jord-0.4.2.0: test/Data/Geo/Jord/KinematicsSpec.hs
module Data.Geo.Jord.KinematicsSpec
( spec
) where
import Data.Geo.Jord
import Data.Maybe (fromJust)
import Test.Hspec
spec :: Spec
spec =
describe "kinematics" $ do
describe "position" $ do
it "computes position at t from p0, bearing and speed" $ do
let p0 = latLongHeight (readLatLong "531914N0014347W") (metres 15000)
let p1 = decimalLatLongHeight 53.1882691 0.1332741 (metres 15000)
let t = Track p0 (decimalDegrees 96.0217) (kilometresPerHour 124.8)
position84 t (hours 1) `shouldBe` p1
it "handles poles" $
-- distance between poles assuming a spherical earth (WGS84) = 20015.114352200002km
-- track at north pole travelling at 20015.114352200002km/h and true north reaches the
-- south pole after 1 hour.
do
let t = Track (decimalLatLong 90 0) zero (kilometresPerHour 20015.114352200002)
position84 t (hours 1) `shouldBe` decimalLatLong (-90) 180.0
it "return p0 if speed is 0" $ do
let p0 = latLongHeight (readLatLong "531914N0014347W") (metres 15000)
let t = Track p0 (decimalDegrees 96.0217) zero
position84 t (hours 1) `shouldBe` p0
it "return p0 if duration is 0" $ do
let p0 = latLongHeight (readLatLong "531914N0014347W") (metres 15000)
let t = Track p0 (decimalDegrees 96.0217) (kilometresPerHour 124.8)
position84 t zero `shouldBe` p0
describe "cpa" $ do
it "handles trailing tracks" $ do
let p1 = decimalLatLong 20 30
let px = destination84 p1 (decimalDegrees 20) (kilometres 1)
let p2 = interpolate p1 px 0.25
let b1 = fromJust (initialBearing p1 px)
let b2 = fromJust (initialBearing p2 px)
let t1 = Track p1 b1 (knots 400)
let t2 = Track p2 b2 (knots 400)
let c = cpa84 t1 t2
-- any time is correct but it should be close to zero since that's
-- our initial value
fmap (\r -> toMilliseconds (cpaTime r) < 5000) c `shouldBe` Just True
fmap cpaDistance c `shouldBe` Just (metres 250.0036)
it "handles heading tracks" $ do
let p1 = decimalLatLong 20 30
let p2 = decimalLatLong 21 31
let b1 = fromJust (initialBearing p1 p2)
let b2 = fromJust (initialBearing p2 p1)
let t1 = Track p1 b1 (knots 400)
let t2 = Track p2 b2 (knots 400)
let c = cpa84 t1 t2
-- distance between p1 and p2 = 152.354309 km
-- speed = 740.8 km/h
-- time = 152.354309 / 740.8 / 2
fmap cpaTime c `shouldBe` Just (milliseconds 370191)
fmap cpaDistance c `shouldBe` Just zero
it "handles tracks at the same position" $ do
let p = decimalLatLong 20 30
let t1 = Track p (decimalDegrees 45) (knots 300)
let t2 = Track p (decimalDegrees 135) (knots 500)
let c = cpa84 t1 t2
fmap cpaTime c `shouldBe` Just zero
fmap cpaDistance c `shouldBe` Just zero
it "computes time to CPA, positions and distance at CPA" $ do
let p1 = decimalLatLong 20 (-60)
let b1 = decimalDegrees 10
let s1 = knots 15
let p2 = decimalLatLong 34 (-50)
let b2 = decimalDegrees 220
let s2 = knots 300
let t1 = Track p1 b1 s1
let t2 = Track p2 b2 s2
let c = cpa84 t1 t2
fmap cpaTime c `shouldBe` Just (milliseconds 11396155)
fmap cpaDistance c `shouldBe` Just (kilometres 124.2317453)
it "returns Nothing if time to CPA is in the past" $ do
let t1 = Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400)
let t2 = Track (decimalLatLong 30.01 30) (decimalDegrees 315) (knots 400)
cpa84 t1 t2 `shouldBe` Nothing
describe "intercept" $ do
it "returns Nothing if target and interceptor are at the same position" $
intercept84
(Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400))
(decimalLatLong 30 30) `shouldBe`
Nothing
it "returns Nothing if interceptor is behing target" $ do
let t = Track (decimalLatLong 45 67) (decimalDegrees 54) (knots 400)
let ip = decimalLatLong 44 66
intercept84 t ip `shouldBe` Nothing
it "handles interceptor on the great circle of target and in front" $ do
let tp = decimalLatLong 20 30
let px = destination84 tp (decimalDegrees 20) (kilometres 1)
let ip = interpolate tp px 0.25
let b = fromJust (initialBearing tp px)
let t = Track tp b (knots 400)
let i = intercept84 t ip
fmap interceptorSpeed i `shouldBe` Just zero
fmap interceptPosition i `shouldBe` Just ip
fmap interceptTime i `shouldBe` Just (seconds 1.215)
it "returns Nothing if interceptor is behing target" $ do
