From 44a2fc13f57454ed54223d028e287e053609971a Mon Sep 17 00:00:00 2001
From: Jeanne-Kamikaze <jeannekamikaze@gmail.com>
Date: Thu, 21 Feb 2013 13:15:55 +0100
Subject: Made vector min/max part of Ord instance
---
Spear/Math/AABB.hs | 4 +-
Spear/Math/Circle.hs | 8 +-
Spear/Math/Matrix3.hs | 480 ++++++++++++++---------------
Spear/Math/Matrix4.hs | 838 +++++++++++++++++++++++++-------------------------
Spear/Math/Plane.hs | 2 +-
Spear/Math/Vector2.hs | 278 ++++++++---------
Spear/Math/Vector3.hs | 40 +--
Spear/Math/Vector4.hs | 349 ++++++++++-----------
8 files changed, 985 insertions(+), 1014 deletions(-)
diff --git a/Spear/Math/AABB.hs b/Spear/Math/AABB.hs
index 55e3083..cd945a6 100644
--- a/Spear/Math/AABB.hs
+++ b/Spear/Math/AABB.hs
@@ -20,9 +20,9 @@ aabb :: [Vector2] -> AABB
aabb [] = error "Attempting to build a BoundingVolume from an empty list!"
aabb (x:xs) = foldr update (AABB x x) xs
- where update p (AABB min max) = AABB (v2min p min) (v2max p max)
+ where update p (AABB pmin pmax) = AABB (min p pmin) (max p pmax)
-- | Return 'True' if the given 'AABB' contains the given point, 'False' otherwise.
aabbpt :: AABB -> Vector2 -> Bool
-aabbpt (AABB min max) v = v >= min && v <= max
+aabbpt (AABB pmin pmax) v = v >= pmin && v <= pmax
diff --git a/Spear/Math/Circle.hs b/Spear/Math/Circle.hs
index a34de0b..daaafc5 100644
--- a/Spear/Math/Circle.hs
+++ b/Spear/Math/Circle.hs
@@ -22,10 +22,10 @@ circle :: [Vector2] -> Circle
circle [] = error "Attempting to build a Circle from an empty list!"
circle (x:xs) = Circle c r
where
- c = min + (max-min)/2
- r = norm $ max - c
- (min,max) = foldr update (x,x) xs
- update p (min,max) = (v2min p min, v2max p max)
+ c = pmin + (pmax-pmin)/2
+ r = norm $ pmax - c
+ (pmin,pmax) = foldr update (x,x) xs
+ update p (pmin,pmax) = (min p pmin, max p pmax)
-- | Return 'True' if the given 'Sphere' contains the given point, 'False' otherwise.
diff --git a/Spear/Math/Matrix3.hs b/Spear/Math/Matrix3.hs
index adc4449..d5e46e9 100644
--- a/Spear/Math/Matrix3.hs
+++ b/Spear/Math/Matrix3.hs
@@ -1,162 +1,162 @@
-module Spear.Math.Matrix3
-(
- Matrix3
- -- * Accessors
-, m00, m01, m02
-, m10, m11, m12
-, m20, m21, m22
-, col0, col1, col2
+module Spear.Math.Matrix3
+(
+ Matrix3
+ -- * Accessors
+, m00, m01, m02
+, m10, m11, m12
+, m20, m21, m22
+, col0, col1, col2
, row0, row1, row2
-, right, up, forward, position
- -- * Construction
-, mat3
+, right, up, forward, position
+ -- * Construction
+, mat3
, mat3fromVec
, transform
, translation
-, rotation
-, Spear.Math.Matrix3.id
+, rotation
+, Spear.Math.Matrix3.id
-- * Transformations
- -- ** Translation
-, transl
-, translv
- -- ** Rotation
-, rot
- -- ** Scale
-, Spear.Math.Matrix3.scale
-, scalev
- -- ** Reflection
-, reflectX
-, reflectY
-, reflectZ
- -- * Operations
+ -- ** Translation
+, transl
+, translv
+ -- ** Rotation
+, rot
+ -- ** Scale
+, Spear.Math.Matrix3.scale
+, scalev
+ -- ** Reflection
+, reflectX
+, reflectY
+, reflectZ
+ -- * Operations
, transpose
, mulp
, muld
, mul
-, inverseTransform
-, Spear.Math.Matrix3.zipWith
-, Spear.Math.Matrix3.map
-)
-where
-
-
-import Spear.Math.Vector2 as V2
-import Spear.Math.Vector3 as V3
-
-import Foreign.Storable
-
-
--- | Represents a 3x3 column major matrix.
-data Matrix3 = Matrix3
- { m00 :: {-# UNPACK #-} !Float, m10 :: {-# UNPACK #-} !Float, m20 :: {-# UNPACK #-} !Float
- , m01 :: {-# UNPACK #-} !Float, m11 :: {-# UNPACK #-} !Float, m21 :: {-# UNPACK #-} !Float
- , m02 :: {-# UNPACK #-} !Float, m12 :: {-# UNPACK #-} !Float, m22 :: {-# UNPACK #-} !Float
- }
-
-
-instance Show Matrix3 where
-
- show (Matrix3 m00 m10 m20 m01 m11 m21 m02 m12 m22) =
- show' m00 ++ ", " ++ show' m10 ++ ", " ++ show' m20 ++ "\n" ++
- show' m01 ++ ", " ++ show' m11 ++ ", " ++ show' m21 ++ "\n" ++
- show' m02 ++ ", " ++ show' m12 ++ ", " ++ show' m22 ++ "\n"
- where
- show' f = if abs f < 0.0000001 then "0" else show f
-
-
-instance Num Matrix3 where
- (Matrix3 a00 a01 a02 a03 a04 a05 a06 a07 a08)
- + (Matrix3 b00 b01 b02 b03 b04 b05 b06 b07 b08)
- = Matrix3 (a00 + b00) (a01 + b01) (a02 + b02)
- (a03 + b03) (a04 + b04) (a05 + b05)
- (a06 + b06) (a07 + b07) (a08 + b08)
-
- (Matrix3 a00 a01 a02 a03 a04 a05 a06 a07 a08)
- - (Matrix3 b00 b01 b02 b03 b04 b05 b06 b07 b08)
- = Matrix3 (a00 - b00) (a01 - b01) (a02 - b02)
- (a03 - b03) (a04 - b04) (a05 - b05)
- (a06 - b06) (a07 - b07) (a08 - b08)
-
- (Matrix3 a00 a10 a20 a01 a11 a21 a02 a12 a22)
- * (Matrix3 b00 b10 b20 b01 b11 b21 b02 b12 b22)
- = Matrix3 (a00 * b00 + a10 * b01 + a20 * b02)
- (a00 * b10 + a10 * b11 + a20 * b12)
- (a00 * b20 + a10 * b21 + a20 * b22)
-
- (a01 * b00 + a11 * b01 + a21 * b02)
- (a01 * b10 + a11 * b11 + a21 * b12)
- (a01 * b20 + a11 * b21 + a21 * b22)
-
- (a02 * b00 + a12 * b01 + a22 * b02)
- (a02 * b10 + a12 * b11 + a22 * b12)
- (a02 * b20 + a12 * b21 + a22 * b22)
-
- abs = Spear.Math.Matrix3.map abs
-
- signum = Spear.Math.Matrix3.map signum
-
- fromInteger i = mat3 i' i' i' i' i' i' i' i' i' where i' = fromInteger i
-
-
-instance Storable Matrix3 where
- sizeOf _ = 36
- alignment _ = 4
-
- peek ptr = do
- a00 <- peekByteOff ptr 0; a01 <- peekByteOff ptr 4; a02 <- peekByteOff ptr 8;
- a10 <- peekByteOff ptr 12; a11 <- peekByteOff ptr 16; a12 <- peekByteOff ptr 20;
- a20 <- peekByteOff ptr 24; a21 <- peekByteOff ptr 28; a22 <- peekByteOff ptr 32;
-
- return $ Matrix3 a00 a10 a20
- a01 a11 a21
- a02 a12 a22
-
- poke ptr (Matrix3 a00 a01 a02
- a10 a11 a12
- a20 a21 a22) = do
- pokeByteOff ptr 0 a00; pokeByteOff ptr 4 a01; pokeByteOff ptr 8 a02;
- pokeByteOff ptr 12 a10; pokeByteOff ptr 16 a11; pokeByteOff ptr 20 a12;
- pokeByteOff ptr 24 a20; pokeByteOff ptr 28 a21; pokeByteOff ptr 32 a22;
-
-
-col0 (Matrix3 a00 _ _ a01 _ _ a02 _ _ ) = vec3 a00 a01 a02
-col1 (Matrix3 _ a10 _ _ a11 _ _ a12 _ ) = vec3 a10 a11 a12
-col2 (Matrix3 _ _ a20 _ _ a21 _ _ a22) = vec3 a20 a21 a22
-
-
-row0 (Matrix3 a00 a10 a20 _ _ _ _ _ _ ) = vec3 a00 a10 a20
-row1 (Matrix3 _ _ _ a01 a11 a21 _ _ _ ) = vec3 a01 a11 a21
+, inverseTransform
+, Spear.Math.Matrix3.zipWith
+, Spear.Math.Matrix3.map
+)
+where
+
+
+import Spear.Math.Vector2 as V2
+import Spear.Math.Vector3 as V3
+
+import Foreign.Storable
+
+
+-- | Represents a 3x3 column major matrix.
