loop/src/Geometry/Vector.hs

{-# LANGUAGE BangPatterns #-}

module Geometry.Vector where

import Geometry.Data

-- | Moves from two to three dimensions, adding zero in z direction.
zeroZ :: Point2 -> Point3
{-# INLINE zeroZ #-}
zeroZ (V2 x y) = V3 x y 0

infixl 6 +.+, -.-

infixl 7 *.*

-- | 2D coordinate-wise addition.
(+.+) :: Point2 -> Point2 -> Point2
{-# INLINE (+.+) #-}
--(+.+) = -- (+)
V2 x1 y1 +.+ V2 x2 y2 =
    let !x = x1 + x2
        !y = y1 + y2
     in V2 x y

-- | 2D coordinate-wise subtraction.
(-.-) :: Point2 -> Point2 -> Point2
{-# INLINE (-.-) #-}
--(-.-) = (-)
V2 x1 y1 -.- V2 x2 y2 =
    let !x = x1 - x2
        !y = y1 - y2
     in V2 x y

-- | 2D scalar multiplication.
(*.*) :: Float -> Point2 -> Point2
{-# INLINE (*.*) #-}
a *.* V2 x2 y2 =
    let !x = a * x2
        !y = a * y2
     in V2 x y

-- | Normalize a vector to length 1.
normalizeV :: Point2 -> Point2
{-# INLINE normalizeV #-}
normalizeV p = (1 / magV p) *.* p

clipV :: Float -> Point2 -> Point2
{-# INLINE clipV #-}
clipV x v
    | magV v > x = x *.* normalizeV v
    | otherwise = v

-- | Angle between two vectors.  Always positive.

-- TODO fix this: it seems to be unstable when the two vectors are very close to
-- each other
angleVV :: Point2 -> Point2 -> Float
{-# INLINE angleVV #-}
angleVV a b
    | a == b = 0
    | otherwise =
        let ma = magV a
            mb = magV b
            d = a `dotV` b
         in acos $ d / (ma * mb)

-- | Safe version of 'angleVV' that returns 0 if either vector is null.
safeAngleVV :: Point2 -> Point2 -> Float
{-# INLINE safeAngleVV #-}
safeAngleVV a b
    | a == V2 0 0 || b == V2 0 0 = 0
    | otherwise = angleVV a b

-- | Dot product.
dotV :: Point2 -> Point2 -> Float
{-# INLINE dotV #-}
dotV (V2 x y) (V2 z w) = x * z + y * w

-- | Given vector, returns the angle, anticlockwise from +ve x-axis, in radians.
argV :: Point2 -> Float
{-# INLINE argV #-}
argV (V2 x y) = normalizeAngle $ atan2 y x

{- | Given vector, returns the angle, anticlockwise from +ve x-axis, in radians.
 Returns Nothing for a 0 0 vector.
-}
safeArgV :: Point2 -> Maybe Float
{-# INLINE safeArgV #-}
safeArgV (V2 0 0) = Nothing
safeArgV v = Just $ argV v

-- | Determinant of the matrix formed by two vectors.
detV :: Point2 -> Point2 -> Float
{-# INLINE detV #-}
detV (V2 x1 y1) (V2 x2 y2) = x1 * y2 - y1 * x2

{- | Given an angle in radians, anticlockwise from +ve x-axis,
 - returns the corresponding unit vector.
-}
unitVectorAtAngle :: Float -> Point2
{-# INLINE unitVectorAtAngle #-}
unitVectorAtAngle r = V2 (cos r) (sin r)

-- | Rotate a vector by an angle (in radians). +ve angle is counter-clockwise.
rotateV :: Float -> Point2 -> Point2
rotateV r (V2 x y) =
    V2
        (x * cos r - y * sin r)
        (x * sin r + y * cos r)
{-# INLINE rotateV #-}

rotateVAround :: Point2 -> Float -> Point2 -> Point2
rotateVAround p r q = rotateV r (q -.- p) +.+ p
{-# INLINE rotateVAround #-}

-- | Convert degrees to radians
degToRad :: Float -> Float
degToRad d = d * pi / 180
{-# INLINE degToRad #-}

-- | Convert radians to degrees
radToDeg :: Float -> Float
radToDeg r = r * 180 / pi
{-# INLINE radToDeg #-}

-- | Normalize an angle to be between 0 and 2*pi radians
normalizeAngle :: Float -> Float
{-# INLINE normalizeAngle #-}
normalizeAngle f
    | f >= 0 && f < 2 * pi = f
    | otherwise = f - 2 * pi * floor' (f / (2 * pi))
  where
    floor' :: Float -> Float
    floor' x = fromIntegral (floor x :: Int)

-- | Rotate vector by pi/2 clockwise.
vNormal :: Point2 -> Point2
{-# INLINE vNormal #-}
vNormal (V2 x y) = V2 y (negate x)

-- | Negate a vector.
vInverse :: Point2 -> Point2
vInverse (V2 x y) = V2 (- x) (- y)

-- | Normalize a vector safely: on (0,0) return (0,0).
squashNormalizeV :: Point2 -> Point2
{-# INLINE squashNormalizeV #-}
squashNormalizeV p
    | magV p == 0 = V2 0 0
    | otherwise = (1 / magV p) *.* p

-- | Normalize a vector safely: on (0,0) return Nothing.
safeNormalizeV :: Point2 -> Maybe Point2
{-# INLINE safeNormalizeV #-}
safeNormalizeV p
    | magV p == 0 = Nothing
    | otherwise = Just $ (1 / magV p) *.* p

-- | Magnitude of a vector.
magV :: Point2 -> Float
{-# INLINE magV #-}
magV (V2 x y) = sqrt $ x ^ (2 :: Int) + y ^ (2 :: Int)

{- | Magnitude of the cross product of two vectors.
Identical to detV.
-}
crossV :: Point2 -> Point2 -> Float
crossV (V2 ax ay) (V2 bx by) = ax * by - ay * bx

-- | TO CHECK Orthographic projection of one vector onto another.
projV :: Point2 -> Point2 -> Point2
projV fromv onv
    | den == 0 = error "tried projecting onto zero vector"
    | otherwise = (fromv `dotV` onv) / den *.* onv
  where
    den = onv `dotV` onv

-- | Return distance between two points.
dist :: Point2 -> Point2 -> Float
{-# INLINE dist #-}
dist !p1 !p2 = magV (p2 -.- p1)

-- | Finds a new angle a given fraction between two other angles
tweenAngles ::
    Float ->
    Float ->
    Float ->
    Float
{-# INLINE tweenAngles #-}
tweenAngles frac a1 a2
    | abs (a1 - a2) < pi = frac * (a1 - a2) + a2
    | otherwise = normalizeAngle $ go frac a1 a2
  where
    go frac' a1' a2'
        | abs (a1' - a2') < pi = frac' * (a1' - a2') + a2'
        | a1' > a2' = go frac' (a1' - 2 * pi) a2'
        | otherwise = go frac' a1' (a2' - 2 * pi)

xV2 :: Point2 -> Float
{-# INLINE xV2 #-}
xV2 (V2 x _) = x

yV2 :: Point2 -> Float
{-# INLINE yV2 #-}
yV2 (V2 _ y) = y

xyzV4 :: V4 a -> V3 a
{-# INLINE xyzV4 #-}
xyzV4 (V4 x y z _) = V3 x y z

xyV3 :: V3 a -> V2 a
{-# INLINE xyV3 #-}
xyV3 (V3 x y _) = V2 x y