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module Spear.Math.Vector3
(
Vector3
-- * Accessors
, x
, y
, z
-- * Construction
, unitX
, unitY
, unitZ
, zero
, fromList
, vec3
, orbit
-- * Operations
, Spear.Math.Vector3.min
, Spear.Math.Vector3.max
, Spear.Math.Vector3.zipWith
, Spear.Math.Vector3.map
, dot
, cross
, normSq
, norm
, scale
, normalise
, neg
)
where
import Foreign.C.Types (CFloat)
import Foreign.Storable
-- | Represents a vector in 3D.
data Vector3 = Vector3 !Float !Float !Float deriving (Eq, Show)
instance Num Vector3 where
Vector3 ax ay az + Vector3 bx by bz = Vector3 (ax + bx) (ay + by) (az + bz)
Vector3 ax ay az - Vector3 bx by bz = Vector3 (ax - bx) (ay - by) (az - bz)
Vector3 ax ay az * Vector3 bx by bz = Vector3 (ax * bx) (ay * by) (az * bz)
abs (Vector3 ax ay az) = Vector3 (abs ax) (abs ay) (abs az)
signum (Vector3 ax ay az) = Vector3 (signum ax) (signum ay) (signum az)
fromInteger i = Vector3 i' i' i' where i' = fromInteger i
instance Fractional Vector3 where
Vector3 ax ay az / Vector3 bx by bz = Vector3 (ax / bx) (ay / by) (az / bz)
fromRational r = Vector3 r' r' r' where r' = fromRational r
instance Ord Vector3 where
Vector3 ax ay az <= Vector3 bx by bz
= (ax <= bx)
|| (az == bx && ay <= by)
|| (ax == bx && ay == by && az <= bz)
Vector3 ax ay az >= Vector3 bx by bz
= (ax >= bx)
|| (ax == bx && ay >= by)
|| (ax == bx && ay == by && az >= bz)
Vector3 ax ay az < Vector3 bx by bz
= (ax < bx)
|| (az == bx && ay < by)
|| (ax == bx && ay == by && az < bz)
Vector3 ax ay az > Vector3 bx by bz
= (ax > bx)
|| (ax == bx && ay > by)
|| (ax == bx && ay == by && az > bz)
sizeFloat = sizeOf (undefined :: CFloat)
instance Storable Vector3 where
sizeOf _ = 3*sizeFloat
alignment _ = alignment (undefined :: CFloat)
peek ptr = do
ax <- peekByteOff ptr 0
ay <- peekByteOff ptr $ 1*sizeFloat
az <- peekByteOff ptr $ 2*sizeFloat
return (Vector3 ax ay az)
poke ptr (Vector3 ax ay az) = do
pokeByteOff ptr 0 ax
pokeByteOff ptr (1*sizeFloat) ay
pokeByteOff ptr (2*sizeFloat) az
x (Vector3 ax _ _ ) = ax
y (Vector3 _ ay _ ) = ay
z (Vector3 _ _ az) = az
-- | Unit vector along the X axis.
unitX :: Vector3
unitX = Vector3 1 0 0
-- | Unit vector along the Y axis.
unitY :: Vector3
unitY = Vector3 0 1 0
-- | Unit vector along the Z axis.
unitZ :: Vector3
unitZ = Vector3 0 0 1
-- | Zero vector.
zero :: Vector3
zero = Vector3 0 0 0
-- | Create a vector from the given list.
fromList :: [Float] -> Vector3
fromList (ax:ay:az:_) = Vector3 ax ay az
-- | Create a 3D vector from the given values.
vec3 :: Float -> Float -> Float -> Vector3
vec3 ax ay az = Vector3 ax ay az
-- | Create a 3D vector as a point on a sphere.
orbit :: Vector3 -- ^ Sphere center.
-> Float -- ^ Sphere radius
-> Float -- ^ Azimuth angle.
-> Float -- ^ Zenith angle.
-> Vector3
orbit center radius anglex angley =
let ax = anglex * pi / 180
ay = angley * pi / 180
sx = sin ax
sy = sin ay
cx = cos ax
cy = cos ay
px = (x center) + radius*cy*sx
py = (y center) + radius*sy
pz = (z center) + radius*cx*cy
in
vec3 px py pz
-- | Create a vector with components set to the minimum of each of the given vectors'.
min :: Vector3 -> Vector3 -> Vector3
min (Vector3 ax ay az) (Vector3 bx by bz) = Vector3 (Prelude.min ax bx) (Prelude.min ay by) (Prelude.min az bz)
-- | Create a vector with components set to the maximum of each of the given vectors'.
max :: Vector3 -> Vector3 -> Vector3
max (Vector3 ax ay az) (Vector3 bx by bz) = Vector3 (Prelude.max ax bx) (Prelude.max ay by) (Prelude.max az bz)
-- | Zip two vectors with the given function.
zipWith :: (Float -> Float -> Float) -> Vector3 -> Vector3 -> Vector3
zipWith f (Vector3 ax ay az) (Vector3 bx by bz) = Vector3 (f ax bx) (f ay by) (f az bz)
-- | Folds a vector from the left.
{-foldl :: (UV.Unbox b) => (a -> b -> a) -> a -> Vector3 b -> a
foldl f acc (Vector3 v) = UV.foldl f acc v
-- | Folds a vector from the right.
foldr :: (UV.Unbox b) => (b -> a -> a) -> a -> Vector3 b -> a
foldr f acc (Vector3 v) = UV.foldr f acc v-}
-- | Map the given function over the given vector.
map :: (Float -> Float) -> Vector3 -> Vector3
map f (Vector3 ax ay az) = Vector3 (f ax) (f ay) (f az)
-- | Compute the given vectors' dot product.
dot :: Vector3 -> Vector3 -> Float
Vector3 ax ay az `dot` Vector3 bx by bz = ax*bx + ay*by + az*bz
-- | Compute the given vectors' cross product.
cross :: Vector3 -> Vector3 -> Vector3
(Vector3 ax ay az) `cross` (Vector3 bx by bz) =
Vector3 (ay * bz - az * by) (az * bx - ax * bz) (ax * by - ay * bx)
-- | Compute the given vector's squared norm.
normSq :: Vector3 -> Float
normSq (Vector3 ax ay az) = ax*ax + ay*ay + az*az
-- | Compute the given vector's norm.
norm :: Vector3 -> Float
norm = sqrt . normSq
-- | Multiply the given vector with the given scalar.
scale :: Float -> Vector3 -> Vector3
scale s (Vector3 ax ay az) = Vector3 (s*ax) (s*ay) (s*az)
-- | Normalise the given vector.
normalise :: Vector3 -> Vector3
normalise v =
let n' = norm v
n = if n' == 0 then 1 else n'
in
scale (1.0 / n) v
-- | Negate the given vector.
neg :: Vector3 -> Vector3
neg (Vector3 ax ay az) = Vector3 (-ax) (-ay) (-az)
|