+data Matrix3 = Matrix3
+ { m00 :: {-# UNPACK #-} !Float, m10 :: {-# UNPACK #-} !Float, m20 :: {-# UNPACK #-} !Float
+ , m01 :: {-# UNPACK #-} !Float, m11 :: {-# UNPACK #-} !Float, m21 :: {-# UNPACK #-} !Float
+ , m02 :: {-# UNPACK #-} !Float, m12 :: {-# UNPACK #-} !Float, m22 :: {-# UNPACK #-} !Float
+ }
+
+
+instance Show Matrix3 where
+
+ show (Matrix3 m00 m10 m20 m01 m11 m21 m02 m12 m22) =
+ show' m00 ++ ", " ++ show' m10 ++ ", " ++ show' m20 ++ "\n" ++
+ show' m01 ++ ", " ++ show' m11 ++ ", " ++ show' m21 ++ "\n" ++
+ show' m02 ++ ", " ++ show' m12 ++ ", " ++ show' m22 ++ "\n"
+ where
+ show' f = if abs f < 0.0000001 then "0" else show f
+
+
+instance Num Matrix3 where
+ (Matrix3 a00 a01 a02 a03 a04 a05 a06 a07 a08)
+ + (Matrix3 b00 b01 b02 b03 b04 b05 b06 b07 b08)
+ = Matrix3 (a00 + b00) (a01 + b01) (a02 + b02)
+ (a03 + b03) (a04 + b04) (a05 + b05)
+ (a06 + b06) (a07 + b07) (a08 + b08)
+
+ (Matrix3 a00 a01 a02 a03 a04 a05 a06 a07 a08)
+ - (Matrix3 b00 b01 b02 b03 b04 b05 b06 b07 b08)
+ = Matrix3 (a00 - b00) (a01 - b01) (a02 - b02)
+ (a03 - b03) (a04 - b04) (a05 - b05)
+ (a06 - b06) (a07 - b07) (a08 - b08)
+
+ (Matrix3 a00 a10 a20 a01 a11 a21 a02 a12 a22)
+ * (Matrix3 b00 b10 b20 b01 b11 b21 b02 b12 b22)
+ = Matrix3 (a00 * b00 + a10 * b01 + a20 * b02)
+ (a00 * b10 + a10 * b11 + a20 * b12)
+ (a00 * b20 + a10 * b21 + a20 * b22)
+
+ (a01 * b00 + a11 * b01 + a21 * b02)
+ (a01 * b10 + a11 * b11 + a21 * b12)
+ (a01 * b20 + a11 * b21 + a21 * b22)
+
+ (a02 * b00 + a12 * b01 + a22 * b02)
+ (a02 * b10 + a12 * b11 + a22 * b12)
+ (a02 * b20 + a12 * b21 + a22 * b22)
+
+ abs = Spear.Math.Matrix3.map abs
+
+ signum = Spear.Math.Matrix3.map signum
+
+ fromInteger i = mat3 i' i' i' i' i' i' i' i' i' where i' = fromInteger i
+
+
+instance Storable Matrix3 where
+ sizeOf _ = 36
+ alignment _ = 4
+
+ peek ptr = do
+ a00 <- peekByteOff ptr 0; a01 <- peekByteOff ptr 4; a02 <- peekByteOff ptr 8;
+ a10 <- peekByteOff ptr 12; a11 <- peekByteOff ptr 16; a12 <- peekByteOff ptr 20;
+ a20 <- peekByteOff ptr 24; a21 <- peekByteOff ptr 28; a22 <- peekByteOff ptr 32;
+
+ return $ Matrix3 a00 a10 a20
+ a01 a11 a21
+ a02 a12 a22
+
+ poke ptr (Matrix3 a00 a01 a02
+ a10 a11 a12
+ a20 a21 a22) = do
+ pokeByteOff ptr 0 a00; pokeByteOff ptr 4 a01; pokeByteOff ptr 8 a02;
+ pokeByteOff ptr 12 a10; pokeByteOff ptr 16 a11; pokeByteOff ptr 20 a12;
+ pokeByteOff ptr 24 a20; pokeByteOff ptr 28 a21; pokeByteOff ptr 32 a22;
+
+
+col0 (Matrix3 a00 _ _ a01 _ _ a02 _ _ ) = vec3 a00 a01 a02
+col1 (Matrix3 _ a10 _ _ a11 _ _ a12 _ ) = vec3 a10 a11 a12
+col2 (Matrix3 _ _ a20 _ _ a21 _ _ a22) = vec3 a20 a21 a22
+
+
+row0 (Matrix3 a00 a10 a20 _ _ _ _ _ _ ) = vec3 a00 a10 a20
+row1 (Matrix3 _ _ _ a01 a11 a21 _ _ _ ) = vec3 a01 a11 a21
row2 (Matrix3 _ _ _ _ _ _ a02 a12 a22) = vec3 a02 a12 a22
right (Matrix3 a00 _ _ a01 _ _ _ _ _) = vec2 a00 a01
up (Matrix3 _ a10 _ _ a11 _ _ _ _) = vec2 a10 a11
forward (Matrix3 _ a10 _ _ a11 _ _ _ _) = vec2 a10 a11
-position (Matrix3 _ _ a20 _ _ a21 _ _ _) = vec2 a20 a21
-
-
--- | Build a matrix from the specified values.
-mat3 = Matrix3
-
-
--- | Build a matrix from three vectors in 3D.
-mat3fromVec :: Vector3 -> Vector3 -> Vector3 -> Matrix3
-mat3fromVec v0 v1 v2 = Matrix3
- (V3.x v0) (V3.x v1) (V3.x v2)
- (V3.y v0) (V3.y v1) (V3.y v2)
- (V3.z v0) (V3.z v1) (V3.z v2)
+position (Matrix3 _ _ a20 _ _ a21 _ _ _) = vec2 a20 a21
+
+
+-- | Build a matrix from the specified values.
+mat3 = Matrix3
+
+
+-- | Build a matrix from three vectors in 3D.
