Digital Elevation Models and Heightmaps

A DEM is a grid of heights

A digital elevation model is a raster: a rectangular grid of cells, like the pixels of a photo, where each cell stores one number, the elevation of the ground at that spot. The file knows where on Earth the grid sits and how big each cell is. Common DEM files are GeoTIFFs, which look like images but hold elevations (usually in meters) instead of colors.

Two numbers describe a DEM for printing purposes:

• Resolution (cell size). How much ground one cell covers. A 30 m DEM has one height for every patch roughly 30 m across; anything smaller than that, such as a narrow ridge or a house, is averaged away or missing.
• Extent. How much ground the file covers. Many datasets come in tiles, so a large area can take several files merged together.

Global datasets often state resolution in arc-seconds, a fraction of a degree of latitude or longitude. USGS gives the ground spacing of its own products north to south: 1/3 arc-second is about 10 m and 1 arc-second is about 30 m Maker spec. East to west, a degree of longitude shrinks toward the poles, so cells in geographic coordinates get narrower the farther you are from the equator.

Surface model or bare earth

"DEM" is used two ways, and the difference matters on a print:

• Bare earth (often called a DTM, digital terrain model). Trees and buildings are removed, leaving the ground. USGS names its 3DEP DEM service the Bare Earth DEM service.
• Surface model (DSM). The top of whatever is there. The Copernicus DEM is, in its provider's words, a digital surface model that represents the surface "including buildings, infrastructure and vegetation."

A city or forest printed from a surface model shows blocks and bumps that are not landforms. Check which kind a dataset is before you blame the printer for a lumpy valley floor.

Where the data comes from

Source	Coverage	Resolution	Terms, as the provider states them
USGS 3D Elevation Program (3DEP), through The National Map	1/3 arc-second: the 48 conterminous states, Alaska, Hawaii and US territories. 1 arc-second: conterminous US, Alaska and most of Canada and Mexico. 1 m: growing coverage from lidar.	About 10 m, about 30 m, and 1 m Maker spec	USGS: "All 3DEP products are available, free of charge and without use restrictions." USGS-produced data is "considered to be in the U.S. Public Domain"; USGS asks for credit such as "Credit: U.S. Geological Survey."
NASA SRTM (Shuttle Radar Topography Mission), 1 arc-second global, distributed by USGS EROS	About 80% of Earth's land, between 60° N and 56° S. Flown February 11 to 22, 2000.	1 arc-second, about 30 m Maker spec; tiles above 50° N and below 50° S are sampled at 2 by 1 arc-second	USGS describes it as open distribution through EarthExplorer. The product page states no separate license; read the terms where you download it.
Copernicus DEM, from the TanDEM-X mission (2011 to 2015)	GLO-30 and GLO-90: worldwide. EEA-10: 39 European countries, download limited to certain users.	30 m, 90 m, and 10 m Maker spec	GLO-30 and GLO-90 are under a free license for registered users. Distributing GLO-30 to the general public requires the notice "© DLR e.V. 2010-2014 and © Airbus Defence and Space GmbH 2014-2018 provided under COPERNICUS by the European Union and ESA; all rights reserved." Adapted or modified data takes a different form: "produced using Copernicus WorldDEM-30 © DLR e.V. 2010-2014 and © Airbus Defence and Space GmbH 2014-2018 provided under COPERNICUS by the European Union and ESA; all rights reserved" (WorldDEM-90 for GLO-90). A print made from the data is adapted data, so use the second form. Read the license before you publish anything made from it.

US 3DEP data is downloaded through The National Map; SRTM tiles from EarthExplorer under the Digital Elevation category, in DTED, BIL or GeoTIFF; Copernicus DEM from the Copernicus Data Space Ecosystem after registering. Use the highest resolution that covers your area, then read the next lesson to see whether your printer can show it.

DEM versus heightmap

A heightmap is an ordinary grayscale image where brightness stands for height: dark is low, bright is high. It is what many modeling programs expect. Blender's Displace modifier, for example, moves each vertex of a mesh by the intensity of a texture, after subtracting a Midlevel value, multiplied by a Strength value. Blender treats brightness as 0.0 to 1.0, not 0 to 255.

The differences that cause trouble:

• A heightmap has no units. Pure white means "highest," not "1,520 m." You supply the height range yourself: in Blender, with Midlevel at 0, the Strength setting is the full height of pure white in scene units.
• A heightmap has no location or cell size. You have to set the horizontal size by hand.
• A heightmap has limited steps. An 8-bit grayscale image can hold only a fixed number of levels:

If you convert a DEM to a heightmap, export it at 16 bits where your software allows, and write down the lowest and highest elevations so you can set the height correctly later.

From grid to printable mesh

Whatever software you use, the conversion follows the same steps:

1. Crop the DEM to the area you want.
2. Make a surface. Each cell becomes a vertex at its X and Y position, raised to its elevation. Neighboring vertices are joined into triangles. A 1,000 by 1,000 cell crop is a million vertices and about two million triangles, Formula so many tools let you resample to fewer cells first.
3. Scale it horizontally to the model size, and vertically by the same scale times any exaggeration (see vertical exaggeration and scale).
4. Close it into a solid. The surface alone is a single open sheet, the same problem as a CNC relief file. Drop walls from the edges to a flat bottom below the lowest point, as in printing a relief STL and bases and thickness.
5. Check and slice. Open it in your slicer, check the dimensions, and step through the layer preview.

Kinetic Terrain Coming soon Kinetic Carving's tool for turning elevation data into printable models.