A DEM is a Digital Elevation Model. A DEM is a digital file consisting of terrain elevations for ground positions at regularly spaced horizontal intervals. DEM's are in the raster format, and cartographic data is recorded, stored, and processed in a cell or pixel. DEM's are normally built from remote sensing, but they can also be made from land surveying. They may be used to generate three-dimensional images or colorized to bring out relief. The image above is a DEM of New Mexico. It shows elevation by colors and shading.
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