+mat3fromVec :: Vector3 -> Vector3 -> Vector3 -> Matrix3
+mat3fromVec v0 v1 v2 = Matrix3
+ (V3.x v0) (V3.x v1) (V3.x v2)
+ (V3.y v0) (V3.y v1) (V3.y v2)
+ (V3.z v0) (V3.z v1) (V3.z v2)
-- | Build a transformation matrix.
transform :: Vector2 -- ^ Right vector
-> Vector2 -- ^ Forward vector
-> Vector2 -- ^ Position
- -> Matrix3 -- ^ Transform
+ -> Matrix3 -- ^ Transform
transform r f p = mat3
(V2.x r) (V2.x f) (V2.x p)
(V2.y r) (V2.y f) (V2.y p)
- 0 0 1
+ 0 0 1
-- | Get the translation part of the given transformation matrix.
@@ -181,14 +181,14 @@ rotation (Matrix3
a00 a10 0
a01 a11 0
a02 a12 1
-
-
--- | Return the identity matrix.
-id :: Matrix3
-id = mat3
- 1 0 0
- 0 1 0
- 0 0 1
+
+
+-- | Return the identity matrix.
+id :: Matrix3
+id = mat3
+ 1 0 0
+ 0 1 0
+ 0 0 1
-- | Create a translation matrix.
@@ -208,71 +208,71 @@ translv v = mat3
1 0 (V2.x v)
0 1 (V2.y v)
0 0 1
-
-
+
+
-- | Create a rotation matrix rotating counter-clockwise about the Z axis.
---
--- The given angle must be in degrees.
-rot :: Float -> Matrix3
-rot angle = mat3
- c (-s) 0
- s c 0
- 0 0 1
- where
- s = sin . fromDeg $ angle
- c = cos . fromDeg $ angle
-
-
--- | Create a scale matrix.
-scale :: Float -> Float -> Float -> Matrix3
-scale sx sy sz = mat3
- sx 0 0
- 0 sy 0
- 0 0 sz
-
-
--- | Create a scale matrix.
-scalev :: Vector3 -> Matrix3
-scalev v = mat3
- sx 0 0
- 0 sy 0
- 0 0 sz
- where
- sx = V3.x v
- sy = V3.y v
- sz = V3.z v
-
-
--- | Create an X reflection matrix.
-reflectX :: Matrix3
-reflectX = mat3
- (-1) 0 0
- 0 1 0
- 0 0 1
-
-
--- | Create a Y reflection matrix.
-reflectY :: Matrix3
-reflectY = mat3
- 1 0 0
- 0 (-1) 0
- 0 0 1
-
-
--- | Create a Z reflection matrix.
-reflectZ :: Matrix3
-reflectZ = mat3
- 1 0 0
- 0 1 0
- 0 0 (-1)
-
-
--- | Transpose the specified matrix.
-transpose :: Matrix3 -> Matrix3
-transpose m = mat3
- (m00 m) (m01 m) (m02 m)
- (m10 m) (m11 m) (m12 m)
- (m20 m) (m21 m) (m22 m)
+--
+-- The given angle must be in degrees.
+rot :: Float -> Matrix3
+rot angle = mat3
+ c (-s) 0
+ s c 0
+ 0 0 1
+ where
+ s = sin . fromDeg $ angle
+ c = cos . fromDeg $ angle
+
+
+-- | Create a scale matrix.
+scale :: Float -> Float -> Float -> Matrix3
+scale sx sy sz = mat3
+ sx 0 0
+ 0 sy 0
+ 0 0 sz
+
+
+-- | Create a scale matrix.
+scalev :: Vector3 -> Matrix3
+scalev v = mat3
+ sx 0 0
+ 0 sy 0
+ 0 0 sz
+ where
+ sx = V3.x v
+ sy = V3.y v
+ sz = V3.z v
+
+
+-- | Create an X reflection matrix.
+reflectX :: Matrix3
+reflectX = mat3
+ (-1) 0 0
+ 0 1 0
+ 0 0 1
+
+
+-- | Create a Y reflection matrix.
+reflectY :: Matrix3
+reflectY = mat3
+ 1 0 0
+ 0 (-1) 0
+ 0 0 1
+
+
+-- | Create a Z reflection matrix.
+reflectZ :: Matrix3
+reflectZ = mat3
+ 1 0 0
+ 0 1 0
+ 0 0 (-1)
+
+
+-- | Transpose the specified matrix.
+transpose :: Matrix3 -> Matrix3
+transpose m = mat3
+ (m00 m) (m01 m) (m02 m)
+ (m10 m) (m11 m) (m12 m)
+ (m20 m) (m21 m) (m22 m)
-- | Transform the given point vector in 2D space with the given matrix.
@@ -292,36 +292,36 @@ muld m v = vec2 x' y'
v' = vec3 (V2.x v) (V2.y v) 0
x' = row0 m `V3.dot` v'
y' = row1 m `V3.dot` v'
-
-
--- | Transform the given vector in 3D space with the given matrix.
-mul :: Matrix3 -> Vector3 -> Vector3
-mul m v = vec3 x' y' z'
- where
- v' = vec3 (V3.x v) (V3.y v) (V3.z v)
- x' = row0 m `V3.dot` v'
- y' = row1 m `V3.dot` v'
- z' = row2 m `V3.dot` v'
-
-
--- | Zip two 'Matrix3' together with the specified function.
-zipWith :: (Float -> Float -> Float) -> Matrix3 -> Matrix3 -> Matrix3
-zipWith f a b = Matrix3
- (f (m00 a) (m00 b)) (f (m10 a) (m10 b)) (f (m20 a) (m20 b))
- (f (m01 a) (m01 b)) (f (m11 a) (m11 b)) (f (m21 a) (m21 b))
- (f (m02 a) (m02 b)) (f (m12 a) (m12 b)) (f (m22 a) (m22 b))
-
-
--- | Map the specified function to the specified 'Matrix3'.
-map :: (Float -> Float) -> Matrix3 -> Matrix3
-map f m = Matrix3
- (f . m00 $ m) (f . m10 $ m) (f . m20 $ m)
- (f . m01 $ m) (f . m11 $ m) (f . m21 $ m)
+
+
+-- | Transform the given vector in 3D space with the given matrix.
+mul :: Matrix3 -> Vector3 -> Vector3
+mul m v = vec3 x' y' z'
+ where
+ v' = vec3 (V3.x v) (V3.y v) (V3.z v)
+ x' = row0 m `V3.dot` v'
+ y' = row1 m `V3.dot` v'
+ z' = row2 m `V3.dot` v'
+
+
+-- | Zip two 'Matrix3' together with the specified function.
+zipWith :: (Float -> Float -> Float) -> Matrix3 -> Matrix3 -> Matrix3
+zipWith f a b = Matrix3
+ (f (m00 a) (m00 b)) (f (m10 a) (m10 b)) (f (m20 a) (m20 b))
+ (f (m01 a) (m01 b)) (f (m11 a) (m11 b)) (f (m21 a) (m21 b))
+ (f (m02 a) (m02 b)) (f (m12 a) (m12 b)) (f (m22 a) (m22 b))
+
+
+-- | Map the specified function to the specified 'Matrix3'.
+map :: (Float -> Float) -> Matrix3 -> Matrix3
+map f m = Matrix3
+ (f . m00 $ m) (f . m10 $ m) (f . m20 $ m)
+ (f . m01 $ m) (f . m11 $ m) (f . m21 $ m)
(f . m02 $ m) (f . m12 $ m) (f . m22 $ m)
-
-
--- | Compute the inverse transform of the given transformation matrix.
-inverseTransform :: Matrix3 -> Matrix3
+
+
+-- | Compute the inverse transform of the given transformation matrix.
