Highway Vertical Curve API

Vertical (parabolic) road-curve geometry as an API, computed locally and deterministically — the K-value, profile-elevation and design-length numbers a highway engineer or surveyor lays a crest or sag curve out with. The geometry endpoint takes the incoming and outgoing grades and the length and returns the algebraic grade difference A = g2 − g1 (negative is a crest, positive a sag), the K value = length ÷ |A| (the headline number on every design chart), the high or low point offset −g1·L/A from the PVC, and — given the PVI station and elevation — the PVC and PVT coordinates and the turning-point station and elevation. The elevation endpoint evaluates the parabola at any station: elevation = PVC elevation + (g1/100)·x + (A/(200·L))·x², with the instantaneous grade g1 + (A/L)·x that sweeps smoothly from g1 to g2 — the smooth change of grade that makes the ride and sight line comfortable. The min-length endpoint gives the AASHTO minimum length for stopping sight distance: crest L = A·S² ÷ 2158 and sag (headlight) L = A·S² ÷ (400 + 3.5·S), with the controlling K, because a crest hides the road over the hump and a sag limits the headlight reach at night. Everything is computed locally and deterministically, so it is instant and private. Ideal for highway- and rail-design tools, surveying and civil-engineering utilities, and CAD/GIS profile work. Pure local computation — no key, no third-party service, instant. US units (ft, %, mph). 3 compute endpoints. For horizontal curves use a horizontal-curve API; for slope conversion a slope API.