let t = Track (decimalLatLong 45 67) (decimalDegrees 181) (knots 400)
let ip = decimalLatLong 44 66
let i = intercept84 t ip
fmap interceptorSpeed i `shouldBe` Just (knots 228.5538171521)
fmap interceptTime i `shouldBe` Just (seconds 808.770)
let interceptor =
Track
ip
(fromJust (fmap interceptorBearing i))
(fromJust (fmap interceptorSpeed i))
fmap interceptPosition i `shouldBe`
Just (position84 interceptor (fromJust (fmap interceptTime i)))
it "returns the minimum speed required for intercept to take place" $ do
let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
let ip = decimalLatLong 20 (-60)
let i = intercept84 t ip
fmap interceptorSpeed i `shouldBe` Just (knots 52.633367756059)
fmap interceptTime i `shouldBe` Just (seconds 5993.831)
let interceptor =
Track
ip
(fromJust (fmap interceptorBearing i))
(fromJust (fmap interceptorSpeed i))
fmap interceptPosition i `shouldBe`
Just (position84 interceptor (fromJust (fmap interceptTime i)))
describe "interceptBySpeed" $ do
it "returns Nothing if target and interceptor are at the same position" $
interceptBySpeed84
(Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400))
(decimalLatLong 30 30)
(knots 400) `shouldBe`
Nothing
it "returns Nothing if interceptor speed is below minimum speed" $ do
let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
let ip = decimalLatLong 20 (-60)
interceptBySpeed84 t ip (knots 50) `shouldBe` Nothing
it "returns the speed needed for intercept to take place" $ do
let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
let ip = decimalLatLong 20 (-60)
let i = interceptBySpeed84 t ip (knots 700)
fmap interceptTime i `shouldBe` Just (seconds 2764.692)
fmap interceptorBearing i `shouldBe` Just (decimalDegrees 25.93541277)
fmap interceptDistance i `shouldBe` Just (kilometres 995.5960805999999)
it "returns the same as intercept when called with minimum speed" $ do
let t = Track (decimalLatLong 45 50) (decimalDegrees 54) (knots 500)
let ip = decimalLatLong 70 30
let mi = intercept84 t ip
let i = interceptBySpeed84 t ip (fromJust (fmap interceptorSpeed mi))
fmap interceptTime i `shouldBe` fmap interceptTime mi
describe "interceptByTime" $ do
it "returns Nothing if duration is zero" $
interceptByTime84
(Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400))
(decimalLatLong 34 (-50))
zero `shouldBe`
Nothing
it "returns Nothing if duration is negative" $
interceptByTime84
(Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400))
(decimalLatLong 34 (-50))
(seconds (-1)) `shouldBe`
Nothing
it "returns Nothing if target and interceptor are at the same position" $
interceptByTime84
(Track (decimalLatLong 30 30) (decimalDegrees 45) (knots 400))
(decimalLatLong 30 30)
(seconds 10) `shouldBe`
Nothing
it "returns the speed needed for intercept to take place" $ do
let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
let ip = decimalLatLong 20 (-60)
let d = seconds 2700
let i = interceptByTime84 t ip d
fmap interceptorSpeed i `shouldBe` Just (knots 730.959238)
fmap interceptorBearing i `shouldBe` Just (decimalDegrees 26.1199030)
fmap interceptPosition i `shouldBe` Just (decimalLatLong 28.1366797 (-55.4559475))
fmap interceptDistance i `shouldBe` Just (metres 1015302.3815)
fmap interceptTime i `shouldBe` Just (seconds 2700)
it "handles the poles" $
-- distance between poles assuming a spherical earth (WGS84) = 20015.114352200002km
-- target at north pole travelling at 500km/h and true north can be intercepted from
-- the south pole by an interceptor travelling at ~ 19515.114352200002km/h and 180 degrees.
do
let t = Track (decimalLatLong 90 0) zero (kilometresPerHour 500)
let ip = decimalLatLong (-90) 0
let i = interceptByTime84 t ip (seconds 3600)
fmap interceptorSpeed i `shouldBe` Just (kilometresPerHour 19515.11434)
fmap interceptorBearing i `shouldBe` Just (decimalDegrees 180)
it "handles the interceptor being at the intercept position at t" $ do
let tp = decimalLatLong 34 (-50)
let t = Track tp (decimalDegrees 220) (knots 600)
let d = seconds 3600
let ip = position84 t d
let i = interceptByTime84 t ip d
fmap interceptorSpeed i `shouldBe` Just zero
fmap interceptorBearing i `shouldBe` initialBearing ip tp