+inverseTransform :: Matrix3 -> Matrix3
inverseTransform mat =
let r = right mat
f = forward mat
@@ -330,8 +330,8 @@ inverseTransform mat =
(V2.x r) (V2.y r) (t `V2.dot` r)
(V2.x f) (V2.y f) (t `V2.dot` f)
0 0 1
-
-
-fromDeg :: (Floating a) => a -> a
-fromDeg = (*pi) . (/180)
-
+
+
+fromDeg :: (Floating a) => a -> a
+fromDeg = (*pi) . (/180)
+
diff --git a/Spear/Math/Matrix4.hs b/Spear/Math/Matrix4.hs
index a4ad651..41bfadd 100644
--- a/Spear/Math/Matrix4.hs
+++ b/Spear/Math/Matrix4.hs
@@ -1,194 +1,194 @@
-module Spear.Math.Matrix4
-(
- Matrix4
- -- * Accessors
-, m00, m01, m02, m03
-, m10, m11, m12, m13
-, m20, m21, m22, m23
-, m30, m31, m32, m33
-, col0, col1, col2, col3
-, row0, row1, row2, row3
-, right, up, forward, position
- -- * Construction
-, mat4
-, mat4fromVec
+module Spear.Math.Matrix4
+(
+ Matrix4
+ -- * Accessors
+, m00, m01, m02, m03
+, m10, m11, m12, m13
+, m20, m21, m22, m23
+, m30, m31, m32, m33
+, col0, col1, col2, col3
+, row0, row1, row2, row3
+, right, up, forward, position
+ -- * Construction
+, mat4
+, mat4fromVec
, transform
, translation
, rotation
-, lookAt
-, Spear.Math.Matrix4.id
- -- * Transformations
- -- ** Translation
-, transl
-, translv
- -- ** Rotation
-, rotX
-, rotY
-, rotZ
-, axisAngle
- -- ** Scale
-, Spear.Math.Matrix4.scale
-, scalev
- -- ** Reflection
-, reflectX
-, reflectY
-, reflectZ
- -- ** Projection
-, ortho
+, lookAt
+, Spear.Math.Matrix4.id
+ -- * Transformations
+ -- ** Translation
+, transl
+, translv
+ -- ** Rotation
+, rotX
+, rotY
+, rotZ
+, axisAngle
+ -- ** Scale
+, Spear.Math.Matrix4.scale
+, scalev
+ -- ** Reflection
+, reflectX
+, reflectY
+, reflectZ
+ -- ** Projection
+, ortho
, perspective
-, planeProj
- -- * Operations
-, Spear.Math.Matrix4.zipWith
-, Spear.Math.Matrix4.map
-, transpose
+, planeProj
+ -- * Operations
+, Spear.Math.Matrix4.zipWith
+, Spear.Math.Matrix4.map
+, transpose
, inverseTransform
-, inverse
-, mul
-, mulp
+, inverse
+, mul
+, mulp
, muld
-, mul'
-)
-where
-
-
-import Spear.Math.Vector3 as V3
-import Spear.Math.Vector4 as V4
-
-import Foreign.Storable
-
-
--- | Represents a 4x4 column major matrix.
-data Matrix4 = Matrix4
- { m00 :: {-# UNPACK #-} !Float, m10 :: {-# UNPACK #-} !Float, m20 :: {-# UNPACK #-} !Float, m30 :: {-# UNPACK #-} !Float
- , m01 :: {-# UNPACK #-} !Float, m11 :: {-# UNPACK #-} !Float, m21 :: {-# UNPACK #-} !Float, m31 :: {-# UNPACK #-} !Float
- , m02 :: {-# UNPACK #-} !Float, m12 :: {-# UNPACK #-} !Float, m22 :: {-# UNPACK #-} !Float, m32 :: {-# UNPACK #-} !Float
- , m03 :: {-# UNPACK #-} !Float, m13 :: {-# UNPACK #-} !Float, m23 :: {-# UNPACK #-} !Float, m33 :: {-# UNPACK #-} !Float
- }
-
-
-instance Show Matrix4 where
-
- show (Matrix4 m00 m10 m20 m30 m01 m11 m21 m31 m02 m12 m22 m32 m03 m13 m23 m33) =
- show' m00 ++ ", " ++ show' m10 ++ ", " ++ show' m20 ++ ", " ++ show' m30 ++ "\n" ++
- show' m01 ++ ", " ++ show' m11 ++ ", " ++ show' m21 ++ ", " ++ show' m31 ++ "\n" ++
- show' m02 ++ ", " ++ show' m12 ++ ", " ++ show' m22 ++ ", " ++ show' m32 ++ "\n" ++
- show' m03 ++ ", " ++ show' m13 ++ ", " ++ show' m23 ++ ", " ++ show' m33 ++ "\n"
- where
- show' f = if abs f < 0.0000001 then "0" else show f
-
-
-instance Num Matrix4 where
- (Matrix4 a00 a01 a02 a03 a04 a05 a06 a07 a08 a09 a10 a11 a12 a13 a14 a15)
- + (Matrix4 b00 b01 b02 b03 b04 b05 b06 b07 b08 b09 b10 b11 b12 b13 b14 b15)
- = Matrix4 (a00 + b00) (a01 + b01) (a02 + b02) (a03 + b03)
- (a04 + b04) (a05 + b05) (a06 + b06) (a07 + b07)
- (a08 + b08) (a09 + b09) (a10 + b10) (a11 + b11)
- (a12 + b12) (a13 + b13) (a14 + b14) (a15 + b15)
-
- (Matrix4 a00 a01 a02 a03 a04 a05 a06 a07 a08 a09 a10 a11 a12 a13 a14 a15)
- - (Matrix4 b00 b01 b02 b03 b04 b05 b06 b07 b08 b09 b10 b11 b12 b13 b14 b15)
- = Matrix4 (a00 - b00) (a01 - b01) (a02 - b02) (a03 - b03)
- (a04 - b04) (a05 - b05) (a06 - b06) (a07 - b07)
- (a08 - b08) (a09 - b09) (a10 - b10) (a11 - b11)
- (a12 - b12) (a13 - b13) (a14 - b14) (a15 - b15)
-
- (Matrix4 a00 a10 a20 a30 a01 a11 a21 a31 a02 a12 a22 a32 a03 a13 a23 a33)
- * (Matrix4 b00 b10 b20 b30 b01 b11 b21 b31 b02 b12 b22 b32 b03 b13 b23 b33)
- = Matrix4 (a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03)
- (a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13)
- (a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23)
- (a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33)
-
- (a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03)
- (a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13)
- (a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23)
- (a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33)
-
- (a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03)
- (a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13)
- (a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23)
- (a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33)
-
- (a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03)
- (a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13)
- (a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23)
- (a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33)
-
- abs = Spear.Math.Matrix4.map abs
-
- signum = Spear.Math.Matrix4.map signum
-
- fromInteger i = mat4 i' i' i' i' i' i' i' i' i' i' i' i' i' i' i' i' where i' = fromInteger i
-
-
-instance Storable Matrix4 where
- sizeOf _ = 64
- alignment _ = 4
-
- peek ptr = do
