Convert GPS coordinates into Unity world space?

Question

I am developing an AR application where a number of historical buildings are spawned around the player depending on his position when a target / QR Code is recognized.

I know the Lat/Lon of these buildings and I have the Lat/Lon of the player. I have already implemented the Harvesine algorithm and can calculate the relative bearing of the buildings:

public static double Harvesine(double lat1, double lon1, double lat2, double lon2) { double R = 6371000; // metres double omega1 = ((lat1 / 180) * Mathf.PI); double omega2 = ((lat2 / 180) * Mathf.PI); double variacionomega1 = (((lat2 - lat1) / 180) * Mathf.PI); double variacionomega2 = (((lon2 - lon1) / 180) * Mathf.PI); double a = Math.Sin(variacionomega1 / 2) * Math.Sin(variacionomega1 / 2) + Math.Cos(omega1) * Math.Cos(omega2) * Math.Sin(variacionomega2 / 2) * Math.Sin(variacionomega2 / 2); double c = 2 * Math.Asin(Math.Sqrt(a)); double d = R * c; return d; } public static double Bearing(double lat1, double lon1, double lat2, double lon2) { double radians; double x = Math.Cos(lat2*Mathf.Deg2Rad) * Math.Sin((lon2 - lon1) * Mathf.Deg2Rad); double y = Math.Cos(lat1 * Math.PI / 180) * Math.Sin(lat2 * Math.PI / 180) - Math.Sin(lat1 * Math.PI / 180) * Math.Cos(lat2 * Math.PI / 180) * Math.Cos((lon2 - lon1) * Math.PI / 180); radians = Math.Atan2(x, y) * 180 / Math.PI; return radians; }

From here, how can I spawn the building relative to the player position? I have the distance (Harvesine) and the angle (Bearing), how can I get the Vector3 location?

I made a library for this purpose, documentation is scarce and it's been over a year since I wrote it, but check it out: github.com/starikcetin/Eflatun.GeoUnity — starikcetin
– starikcetin, Commented Sep 10, 2020 at 1:16

DMGregory · Accepted Answer · 2020-09-09 23:06:04Z

Presumably you considered just converting your angle and distance from polar coordinates into a Cartesian vector in the usual way?

public static Vector3 FromPolar(float angleRadians, float radius) { return new Vector3(Mathf.Sin(angleRadians), 0 Mathf.Cos(angleRadians)) * radius; }

You can now add that offset to the player position to spawn the building at that displacement from the player.

Thanks! It's so simple when you know the math! I'm from the humanities so I struggle sometimes with trig and stuff... — Steffan
– Steffan, Commented Sep 10, 2020 at 0:28

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