```{-# OPTIONS -fno-warn-missing-methods #-}
{-# LANGUAGE TypeSynonymInstances #-}

-- | Geometric functions concerning vectors.
module Graphics.Gloss.Data.Vector
( Vector
, magV
, argV
, dotV
, detV
, mulSV
, rotateV
, angleVV
, normalizeV
, unitVectorAtAngle )
where
import Graphics.Gloss.Data.Picture
import Graphics.Gloss.Geometry.Angle

-- | The magnitude of a vector.
magV :: Vector -> Float
magV :: Vector -> Float
magV (Float
x, Float
y)
= Float -> Float
forall a. Floating a => a -> a
sqrt (Float
x Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
x Float -> Float -> Float
forall a. Num a => a -> a -> a
+ Float
y Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
y)
{-# INLINE magV #-}

-- | The angle of this vector, relative to the +ve x-axis.
argV :: Vector -> Float
argV :: Vector -> Float
argV (Float
x, Float
y)
= Float -> Float
normalizeAngle (Float -> Float) -> Float -> Float
forall a b. (a -> b) -> a -> b
\$ Float -> Float -> Float
forall a. RealFloat a => a -> a -> a
atan2 Float
y Float
x
{-# INLINE argV #-}

-- | The dot product of two vectors.
dotV :: Vector -> Vector -> Float
dotV :: Vector -> Vector -> Float
dotV (Float
x1, Float
x2) (Float
y1, Float
y2)
= Float
x1 Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
y1 Float -> Float -> Float
forall a. Num a => a -> a -> a
+ Float
x2 Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
y2
{-# INLINE dotV #-}

-- | The determinant of two vectors.
detV :: Vector -> Vector -> Float
detV :: Vector -> Vector -> Float
detV (Float
x1, Float
y1) (Float
x2, Float
y2)
= Float
x1 Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
y2 Float -> Float -> Float
forall a. Num a => a -> a -> a
- Float
y1 Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
x2
{-# INLINE detV #-}

-- | Multiply a vector by a scalar.
mulSV :: Float -> Vector -> Vector
mulSV :: Float -> Vector -> Vector
mulSV Float
s (Float
x, Float
y)
= (Float
s Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
x, Float
s Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
y)
{-# INLINE mulSV #-}

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

-- | Compute the inner angle (in radians) between two vectors.
angleVV :: Vector -> Vector -> Float
angleVV :: Vector -> Vector -> Float
angleVV Vector
p1 Vector
p2
= let  m1 :: Float
m1      = Vector -> Float
magV Vector
p1
m2 :: Float
m2      = Vector -> Float
magV Vector
p2
d :: Float
d       = Vector
p1 Vector -> Vector -> Float
`dotV` Vector
p2
forall a. Floating a => a -> a
acos (Float -> Float) -> Float -> Float
forall a b. (a -> b) -> a -> b
\$ Float
d Float -> Float -> Float
forall a. Fractional a => a -> a -> a
/ (Float
m1 Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
m2)

in   Float
{-# INLINE angleVV #-}

-- | Normalise a vector, so it has a magnitude of 1.
normalizeV :: Vector -> Vector
normalizeV :: Vector -> Vector
normalizeV Vector
v    = Float -> Vector -> Vector
mulSV (Float
1 Float -> Float -> Float
forall a. Fractional a => a -> a -> a
/ Vector -> Float
magV Vector
v) Vector
v
{-# INLINE normalizeV #-}

-- | Produce a unit vector at a given angle relative to the +ve x-axis.
--      The provided angle is in radians.
unitVectorAtAngle :: Float -> Vector
unitVectorAtAngle :: Float -> Vector
unitVectorAtAngle Float
r
= (Float -> Float
forall a. Floating a => a -> a
cos Float
r, Float -> Float
forall a. Floating a => a -> a
sin Float
r)
{-# INLINE unitVectorAtAngle #-}

```