module Eventloop.Utility.Vectors where
type Angle = Float
type Radians = Float
type Length = Float
type X = Float
type Y = Float
type Offset = (X, Y)
data PolarCoord = PolarCoord (Length, Radians)
deriving (Show, Eq)
data Point = Point (X, Y)
deriving (Show, Eq)
degreesToRadians :: Angle -> Radians
degreesToRadians d = (pi / 180) * d
radiansToDegrees :: Radians -> Angle
radiansToDegrees rads = (180 / pi) * rads
lengthToPoint :: Point -> Length
lengthToPoint = lengthBetweenPoints originPoint
lengthBetweenPoints :: Point -> Point -> Length
lengthBetweenPoints p1 p2 = sqrt (x'^2 + y'^2)
where
(x', y') = differenceBetweenPoints p1 p2
differenceBetweenPoints :: Point -> Point -> (X, Y)
differenceBetweenPoints (Point (x1, y1)) (Point (x2, y2)) = (x2 x1, y2 y1)
originPoint = Point (0,0)
class (RotateLeftAround a) => Vector2D a where
(|+|) :: a -> a -> a
(|-|) :: a -> a -> a
negateVector :: a -> a
instance Vector2D PolarCoord where
pc1 |+| pc2 = toPolarCoord $ (toPoint pc1) |+| (toPoint pc2)
pc1 |-| pc2 = toPolarCoord $ (toPoint pc1) |-| (toPoint pc2)
negateVector pc1 = rotateLeftAround (Point (0,0)) 180 pc1
instance Vector2D Point where
(Point (x1, y1)) |+| (Point (x2, y2)) = Point (x1 + x2, y1 + y2)
(Point (x1, y1)) |-| (Point (x2, y2)) = Point (x2 x1, y2 y1)
negateVector (Point (x, y)) = Point (x, y)
class ToPoint a where
toPoint :: a -> Point
instance ToPoint PolarCoord where
toPoint (PolarCoord (len, rads)) = Point (len * (cos rads), len * (sin rads))
class ToPolarCoord a where
toPolarCoord :: a -> PolarCoord
instance ToPolarCoord Point where
toPolarCoord (Point (x, y)) | x == 0 && y == 0 = PolarCoord (0.0, 0.0)
| x == 0 && y > 0 = PolarCoord (y, 0.5 * pi)
| x == 0 && y < 0 = PolarCoord (y, 1.5 * pi)
| x > 0 && y == 0 = PolarCoord (x, 0.0 * pi)
| x < 0 && y == 0 = PolarCoord (x, 1.0 * pi)
| x > 0 && y > 0 = PolarCoord (len, 0.0 * pi + localRads)
| x < 0 && y > 0 = PolarCoord (len, 0.5 * pi + localRads)
| x < 0 && y < 0 = PolarCoord (len, 1.0 * pi + localRads)
| x > 0 && y < 0 = PolarCoord (len, 1.5 * pi + localRads)
where
x' = abs x
y' = abs y
localRads = atan (y' / x')
len = lengthToPoint (Point (x, y))
class RotateLeftAround a where
rotateLeftAround :: Point -> Angle -> a -> a
instance RotateLeftAround PolarCoord where
rotateLeftAround rotatePoint aDeg = toPolarCoord.(rotateLeftAround rotatePoint aDeg).toPoint
instance RotateLeftAround Point where
rotateLeftAround rotatePoint aDeg p = p'' |+| rotatePoint
where
p' = rotatePoint |-| p
pc'@(PolarCoord (len', rads')) = toPolarCoord p'
aRads = degreesToRadians aDeg
pc'' = PolarCoord (len', rads' + aRads)
p'' = toPoint pc''