- a00 <- peekByteOff ptr 0; a01 <- peekByteOff ptr 4; a02 <- peekByteOff ptr 8; a03 <- peekByteOff ptr 12;
- a10 <- peekByteOff ptr 16; a11 <- peekByteOff ptr 20; a12 <- peekByteOff ptr 24; a13 <- peekByteOff ptr 28;
- a20 <- peekByteOff ptr 32; a21 <- peekByteOff ptr 36; a22 <- peekByteOff ptr 40; a23 <- peekByteOff ptr 44;
- a30 <- peekByteOff ptr 48; a31 <- peekByteOff ptr 52; a32 <- peekByteOff ptr 56; a33 <- peekByteOff ptr 60;
-
- return $ Matrix4 a00 a10 a20 a30
- a01 a11 a21 a31
- a02 a12 a22 a32
- a03 a13 a23 a33
-
- poke ptr (Matrix4 a00 a10 a20 a30
- a01 a11 a21 a31
- a02 a12 a22 a32
- a03 a13 a23 a33) = do
- pokeByteOff ptr 0 a00; pokeByteOff ptr 4 a01; pokeByteOff ptr 8 a02; pokeByteOff ptr 12 a03;
- pokeByteOff ptr 16 a10; pokeByteOff ptr 20 a11; pokeByteOff ptr 24 a12; pokeByteOff ptr 28 a13;
- pokeByteOff ptr 32 a20; pokeByteOff ptr 36 a21; pokeByteOff ptr 40 a22; pokeByteOff ptr 44 a23;
- pokeByteOff ptr 48 a30; pokeByteOff ptr 52 a31; pokeByteOff ptr 56 a32; pokeByteOff ptr 60 a33;
-
-
-col0 (Matrix4 a00 _ _ _ a01 _ _ _ a02 _ _ _ a03 _ _ _ ) = vec4 a00 a01 a02 a03
-col1 (Matrix4 _ a10 _ _ _ a11 _ _ _ a12 _ _ _ a13 _ _ ) = vec4 a10 a11 a12 a13
-col2 (Matrix4 _ _ a20 _ _ _ a21 _ _ _ a22 _ _ _ a23 _ ) = vec4 a20 a21 a22 a23
-col3 (Matrix4 _ _ _ a30 _ _ _ a31 _ _ _ a32 _ _ _ a33) = vec4 a30 a31 a32 a33
-
-
-row0 (Matrix4 a00 a01 a02 a03 _ _ _ _ _ _ _ _ _ _ _ _ ) = vec4 a00 a01 a02 a03
-row1 (Matrix4 _ _ _ _ a10 a11 a12 a13 _ _ _ _ _ _ _ _ ) = vec4 a10 a11 a12 a13
-row2 (Matrix4 _ _ _ _ _ _ _ _ a20 a21 a22 a23 _ _ _ _ ) = vec4 a20 a21 a22 a23
-row3 (Matrix4 _ _ _ _ _ _ _ _ _ _ _ _ a30 a31 a32 a33) = vec4 a30 a31 a32 a33
-
-
-right (Matrix4 a00 _ _ _ a01 _ _ _ a02 _ _ _ _ _ _ _) = vec3 a00 a01 a02
-up (Matrix4 _ a10 _ _ _ a11 _ _ _ a12 _ _ _ _ _ _) = vec3 a10 a11 a12
-forward (Matrix4 _ _ a20 _ _ _ a21 _ _ _ a22 _ _ _ _ _) = vec3 a20 a21 a22
-position (Matrix4 _ _ _ a30 _ _ _ a31 _ _ _ a32 _ _ _ _) = vec3 a30 a31 a32
-
-
--- | Build a matrix from the specified values.
-mat4 = Matrix4
-
-
--- | Build a matrix from four vectors in 4D.
-mat4fromVec :: Vector4 -> Vector4 -> Vector4 -> Vector4 -> Matrix4
-mat4fromVec v0 v1 v2 v3 = Matrix4
- (V4.x v0) (V4.x v1) (V4.x v2) (V4.x v3)
- (V4.y v0) (V4.y v1) (V4.y v2) (V4.y v3)
- (V4.z v0) (V4.z v1) (V4.z v2) (V4.z v3)
- (V4.w v0) (V4.w v1) (V4.w v2) (V4.w v3)
-
-
--- | Build a transformation 'Matrix4' from the given vectors.
-transform :: Vector3 -- ^ Right vector.
- -> Vector3 -- ^ Up vector.
- -> Vector3 -- ^ Forward vector.
- -> Vector3 -- ^ Position.
- -> Matrix4
-
-transform right up fwd pos = mat4
- (V3.x right) (V3.x up) (V3.x fwd) (V3.x pos)
- (V3.y right) (V3.y up) (V3.y fwd) (V3.y pos)
- (V3.z right) (V3.z up) (V3.z fwd) (V3.z pos)
- 0 0 0 1
+, mul'
+)
+where
+
+
+import Spear.Math.Vector3 as V3
+import Spear.Math.Vector4 as V4
+
+import Foreign.Storable
+
+
+-- | Represents a 4x4 column major matrix.
+data Matrix4 = Matrix4
+ { m00 :: {-# UNPACK #-} !Float, m10 :: {-# UNPACK #-} !Float, m20 :: {-# UNPACK #-} !Float, m30 :: {-# UNPACK #-} !Float
+ , m01 :: {-# UNPACK #-} !Float, m11 :: {-# UNPACK #-} !Float, m21 :: {-# UNPACK #-} !Float, m31 :: {-# UNPACK #-} !Float
+ , m02 :: {-# UNPACK #-} !Float, m12 :: {-# UNPACK #-} !Float, m22 :: {-# UNPACK #-} !Float, m32 :: {-# UNPACK #-} !Float
+ , m03 :: {-# UNPACK #-} !Float, m13 :: {-# UNPACK #-} !Float, m23 :: {-# UNPACK #-} !Float, m33 :: {-# UNPACK #-} !Float
+ }
+
+
+instance Show Matrix4 where
+
+ show (Matrix4 m00 m10 m20 m30 m01 m11 m21 m31 m02 m12 m22 m32 m03 m13 m23 m33) =
+ show' m00 ++ ", " ++ show' m10 ++ ", " ++ show' m20 ++ ", " ++ show' m30 ++ "\n" ++
+ show' m01 ++ ", " ++ show' m11 ++ ", " ++ show' m21 ++ ", " ++ show' m31 ++ "\n" ++
+ show' m02 ++ ", " ++ show' m12 ++ ", " ++ show' m22 ++ ", " ++ show' m32 ++ "\n" ++
+ show' m03 ++ ", " ++ show' m13 ++ ", " ++ show' m23 ++ ", " ++ show' m33 ++ "\n"
+ where
+ show' f = if abs f < 0.0000001 then "0" else show f
+
+
+instance Num Matrix4 where
+ (Matrix4 a00 a01 a02 a03 a04 a05 a06 a07 a08 a09 a10 a11 a12 a13 a14 a15)
+ + (Matrix4 b00 b01 b02 b03 b04 b05 b06 b07 b08 b09 b10 b11 b12 b13 b14 b15)
+ = Matrix4 (a00 + b00) (a01 + b01) (a02 + b02) (a03 + b03)
+ (a04 + b04) (a05 + b05) (a06 + b06) (a07 + b07)
+ (a08 + b08) (a09 + b09) (a10 + b10) (a11 + b11)
+ (a12 + b12) (a13 + b13) (a14 + b14) (a15 + b15)
+
+ (Matrix4 a00 a01 a02 a03 a04 a05 a06 a07 a08 a09 a10 a11 a12 a13 a14 a15)
+ - (Matrix4 b00 b01 b02 b03 b04 b05 b06 b07 b08 b09 b10 b11 b12 b13 b14 b15)
+ = Matrix4 (a00 - b00) (a01 - b01) (a02 - b02) (a03 - b03)
+ (a04 - b04) (a05 - b05) (a06 - b06) (a07 - b07)
+ (a08 - b08) (a09 - b09) (a10 - b10) (a11 - b11)
+ (a12 - b12) (a13 - b13) (a14 - b14) (a15 - b15)
+
+ (Matrix4 a00 a10 a20 a30 a01 a11 a21 a31 a02 a12 a22 a32 a03 a13 a23 a33)
+ * (Matrix4 b00 b10 b20 b30 b01 b11 b21 b31 b02 b12 b22 b32 b03 b13 b23 b33)
+ = Matrix4 (a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03)
+ (a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13)
+ (a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23)
+ (a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33)
+
+ (a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03)
+ (a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13)
+ (a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23)
