Terrain-Aware Exploitation Geometry on Real Elevation Data

Reading the scene

The cardinal point is the notional facility. The gold raster is the ground from which an observer of the chosen eye height sees the facility target; the darker raster is terrain-masked. Each coloured outline is one modality's envelope, the farthest admitted distance at every bearing, and the thick cardinal outline is the MTEBB union. The dashed circles are the statutory and shadow buffers for comparison.

Pale routes are least-cost vehicle paths from the facility to eight perimeter access points plus a perimeter ring. Gold routes are the three edges that carry the most shortest paths; the selected one is cardinal, and the purple raster marks terrain that overlooks it with an elevation advantage. Click anywhere to draw a sight line and its profile, or switch to UAS mode to fly an approach: cardinal segments are visible to the facility sensor, purple segments are masked, and the spokes show where the operator's control link closes.

Specification

Model notes

Line of sight and viewshed

Straight sight lines against terrain lifted by the earth-curvature term d₁d₂/2kR, sampled at the grid cell. Clearance is compared with ±2σ of the terrain model, so the map shows where the data cannot decide.

RF

Free-space path loss with single knife-edge diffraction from the dominant obstruction (Fresnel–Kirchhoff parameter, ITU-R P.526 approximation), a clutter term per kilometre, and k = 4/3 refraction. The envelope is where the received power clears the sensitivity.

Mobility

Dijkstra cost distance on the 8-connected grid with Tobler's hiking function on foot or a linear slope penalty with a cutoff for vehicles; the derived routes carry a fixed road speed.

Chokepoints

Least-cost routes form a network whose shared segments are collapsed into weighted edges; edge betweenness (Brandes) ranks them, and corridor width measures the physical constriction.

UAS

Ground speed from airspeed and the wind vector resolved along and across track; endurance sets reach, terrain line of sight from operator to aircraft sets the control-link constraint, and the facility sensor's line of sight to the aircraft sets exposure.

Validation and uncertainty

The analysis library is pure TypeScript with unit tests for the local frame, Terrarium decoding, bilinear sampling, curvature, Fresnel geometry, knife-edge loss, Tobler and vehicle speed laws, Dijkstra cost distance, edge betweenness on a barbell graph, envelope areas, and wind resolution. The synthetic Stage 0 scene and this real-terrain scene share the same envelope semantics, so results can be compared.

Terrarium tiles mix sources; in the United States the underlying data is largely USGS 3DEP at 10 m, elsewhere SRTM at 30 m. The default σ of 6 m covers source error plus resampling to a 60 m grid; raise it where the source is coarser. Routes are terrain-derived and notional, and no parcel, owner, or facility is represented.