Great-Circle Waypoints
List N intermediate points along the great-circle route between two coordinates.
Overview
The Great-Circle Waypoints generator lists N intermediate points along the great-circle route between two latitude/longitude coordinates. Specify the endpoints, choose how many waypoints you want, and the tool returns evenly-spaced coordinates along the shortest path over the sphere - the same path a long-haul airliner or a transoceanic ship follows.
The line that looks straight on a Mercator map is rarely the shortest route between two distant cities. A trip from New York to Beijing curves up through the Arctic; a flight from Buenos Aires to Sydney dips deep into the Southern Ocean. Waypoint lists like the one this tool produces are the simplest way to plot that curve on a map, sanity-check a route against airspace boundaries, or feed intermediate coordinates into a downstream tool such as a distance calculator or a weather lookup.
How it works
Great-circle interpolation uses the spherical linear interpolation (slerp) formula. The total angular distance d between the two endpoints is computed first using the haversine formula. For each fraction f between 0 and 1, the intermediate point is A · sin((1-f)·d) / sin(d) + B · sin(f·d) / sin(d) in 3D unit-vector space, where A and B are the endpoints projected onto the unit sphere. The result is converted back to latitude and longitude.
This produces points that are equally spaced in terms of along-route distance, not in terms of lat/lng. The line that connects them, when drawn on a Mercator map, is the characteristic curved arc that defines great-circle navigation.
Examples
- London (51.51, -0.13) to Tokyo (35.68, 139.69) with 5 waypoints - intermediate points trace a path up through northern Scandinavia, across Siberia, then south into Japan.
- Sydney (-33.87, 151.21) to Cape Town (-33.93, 18.42) with 10 waypoints - the route dives south into the Southern Ocean before climbing back up to Africa.
- New York (40.71, -74.01) to London (51.51, -0.13) with 3 waypoints - waypoints at roughly 47°N 49°W, 51°N 28°W and 52°N 14°W, illustrating the slight northward arc.
- Two points on the equator, 90 degrees apart - waypoints stay on the equator and are evenly spaced in longitude.
FAQ
How many waypoints should I request?
For a clean map polyline, 20 waypoints is usually plenty for any route. For long polar routes, 50 to 100 gives a smoother visual curve. More than a few hundred rarely improves accuracy.
Are the waypoints evenly spaced in kilometres?
Yes. Each step covers the same angular and (on a sphere) the same metric distance along the route.
Will the route always look curved on a Mercator map?
Only when the endpoints are far apart and not on the same parallel or meridian. Short routes and pure north-south routes look straight on Mercator.
Does it handle the antimeridian?
Yes. The 3D unit-vector math is wraparound-safe, so routes crossing the date line interpolate correctly without longitude jumps.