+ (a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33)
+
+ (a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03)
+ (a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13)
+ (a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23)
+ (a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33)
+
+ (a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03)
+ (a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13)
+ (a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23)
+ (a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33)
+
+ abs = Spear.Math.Matrix4.map abs
+
+ signum = Spear.Math.Matrix4.map signum
+
+ fromInteger i = mat4 i' i' i' i' i' i' i' i' i' i' i' i' i' i' i' i' where i' = fromInteger i
+
+
+instance Storable Matrix4 where
+ sizeOf _ = 64
+ alignment _ = 4
+
+ peek ptr = do
+ a00 <- peekByteOff ptr 0; a01 <- peekByteOff ptr 4; a02 <- peekByteOff ptr 8; a03 <- peekByteOff ptr 12;
+ a10 <- peekByteOff ptr 16; a11 <- peekByteOff ptr 20; a12 <- peekByteOff ptr 24; a13 <- peekByteOff ptr 28;
+ a20 <- peekByteOff ptr 32; a21 <- peekByteOff ptr 36; a22 <- peekByteOff ptr 40; a23 <- peekByteOff ptr 44;
+ a30 <- peekByteOff ptr 48; a31 <- peekByteOff ptr 52; a32 <- peekByteOff ptr 56; a33 <- peekByteOff ptr 60;
+
+ return $ Matrix4 a00 a10 a20 a30
+ a01 a11 a21 a31
+ a02 a12 a22 a32
+ a03 a13 a23 a33
+
+ poke ptr (Matrix4 a00 a10 a20 a30
+ a01 a11 a21 a31
+ a02 a12 a22 a32
+ a03 a13 a23 a33) = do
+ pokeByteOff ptr 0 a00; pokeByteOff ptr 4 a01; pokeByteOff ptr 8 a02; pokeByteOff ptr 12 a03;
+ pokeByteOff ptr 16 a10; pokeByteOff ptr 20 a11; pokeByteOff ptr 24 a12; pokeByteOff ptr 28 a13;
+ pokeByteOff ptr 32 a20; pokeByteOff ptr 36 a21; pokeByteOff ptr 40 a22; pokeByteOff ptr 44 a23;
+ pokeByteOff ptr 48 a30; pokeByteOff ptr 52 a31; pokeByteOff ptr 56 a32; pokeByteOff ptr 60 a33;
+
+
+col0 (Matrix4 a00 _ _ _ a01 _ _ _ a02 _ _ _ a03 _ _ _ ) = vec4 a00 a01 a02 a03
+col1 (Matrix4 _ a10 _ _ _ a11 _ _ _ a12 _ _ _ a13 _ _ ) = vec4 a10 a11 a12 a13
+col2 (Matrix4 _ _ a20 _ _ _ a21 _ _ _ a22 _ _ _ a23 _ ) = vec4 a20 a21 a22 a23
+col3 (Matrix4 _ _ _ a30 _ _ _ a31 _ _ _ a32 _ _ _ a33) = vec4 a30 a31 a32 a33
+
+
+row0 (Matrix4 a00 a01 a02 a03 _ _ _ _ _ _ _ _ _ _ _ _ ) = vec4 a00 a01 a02 a03
+row1 (Matrix4 _ _ _ _ a10 a11 a12 a13 _ _ _ _ _ _ _ _ ) = vec4 a10 a11 a12 a13
+row2 (Matrix4 _ _ _ _ _ _ _ _ a20 a21 a22 a23 _ _ _ _ ) = vec4 a20 a21 a22 a23
+row3 (Matrix4 _ _ _ _ _ _ _ _ _ _ _ _ a30 a31 a32 a33) = vec4 a30 a31 a32 a33
+
+
+right (Matrix4 a00 _ _ _ a01 _ _ _ a02 _ _ _ _ _ _ _) = vec3 a00 a01 a02
+up (Matrix4 _ a10 _ _ _ a11 _ _ _ a12 _ _ _ _ _ _) = vec3 a10 a11 a12
+forward (Matrix4 _ _ a20 _ _ _ a21 _ _ _ a22 _ _ _ _ _) = vec3 a20 a21 a22
+position (Matrix4 _ _ _ a30 _ _ _ a31 _ _ _ a32 _ _ _ _) = vec3 a30 a31 a32
+
+
+-- | Build a matrix from the specified values.
+mat4 = Matrix4
+
+
+-- | Build a matrix from four vectors in 4D.
+mat4fromVec :: Vector4 -> Vector4 -> Vector4 -> Vector4 -> Matrix4
+mat4fromVec v0 v1 v2 v3 = Matrix4
+ (V4.x v0) (V4.x v1) (V4.x v2) (V4.x v3)
+ (V4.y v0) (V4.y v1) (V4.y v2) (V4.y v3)
+ (V4.z v0) (V4.z v1) (V4.z v2) (V4.z v3)
+ (V4.w v0) (V4.w v1) (V4.w v2) (V4.w v3)
+
+
+-- | Build a transformation 'Matrix4' from the given vectors.
+transform :: Vector3 -- ^ Right vector.
+ -> Vector3 -- ^ Up vector.
+ -> Vector3 -- ^ Forward vector.
+ -> Vector3 -- ^ Position.
+ -> Matrix4
+
+transform right up fwd pos = mat4
+ (V3.x right) (V3.x up) (V3.x fwd) (V3.x pos)
+ (V3.y right) (V3.y up) (V3.y fwd) (V3.y pos)
+ (V3.z right) (V3.z up) (V3.z fwd) (V3.z pos)
+ 0 0 0 1
-- | Get the translation part of the given transformation matrix.
@@ -230,198 +230,198 @@ lookAt pos target =
u = r `cross` fwd
in
transform r u (-fwd) pos
-
-
--- | Zip two matrices together with the specified function.
-zipWith :: (Float -> Float -> Float) -> Matrix4 -> Matrix4 -> Matrix4
-zipWith f a b = Matrix4
- (f (m00 a) (m00 b)) (f (m10 a) (m10 b)) (f (m20 a) (m20 b)) (f (m30 a) (m30 b))
- (f (m01 a) (m01 b)) (f (m11 a) (m11 b)) (f (m21 a) (m21 b)) (f (m31 a) (m31 b))
- (f (m02 a) (m02 b)) (f (m12 a) (m12 b)) (f (m22 a) (m22 b)) (f (m32 a) (m32 b))
- (f (m03 a) (m03 b)) (f (m13 a) (m13 b)) (f (m23 a) (m23 b)) (f (m33 a) (m33 b))
-
-
--- | Map the specified function to the specified matrix.
-map :: (Float -> Float) -> Matrix4 -> Matrix4
-map f m = Matrix4
- (f . m00 $ m) (f . m10 $ m) (f . m20 $ m) (f . m30 $ m)
- (f . m01 $ m) (f . m11 $ m) (f . m21 $ m) (f . m31 $ m)
- (f . m02 $ m) (f . m12 $ m) (f . m22 $ m) (f . m32 $ m)
- (f . m03 $ m) (f . m13 $ m) (f . m23 $ m) (f . m33 $ m)
-
-
--- | Return the identity matrix.
-id :: Matrix4
-id = mat4
- 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- 0 0 0 1
-
-
--- | Create a translation matrix.
-transl :: Float -> Float -> Float -> Matrix4
-transl x y z = mat4
- 1 0 0 x
- 0 1 0 y
- 0 0 1 z
- 0 0 0 1
-
-
--- | Create a translation matrix.
-translv :: Vector3 -> Matrix4
-translv v = mat4
- 1 0 0 (V3.x v)
- 0 1 0 (V3.y v)
- 0 0 1 (V3.z v)
- 0 0 0 1
-
-
--- | Create a rotation matrix rotating about the X axis.
--- The given angle must be in degrees.
-rotX :: Float -> Matrix4
-rotX angle = mat4
- 1 0 0 0
- 0 c (-s) 0
- 0 s c 0
- 0 0 0 1
- where
- s = sin . toRAD $ angle
- c = cos . toRAD $ angle
-
-
--- | Create a rotation matrix rotating about the Y axis.
--- The given angle must be in degrees.
