vector or raster-based. The vector model expresses the irregular spatiality of the data sampling. It is based on elevation data at an irregular horizontal point set, on coordinate triplets of 3D spatial points. The elevation can be estimated between these points by some interpolation method. The easiest and most used way to do it is the application of the triangulated irregular n network (TIN). We lay an ideal triangulation net to our point set. In the practice, ’ideal’ means that the sum of all triangle edges should be minimum at the whole network (Fig. 46). This way, we can arrange one and just one triangle to any point of the interpretation range on the base plane, or the point itself is an original network point. Using the planes (or any more complex but unambiguous function) fit to the different triangles, we can estimate any for any horizontal point on the interpretation range.

For our discussed practice of the geo-reference, the rectification of scanned maps and datasets requires the raster data model. This makes necessary the application of the raster variants of the elevation and terrain models. It is quite easy to estimate the elevation values at the points of any selected raster net, using the above mentioned TIN-based models. For shorter software runtime and the data-level compatibility, these raster grids are usually not realized by dynamic queries. It is easier just once to fill a raster file with data, by the TIN→GRID conversion. According to the direction of the conversion, the information content of the resulted elevation or terrain model is less than the one of the original triangulated network: the original network cannot be reconstructed from the grid data. In the followings, we discuss these grid-based, raster models.