## Digital Elevation Models (DEMS)

A digital elevation model (DEM) or sometimes referred to as a digital terrain model (DTM) is a quantitative representation of the topography of the Earth. DEMs are used as a source of elevation (and to create other digital terrain models) for many different purposes

## 3D Perspective Views

Most imagery (and/or spatial data) that we view in geomatics is typically viewed vertically downwards from the source toward the map or image. This typical aerial view that we are accustomed to using, allows an abundant amount of information to be represented spatially within a two dimensional cartesian representation. However, occasionally it is useful for us to change our focus from the default traditional view and use a more complex three dimensional visualization view of the data.

This type of terrain model is commonly referred to as a perspective view and often reveals additional information by allowing us to observe the same data obliquely.. In order to do this each location of the image needs to be transformed from the traditional 2-D to a 3-D projection coordinate system.

A perspective view is not really a new tool as it has been around for centuries, but it has become a popular component of most geomatics projects. “A Perspective is a rational demonstration by which experience confirms that the images of all things are transmitted to the eye by pyramidal lines. Those bodies of equal size will make greater or lesser angles in their pyramids according to the different distances between the one and the other. By a pyramid of lines, means those which depart from the superficial edges of bodies and converge over a distance to be drawn together in a single point” (Leonardo da Vinci)¹.

Data integration and overlays are very common with perspective views because it allows traditional flat images to become new products by incorporating an elevation component and providing a new look at the same data. It is also probably used more so for visual appeal then as another method of extracting data.

Sample image on the right is a 3D perspective view of Cape George, Nova Scotia (just north of Antigonish), created with LandSat imagery drapped over a digital elevation model (DEM).

[* quote 1 is from – O’Connor and Robertson (2003) Mathematics and art – perspective www-groups.dcs.st-and.ac.uk/~history/HistTopics/Art.htmlJanuary]

3D Perspective View Samples

## Digital Terrain Modeling – Shaded Relief Models

A shaded relief model uses different color shades according to the varying levels of elevation and azimuth to create an enhanced simulated terrain. The shading is done with the assumption of a defined light source at a fixed location, shone across the surface. The user-specified light source will then determine the positions of shadows and highlighted slopes making ones facing light source appear bright and those facing away appear dark. By default shaded relief models are created with a grey scale ramp that represent the surface reflectance from the light source at any altitude and any azimuth however adding color to it can add an extra chromo stereoscopic component to it.
Assuming that a straight line is drawn connecting the user defined point source to the top left pixel of the image, the azimuth angle is the aspect of this line in degrees clockwise from north; the elevation angle is the elevation of the line in degrees from the horizontal.

The shaded grey level for each cell is the result of a calculation from the cosine of the angle between the normal vector to the surface (i.e. slope andaspect) and the direction of illumination. All surfaces not illuminated by the light source such as a slope of 90 degrees will be set to 0. An elevation exaggeration is sometimes added to help enhance the features of a fairly homogeneous surface.

In the example shown to the right, a raster aspect map of Lismore, Nova Scotia was derived from a digital elevation model (DEM) calculated with an azimuth angle of 315 degrees and an elevation angle of 45 degrees.