-rotY :: Float -> Matrix4
-rotY angle = mat4
- c 0 s 0
- 0 1 0 0
- (-s) 0 c 0
- 0 0 0 1
- where
- s = sin . toRAD $ angle
- c = cos . toRAD $ angle
-
-
--- | Create a rotation matrix rotating about the Z axis.
--- The given angle must be in degrees.
-rotZ :: Float -> Matrix4
-rotZ angle = mat4
- c (-s) 0 0
- s c 0 0
- 0 0 1 0
- 0 0 0 1
- where
- s = sin . toRAD $ angle
- c = cos . toRAD $ angle
-
-
--- | Create a rotation matrix rotating about the specified axis.
--- The given angle must be in degrees.
-axisAngle :: Vector3 -> Float -> Matrix4
-axisAngle v angle = mat4
- (c + omc*x^2) (omc*xy-sz) (omc*xz+sy) 0
- (omc*xy+sz) (c+omc*y^2) (omc*yz-sx) 0
- (omc*xz-sy) (omc*yz+sx) (c+omc*z^2) 0
- 0 0 0 1
- where
- x = V3.x v
- y = V3.y v
- z = V3.z v
- s = sin . toRAD $ angle
- c = cos . toRAD $ angle
- xy = x*y
- xz = x*z
- yz = y*z
- sx = s*x
- sy = s*y
- sz = s*z
- omc = 1 - c
-
-
--- | Create a scale matrix.
-scale :: Float -> Float -> Float -> Matrix4
-scale sx sy sz = mat4
- sx 0 0 0
- 0 sy 0 0
- 0 0 sz 0
- 0 0 0 1
-
-
--- | Create a scale matrix.
-scalev :: Vector3 -> Matrix4
-scalev v = mat4
- sx 0 0 0
- 0 sy 0 0
- 0 0 sz 0
- 0 0 0 1
- where
- sx = V3.x v
- sy = V3.y v
- sz = V3.z v
-
-
--- | Create an X reflection matrix.
-reflectX :: Matrix4
-reflectX = mat4
- (-1) 0 0 0
- 0 1 0 0
- 0 0 1 0
- 0 0 0 1
-
-
--- | Create a Y reflection matrix.
-reflectY :: Matrix4
-reflectY = mat4
- 1 0 0 0
- 0 (-1) 0 0
- 0 0 1 0
- 0 0 0 1
-
-
--- | Create a Z reflection matrix.
-reflectZ :: Matrix4
-reflectZ = mat4
- 1 0 0 0
- 0 1 0 0
- 0 0 (-1) 0
- 0 0 0 1
-
-
--- | Create an orthogonal projection matrix.
-ortho :: Float -- ^ Left.
- -> Float -- ^ Right.
- -> Float -- ^ Bottom.
- -> Float -- ^ Top.
- -> Float -- ^ Near clip.
- -> Float -- ^ Far clip.
- -> Matrix4
-
-ortho l r b t n f =
- let tx = (-(r+l)/(r-l))
- ty = (-(t+b)/(t-b))
- tz = (-(f+n)/(f-n))
- in mat4
- (2/(r-l)) 0 0 tx
- 0 (2/(t-b)) 0 ty
- 0 0 ((-2)/(f-n)) tz
- 0 0 0 1
-
-
--- | Create a perspective projection matrix.
-perspective :: Float -- ^ Fovy - Vertical field of view angle in degrees.
- -> Float -- ^ Aspect ratio.
- -> Float -- ^ Near clip distance.
- -> Float -- ^ Far clip distance
- -> Matrix4
-perspective fovy r near far =
- let f = 1 / tan (toRAD fovy / 2)
- a = near - far
- in mat4
- (f/r) 0 0 0
- 0 f 0 0
- 0 0 ((near+far)/a) (2*near*far/a)
- 0 0 (-1) 0
+
+
+-- | Zip two matrices together with the specified function.
+zipWith :: (Float -> Float -> Float) -> Matrix4 -> Matrix4 -> Matrix4
+zipWith f a b = Matrix4
+ (f (m00 a) (m00 b)) (f (m10 a) (m10 b)) (f (m20 a) (m20 b)) (f (m30 a) (m30 b))
+ (f (m01 a) (m01 b)) (f (m11 a) (m11 b)) (f (m21 a) (m21 b)) (f (m31 a) (m31 b))
+ (f (m02 a) (m02 b)) (f (m12 a) (m12 b)) (f (m22 a) (m22 b)) (f (m32 a) (m32 b))
+ (f (m03 a) (m03 b)) (f (m13 a) (m13 b)) (f (m23 a) (m23 b)) (f (m33 a) (m33 b))
+
+
+-- | Map the specified function to the specified matrix.
+map :: (Float -> Float) -> Matrix4 -> Matrix4
+map f m = Matrix4
+ (f . m00 $ m) (f . m10 $ m) (f . m20 $ m) (f . m30 $ m)
+ (f . m01 $ m) (f . m11 $ m) (f . m21 $ m) (f . m31 $ m)
+ (f . m02 $ m) (f . m12 $ m) (f . m22 $ m) (f . m32 $ m)
+ (f . m03 $ m) (f . m13 $ m) (f . m23 $ m) (f . m33 $ m)
+
+
+-- | Return the identity matrix.
+id :: Matrix4
+id = mat4
+ 1 0 0 0
+ 0 1 0 0
+ 0 0 1 0
+ 0 0 0 1
+
+
+-- | Create a translation matrix.
+transl :: Float -> Float -> Float -> Matrix4
+transl x y z = mat4
+ 1 0 0 x
+ 0 1 0 y
+ 0 0 1 z
+ 0 0 0 1
+
+
+-- | Create a translation matrix.
+translv :: Vector3 -> Matrix4
+translv v = mat4
+ 1 0 0 (V3.x v)
+ 0 1 0 (V3.y v)
+ 0 0 1 (V3.z v)
+ 0 0 0 1
+
+
+-- | Create a rotation matrix rotating about the X axis.
+-- The given angle must be in degrees.
+rotX :: Float -> Matrix4
+rotX angle = mat4
+ 1 0 0 0
+ 0 c (-s) 0
+ 0 s c 0
+ 0 0 0 1
+ where
+ s = sin . toRAD $ angle
+ c = cos . toRAD $ angle
+
+
+-- | Create a rotation matrix rotating about the Y axis.
+-- The given angle must be in degrees.
+rotY :: Float -> Matrix4
+rotY angle = mat4
+ c 0 s 0
+ 0 1 0 0
+ (-s) 0 c 0
+ 0 0 0 1
+ where
+ s = sin . toRAD $ angle
+ c = cos . toRAD $ angle
+
+
+-- | Create a rotation matrix rotating about the Z axis.
+-- The given angle must be in degrees.
+rotZ :: Float -> Matrix4
+rotZ angle = mat4
+ c (-s) 0 0
+ s c 0 0
+ 0 0 1 0
+ 0 0 0 1
+ where
+ s = sin . toRAD $ angle
+ c = cos . toRAD $ angle
+
+
+-- | Create a rotation matrix rotating about the specified axis.
+-- The given angle must be in degrees.
+axisAngle :: Vector3 -> Float -> Matrix4
+axisAngle v angle = mat4
+ (c + omc*x^2) (omc*xy-sz) (omc*xz+sy) 0
+ (omc*xy+sz) (c+omc*y^2) (omc*yz-sx) 0
+ (omc*xz-sy) (omc*yz+sx) (c+omc*z^2) 0
+ 0 0 0 1
+ where
+ x = V3.x v
+ y = V3.y v
+ z = V3.z v
+ s = sin . toRAD $ angle
+ c = cos . toRAD $ angle
+ xy = x*y
+ xz = x*z
+ yz = y*z
+ sx = s*x
+ sy = s*y
+ sz = s*z
+ omc = 1 - c
+
+
+-- | Create a scale matrix.
