Visualization Modes Description

Grouped as they are in the panel — Terrain Analysis (surface derivatives + neighborhood statistics), Relief Visualization (multi-scale relief / visibility) and Light (normal-based shading). Most are supported by — and inspired by — gdaldem and the RVT (Relief Visualization Toolbox) QGIS plugin.

Terrain Analysis

Surface derivatives

• Slope: magnitude of the gradient
• Aspect: direction of the gradient
• Curvature: rate of slope change — Profile, Plan, Mean/Combined, Gaussian (Det Hessian), or Casorati
  • Profile (Flow Acceleration): rate of slope change along the steepest-descent direction, affects flow acceleration
  • Plan (Convergence/Divergence): rate of aspect change across contours, affects flow convergence/divergence — equivalent to the divergence of the normalized gradient field, div(∇z/|∇z|)
  • Mean/Combined: discrete Laplacian (∇²z) — mean curvature H = (κ₁+κ₂)/2, general surface bending that doesn't separate flow direction from contour direction
  • Gaussian Curvature (Det Hessian): determinant of the Hessian (fxx·fyy − fxy²) — Gaussian curvature K = κ₁·κ₂, a blob/saddle detector, positive at bowl/dome-shaped extrema and negative at saddle points
  • Casorati: κ = √((κ₁²+κ₂²)/2) — RMS of the two principal curvatures (Koch, 1993); always ≥ 0, measures how curved the surface is regardless of shape (dome, ridge, saddle, valley and bowl all read the same), zero only on flat ground

Neighborhood statistics

• TRI (Terrain Ruggedness Index): mean elevation difference to neighbors
• TPI (Topographic Position Index): elevation relative to neighborhood mean
• Roughness: max−min elevation in a neighborhood
• Shape Index: SI = (2/π)·atan2(κ₁+κ₂, κ₁−κ₂) — Koenderink & van Doorn (1992); scale-free and bounded to [−1, 1] regardless of curvature magnitude: +1 dome/peak, +0.5 ridge, 0 saddle, −0.5 valley, −1 pit/bowl

Principal Components (PCA)

A local 2D PCA of the window's gradient vectors, via the Förstner/Harris structure tensor (box-averaged Ixx/Iyy/Ixy over a 5×5 window) — the same tensor behind all three modes below.

• Blobness: det(J)/trace(J) — large where the gradient direction varies in every direction (peaks, pits, saddles, knolls), near zero on a uniform slope or straight ridge/valley; conflates shape with steepness
• Eigenvalue Ratio: λmin/λmax of the structure tensor (0–100%) — shape only, independent of steepness: 0% is a coherent linear feature (slope/ridge/valley), 100% is an isotropic blob (peak/pit/saddle)
• Dominant Orientation: axis (0–180°) of the tensor's dominant eigenvector — which way a linear feature (ridge, valley, fault line) runs; most meaningful where Eigenvalue Ratio is low

Relief Visualization

• LRM (Local Relief Model): raw elevation minus a low-pass-filtered version, isolating small features from large-scale topography — the low-pass mean is bilinearly interpolated from a lower-resolution tile further up the pyramid tree. Conceptually close to HAG (Height Above Ground), but with the "ground" being that smoothed local trend surface rather than a classified bare-earth model.
• SVF (Sky-View Factor): the fraction of the sky hemisphere visible from a point (0–1), estimated from horizon angles sampled in many directions — darkens enclosed valleys and pits, brightens exposed ridges and summits, independent of any light direction
• Openness (Positive / Negative): the mean zenith (positive) or nadir (negative) horizon angle over a search radius — positive openness emphasizes convex, exposed features (ridges, crests), negative openness emphasizes concave ones (channels, pits); a diffuse, illumination-free relief
• Local Dominance: how much a location visually towers over its surroundings — the mean angular drop to the terrain around it across a radius range, highlighting locally elevated features such as mounds, plateaus and terraces

Light

• Matcap (material capture): looks up a surface colour from a pre-lit sphere image using the surface normal as UV coordinates — a stylized, art-directable shading that doesn't depend on a directional light
• Phong: real ambient + diffuse + specular shading from a compass-fixed (or camera-relative) light direction — a physically-plausible 3D-relief render; the "Live" renderer is a per-fragment GPU shader draped on the terrain mesh, "Legacy" the raster-tile pipeline (still the globe-capable one) — see the Lighting Effects panel
• Shadows: hard cast shadows — darkens a pixel wherever nearby terrain rises above the sun's own angle in the sky, blocking direct light (a single-ray horizon-angle march toward the sun's azimuth); shares Phong/Hillshade's light direction, no separate control of its own beyond opacity and search radius

Neighborhood usually refers to a 3×3 kernel centered on the pixel.

Terrain Encoding Functions

TerrainRGB: height = -10000 + ((R * 256 * 256 + G * 256 + B) * 0.1)

Terrarium: height = (R * 256 + G + B / 256) - 32768