Created
April 12, 2015 22:01
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"Reverse Haversine" Formula implementation in Clojure
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; "Reverse haversine" to derive lat/long from start point, bearing (degrees clockwise from north), & distance (km) | |
; φ2 = asin( (sin φ1 ⋅ cos δ) + (cos φ1 ⋅ sin δ ⋅ cos θ) ) | |
; λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 ) | |
; where φ is latitude, λ is longitude, θ is the bearing (clockwise from north), δ is the angular distance d/R; d being the distance travelled, R the earth’s radius | |
(defn reverse-haversine | |
"Implementation of the reverse of Haversine formula. Takes one set of latitude/longitude as a start point, a bearing, and a distance, and returns the resultant lat/long pair." | |
[{lon :lng lat :lat bearing :bearing distance :distance}] | |
(let [R 6378.137 ; Radius of Earth in km | |
lat1 (Math/toRadians lat) | |
lon1 (Math/toRadians lon) | |
angdist (/ distance R) | |
theta (Math/toRadians bearing) | |
lat2 (Math/toDegrees (Math/asin (+ | |
(* (Math/sin lat1) (Math/cos angdist)) | |
(* (Math/cos lat1) (Math/sin angdist) (Math/cos theta))))) | |
lon2 (Math/toDegrees (+ lon1 | |
(Math/atan2 | |
(* (Math/sin theta) (Math/sin angdist) (Math/cos lat1)) | |
(- (Math/cos angdist) (* (Math/sin lat1) (Math/sin lat2))))))] | |
{:lat lat2 | |
:lng lon2})) |
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