Terrain and elevation data

Without elevation, a 3D map is just a 2D map at an angle. Hillshading, terrain exaggeration, and depth cues all come from the same source: a raster grid where every pixel encodes a height value. This chapter covers how that data is stored, decoded, and put to work.

Digital Elevation Models (DEM)

A DEM is a raster where each pixel encodes the elevation of that geographic cell.

Dataset	Resolution	Coverage	Access
SRTM (NASA)	30 m	±60° lat	Free
ASTER	30 m	±83° lat	Free
Copernicus DEM	30 m	Global	Free
Mapbox Terrain-DEM	Variable	Global	API key
USGS 3DEP	1 m (US)	USA	Free

Resolution here means the geographic footprint of one pixel. At 30 m resolution, a pixel covers a 30 m × 30 m cell on the ground, fine enough to see individual buildings, but not individual cars. The vertical accuracy is typically ±5–15 m for 30 m DEMs, meaning the stored elevation value can be 5–15 m off from the true elevation.

Terrain RGB encoding

Raw elevation floats don't fit in PNG pixels. Mapbox's Terrain-DEM tiles encode elevation into RGB channels:

$$\text{elevation (m)} = -10{,}000 + (R \times 6553.6 + G \times 25.6 + B \times 0.1)$$

// Decode a pixel from a Terrain-DEM tile
function decodeElevation(r, g, b) {
  return -10_000 + (r * 6553.6 + g * 25.6 + b * 0.1);
}

// Fetch and decode a terrain tile
async function getElevationAt(lat, lon, zoom = 12) {
  const tx = lonToTileX(lon, zoom), ty = latToTileY(lat, zoom);
  const img = await fetchTileAsImageData(zoom, tx, ty);
  const [r, g, b] = pixelAt(img, lat, lon, zoom, tx, ty);
  return decodeElevation(r, g, b);
}

The encoding spreads a 24-bit value across three 8-bit channels. R is the most significant byte (scaled by 6553.6 = 256² / 10), G the middle byte, B the least significant (scaled by 0.1 = 1/10). The -10,000 offset allows encoding values below sea level down to the deepest ocean trenches (~−9,000 m).

The Terrarium format (Mapzen/AWS) uses a different encoding:

$$\text{elevation (m)} = (R \times 256 + G + B / 256) - 32{,}768$$

Hillshading

Hillshading simulates sunlight on terrain, producing the shadow effect that makes mountains look 3D on a map. The math:

1. Surface normal at each pixel: computed from the elevation gradient
2. Light direction: typically northwest (azimuth 315°, altitude 45°)
3. Intensity: dot product of normal and light direction

$$\text{normal} = \text{normalize}\!\left(-\frac{\partial z}{\partial x},\, -\frac{\partial z}{\partial y},\, 1\right)$$ $$\text{intensity} = \max(0,\; \hat{n} \cdot \hat{L})$$

The northwest light source is a cartographic convention: terrain lit from the northwest matches what humans expect from light coming from the upper-left of a printed page. Lighting from other directions can make valleys look like ridges (the "relief inversion" illusion), because the human visual system expects top-lit surfaces to be convex.

// Fragment shader for hillshading
float dzdx = (elevRight - elevLeft) / (2.0 * cellSize);
float dzdy = (elevBottom - elevTop) / (2.0 * cellSize);

vec3 normal = normalize(vec3(-dzdx, -dzdy, 1.0));
vec3 light  = normalize(vec3(cos(azimuth), sin(azimuth), sin(altitude)));

float intensity = max(0.0, dot(normal, light));
gl_FragColor = vec4(vec3(intensity), 1.0);