TerrainHorizonSweep

THE SCHEDULE FOR AN ADAPTIVE TERRAIN-HORIZON SWEEP. Deriving an azimuth/elevation mask from terrain means asking, for one azimuth, "what is the highest thing I can see along this ray". The naive answer walks a fixed ladder of ranges. That is what an az-el mask demo did until 2026-08-15, with 26 log-spaced samples out to 40 km, and it under- derived badly at coastal sites: the ladder's outer gaps were kilometres wide, small islands fell BETWEEN two samples, and the mask sat at sea level with a peak of 0.0 while the renderer — correctly — drew terrain sticking through the volume. The fix is not "more samples everywhere". Terrain contributes elevation `atan(h / d)`, so a metre of height is worth a thousand times more at 10 m than at 10 km: the sweep must be DENSE CLOSE IN AND ABSENT FAR OUT (owner 2026-08-15). This module is the pure arithmetic of that schedule, separated from any sampling so the guarantee is assertable without terrain, a network, or a GL context: RINGS ARE GEOMETRIC. Ring i sits at `minimumRange * (1 + relativeStep)^i`, so the radial gap at distance d is exactly `relativeStep * d` — sample DENSITY falls as 1/d, which is constant angular resolution of the horizon profile. The gap is also the island guarantee: any feature whose radial extent along the ray is at least `relativeStep * d` cannot fall between two rings. AZIMUTHS TERMINATE. Beyond distance d, the highest elevation ANY terrain could still contribute is bounded by the tallest ground on Earth seen at that range, minus how far the Earth has curved away underneath it: bound(d) = atan((hMax - hObserver) / d) - d / (2 * R) Once that bound drops to or below the mask already accumulated for an azimuth, nothing further out can raise it, and sampling that azimuth outward is provably wasted. A site under a 50-degree valley wall stops at about 8 km; an open-ocean azimuth with a mask of 0 runs to roughly 340 km, where the bound crosses zero on curvature alone. By the outer ranges the sweep is taking no samples at all. `hMax` defaults to 9,000 m: above Everest (8,849 m), so the bound is conservative anywhere on Earth, while still being small enough that the termination bites within a few kilometres at any site with real relief. It is an option so a caller with a tighter regional maximum can terminate sooner.