A circle on the surface of the Earth which lies in a plane passing through the Earth's centre. Every two distinct and non-antipodal points on the surface of the Earth define a Great Circle.

It is internally represented as its normal vector - i.e. the normal vector to the plane containing the great circle.

See greatCircle, greatCircleE, greatCircleF or greatCircleBearing constructors.

GreatCircle passing by both given positions. errors if given positions are equal or antipodal.

GreatCircle passing by both given positions. A Left indicates that given positions are equal or antipodal.

GreatCircle passing by both given positions. fails if given positions are equal or antipodal.

GreatCircle passing by the given position and heading on given bearing.

angularDistance p1 p2 n computes the angle between the horizontal positions p1 and p2. If n is Nothing, the angle is always in [0..180], otherwise it is in [-180, +180], signed + if p1 is clockwise looking along n, - in opposite direction.

antipode p computes the antipodal horizontal position of p: the horizontal position on the surface of the Earth which is diametrically opposite to p.

crossTrackDistance p gc computes the signed distance horizontal position p to great circle gc. Returns a negative Length if position if left of great circle, positive Length if position if right of great circle; the orientation of the great circle is therefore important:

    let gc1 = greatCircle (decimalLatLong 51 0) (decimalLatLong 52 1)
    let gc2 = greatCircle (decimalLatLong 52 1) (decimalLatLong 51 0)
    crossTrackDistance p gc1 == (- crossTrackDistance p gc2)

crossTrackDistance using the mean radius of the WGS84 reference ellipsoid.

destination p b d r computes the destination position from position p having travelled the distance d on the initial bearing (compass angle) b (bearing will normally vary before destination is reached) and using the earth radius r.

destination using the mean radius of the WGS84 reference ellipsoid.

finalBearing p1 p2 computes the final bearing arriving at p2 from p1 in compass angle.

Compass angles are clockwise angles from true north: 0 = north, 90 = east, 180 = south, 270 = west.

The final bearing will differ from the initialBearing by varying degrees according to distance and latitude.

Returns Nothing if both horizontal positions are equals.

initialBearing p1 p2 computes the initial bearing from p1 to p2 in compass angle.

Compass angles are clockwise angles from true north: 0 = north, 90 = east, 180 = south, 270 = west.

Returns Nothing if both horizontal positions are equals.

interpolate p0 p1 f# computes the horizontal position at fraction f between the p0 and p1@.

Special conditions:

    interpolate p0 p1 0.0 == p0
    interpolate p0 p1 1.0 == p1

errors if f || f 1.0

Computes the intersections between the two given GreatCircles. Two GreatCircles intersect exactly twice unless there are equal (regardless of orientation), in which case Nothing is returned.

insideSurface p ps determines whether the p is inside the polygon defined by the list of positions ps. The polygon is closed if needed (i.e. if head ps /= last ps).

Uses the angle summation test: on a sphere, due to spherical excess, enclosed point angles will sum to less than 360°, and exterior point angles will be small but non-zero.

Always returns False if ps does not at least defines a triangle.

mean ps computes the mean geographic horitzontal position of ps, if it is defined.

The geographic mean is not defined for antipodals position (since they cancel each other).

Special conditions:

    mean [] == Nothing
    mean [p] == Just p
    mean [p1, p2, p3] == Just circumcentre
    mean [p1, .., antipode p1] == Nothing

surfaceDistance p1 p2 computes the surface distance (length of geodesic) between the positions p1 and p2.

surfaceDistance using the mean radius of the WGS84 reference ellipsoid.