module GIS.Math.Spherical ( areaPolygon
, perimeterPolygon
, relativeCompactness
, totalPerimeter
, areaTriangle
, areaConvex
, distance
) where
import Control.Composition
import GIS.Math.Projections
import GIS.Math.Utils
import GIS.Types
areaTriangle :: Point -> Point -> Point -> Double
areaTriangle x1 x2 x3 = r^(2 :: Int) * e
where r = 6371
e = 4 * atan(sqrt(tan(s/2) * tan((s - a)/2) * tan((s - b)/2) * tan((s - c)/2)))
s = (a + b + c) / 2
a = distanceRad x1 x2
b = distanceRad x1 x3
c = distanceRad x2 x3
distanceRad = on centralAngle toRadians
relativeCompactness :: Polygon -> Double
relativeCompactness = (*scale) . compactness1
where scale = 1/4*pi
compactness1 :: Polygon -> Double
compactness1 p = areaPolygon p/perimeterPolygon p^(2 :: Int)
areaConvex :: Polygon -> Double
areaConvex (base1:base2:pts) = fst $ foldr stepArea (0,base2) pts
where stepArea point (sum', base) = (sum' + areaTriangle base1 base point, point)
areaConvex _ = error "attempted to take area of polygon with < 3 points"
areaPolygon :: Polygon -> Double
areaPolygon = (*factor) . areaPolyRectangular . fmap (bonne . toRadians)
where factor = 1717856/4.219690791828533e-2
totalPerimeter :: [Polygon] -> Double
totalPerimeter = sum . fmap perimeterPolygon
perimeterPolygon :: Polygon -> Double
perimeterPolygon [x1, x2] = distance x1 x2
perimeterPolygon (x1:x2:points) = perimeterPolygon (x2:points) + distance x1 x2
perimeterPolygon _ = error "Attempted to take area of polygon with no points"
areaPolyRectangular :: Polygon -> Double
areaPolyRectangular (pt:pts) = abs . (*0.5) . fst $ foldr areaPolyCalc (0,pt) pts
where areaPolyCalc (x2, y2) (sum',(x1,y1)) = (sum' + (x1 * y2 - x2 * y1),(x2,y2))
areaPolyRectangular _ = error "Attempted to take area of polygon with no points"
distance :: Point -> Point -> Double
distance = (*6371) .* on centralAngle toRadians
centralAngle :: Point -> Point -> Double
centralAngle (long1, lat1) (long2, lat2) =
acos $ sin lat1 * sin lat2 + cos lat1 * cos lat2 * cos (long1 - long2)