geo_maths.gd

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# geo_maths.gd

# geospatial mathematics utilities for earth globe

# translated from geographical-adventures geomaths.cs

class_name GeoMaths

const EARTH_RADIUS_KM: float = 6371.0

const EARTH_CIRCUMFERENCE_KM: float = EARTH_RADIUS_KM * PI * 2.0

# convert point on unit sphere to coordinate (longitude, latitude in radians)

static func point_to_coordinate(point_on_unit_sphere: Vector3) -> Vector2:

    var latitude = asin(point_on_unit_sphere.y)

    var a = point_on_unit_sphere.x

    var b = -point_on_unit_sphere.z

    var longitude = atan2(a, b)

    return Vector2(longitude, latitude)

# calculate point on sphere given longitude and latitude (in radians) and radius

static func coordinate_to_point(longitude: float, latitude: float, radius: float = 1.0) -> Vector3:

    var y = sin(latitude)

    var r = cos(latitude) # radius of 2d circle cut through sphere at y

    var x = sin(longitude) * r

    var z = -cos(longitude) * r

    return Vector3(x, y, z) * radius

# convert coordinate (lon, lat in radians) to uv texture coordinates [0,1]

static func coordinate_to_uv(longitude: float, latitude: float) -> Vector2:

    var u = (longitude + PI) / (2.0 * PI)

    var v = (latitude + PI / 2.0) / PI

    return Vector2(u, v)

# convert point on unit sphere to uv coordinates

static func point_to_uv(point_on_unit_sphere: Vector3) -> Vector2:

    var coord = point_to_coordinate(point_on_unit_sphere)

    return coordinate_to_uv(coord.x, coord.y)

# convert uv coordinates to coordinate (lon, lat in radians)

static func uv_to_coordinate(uv: Vector2) -> Vector2:

    var longitude = (uv.x - 0.5) * 2.0 * PI

    var latitude = (uv.y - 0.5) * PI

    return Vector2(longitude, latitude)

# convert uv coordinates to point on unit sphere

static func uv_to_point_on_sphere(uv: Vector2) -> Vector3:

    var coord = uv_to_coordinate(uv)

    return coordinate_to_point(coord.x, coord.y)

# calculate distance between two points on unit sphere (result in radians)

static func distance_between_points_on_unit_sphere(a: Vector3, b: Vector3) -> float:

    # more precise for small distances than acos(dot(a,b))

    return atan2(a.cross(b).length(), a.dot(b))