+scale :: Float -> Float -> Float -> Matrix4
+scale sx sy sz = mat4
+ sx 0 0 0
+ 0 sy 0 0
+ 0 0 sz 0
+ 0 0 0 1
+
+
+-- | Create a scale matrix.
+scalev :: Vector3 -> Matrix4
+scalev v = mat4
+ sx 0 0 0
+ 0 sy 0 0
+ 0 0 sz 0
+ 0 0 0 1
+ where
+ sx = V3.x v
+ sy = V3.y v
+ sz = V3.z v
+
+
+-- | Create an X reflection matrix.
+reflectX :: Matrix4
+reflectX = mat4
+ (-1) 0 0 0
+ 0 1 0 0
+ 0 0 1 0
+ 0 0 0 1
+
+
+-- | Create a Y reflection matrix.
+reflectY :: Matrix4
+reflectY = mat4
+ 1 0 0 0
+ 0 (-1) 0 0
+ 0 0 1 0
+ 0 0 0 1
+
+
+-- | Create a Z reflection matrix.
+reflectZ :: Matrix4
+reflectZ = mat4
+ 1 0 0 0
+ 0 1 0 0
+ 0 0 (-1) 0
+ 0 0 0 1
+
+
+-- | Create an orthogonal projection matrix.
+ortho :: Float -- ^ Left.
+ -> Float -- ^ Right.
+ -> Float -- ^ Bottom.
+ -> Float -- ^ Top.
+ -> Float -- ^ Near clip.
+ -> Float -- ^ Far clip.
+ -> Matrix4
+
+ortho l r b t n f =
+ let tx = (-(r+l)/(r-l))
+ ty = (-(t+b)/(t-b))
+ tz = (-(f+n)/(f-n))
+ in mat4
+ (2/(r-l)) 0 0 tx
+ 0 (2/(t-b)) 0 ty
+ 0 0 ((-2)/(f-n)) tz
+ 0 0 0 1
+
+
+-- | Create a perspective projection matrix.
+perspective :: Float -- ^ Fovy - Vertical field of view angle in degrees.
+ -> Float -- ^ Aspect ratio.
+ -> Float -- ^ Near clip distance.
+ -> Float -- ^ Far clip distance
+ -> Matrix4
+perspective fovy r near far =
+ let f = 1 / tan (toRAD fovy / 2)
+ a = near - far
+ in mat4
+ (f/r) 0 0 0
+ 0 f 0 0
+ 0 0 ((near+far)/a) (2*near*far/a)
+ 0 0 (-1) 0
-- | Create a plane projection matrix.
@@ -442,19 +442,19 @@ planeProj n d l =
(-nx*ly) (d + c - ny*ly) (-nz*ly) (-ly*d)
(-nx*lz) (-ny*lz) (d + c - nz*lz) (-lz*d)
(-nx) (-ny) (-nz) c
-
-
--- | Transpose the specified matrix.
-transpose :: Matrix4 -> Matrix4
-transpose m = mat4
- (m00 m) (m01 m) (m02 m) (m03 m)
- (m10 m) (m11 m) (m12 m) (m13 m)
- (m20 m) (m21 m) (m22 m) (m23 m)
- (m30 m) (m31 m) (m32 m) (m33 m)
-
-
--- | Invert the given transformation matrix.
-inverseTransform :: Matrix4 -> Matrix4
+
+
+-- | Transpose the specified matrix.
+transpose :: Matrix4 -> Matrix4
+transpose m = mat4
+ (m00 m) (m01 m) (m02 m) (m03 m)
+ (m10 m) (m11 m) (m12 m) (m13 m)
+ (m20 m) (m21 m) (m22 m) (m23 m)
+ (m30 m) (m31 m) (m32 m) (m33 m)
+
+
+-- | Invert the given transformation matrix.
+inverseTransform :: Matrix4 -> Matrix4
inverseTransform mat =
let
r = right mat
@@ -611,26 +611,26 @@ inverse mat =
(m00' * det) (m04' * det) (m08' * det) (m12' * det)
(m01' * det) (m05' * det) (m09' * det) (m13' * det)
(m02' * det) (m06' * det) (m10' * det) (m14' * det)
- (m03' * det) (m07' * det) (m11' * det) (m15' * det)
-
-
--- | Transform the given vector in 3D space with the given matrix.
-mul :: Float -> Matrix4 -> Vector3 -> Vector3
-mul w m v = vec3 x' y' z'
- where
- v' = vec4 (V3.x v) (V3.y v) (V3.z v) w
- x' = row0 m `V4.dot` v'
- y' = row1 m `V4.dot` v'
- z' = row2 m `V4.dot` v'
-
-
--- | Transform the given point vector in 3D space with the given matrix.
-mulp :: Matrix4 -> Vector3 -> Vector3
-mulp = mul 1
-
-
--- | Transform the given directional vector in 3D space with the given matrix.
-muld :: Matrix4 -> Vector3 -> Vector3
+ (m03' * det) (m07' * det) (m11' * det) (m15' * det)
+
+
+-- | Transform the given vector in 3D space with the given matrix.
+mul :: Float -> Matrix4 -> Vector3 -> Vector3
+mul w m v = vec3 x' y' z'
+ where
+ v' = vec4 (V3.x v) (V3.y v) (V3.z v) w
+ x' = row0 m `V4.dot` v'
+ y' = row1 m `V4.dot` v'
+ z' = row2 m `V4.dot` v'
+
+
+-- | Transform the given point vector in 3D space with the given matrix.
+mulp :: Matrix4 -> Vector3 -> Vector3
+mulp = mul 1
+
+
+-- | Transform the given directional vector in 3D space with the given matrix.
+muld :: Matrix4 -> Vector3 -> Vector3
muld = mul 0
@@ -639,13 +639,13 @@ muld = mul 0
-- The vector is brought from homogeneous space to 3D space by performing a
-- perspective divide.
mul' :: Float -> Matrix4 -> Vector3 -> Vector3
-mul' w m v = vec3 (x'/w') (y'/w') (z'/w')
- where
- v' = vec4 (V3.x v) (V3.y v) (V3.z v) w
- x' = row0 m `V4.dot` v'
- y' = row1 m `V4.dot` v'
+mul' w m v = vec3 (x'/w') (y'/w') (z'/w')
+ where
+ v' = vec4 (V3.x v) (V3.y v) (V3.z v) w
+ x' = row0 m `V4.dot` v'
+ y' = row1 m `V4.dot` v'
z' = row2 m `V4.dot` v'
- w' = row3 m `V4.dot` v'
-
-
-toRAD = (*pi) . (/180)
+ w' = row3 m `V4.dot` v'
+
+
+toRAD = (*pi) . (/180)
diff --git a/Spear/Math/Plane.hs b/Spear/Math/Plane.hs
index 8772a42..6fabbec 100644
--- a/Spear/Math/Plane.hs
+++ b/Spear/Math/Plane.hs
@@ -7,7 +7,7 @@ module Spear.Math.Plane
where
-import Spear.Math.Vector3 as Vector
+import Spear.Math.Vector3
data PointPlanePos = Front | Back | Contained deriving (Eq, Ord, Show)
diff --git a/Spear/Math/Vector2.hs b/Spear/Math/Vector2.hs
index ace86fe..581a64f 100644
--- a/Spear/Math/Vector2.hs
+++ b/Spear/Math/Vector2.hs
@@ -1,155 +1,145 @@
-module Spear.Math.Vector2
-(
- Vector2
- -- * Accessors
-, x
-, y
- -- * Construction
-, unitx
-, unity
-, zero
-, fromList
-, vec2
- -- * Operations
-, v2min
-, v2max
-, dot
-, normSq
-, norm
-, scale
-, normalise
+module Spear.Math.Vector2
+(
+ Vector2
+ -- * Accessors
+, x
+, y
+ -- * Construction
+, unitx
+, unity
+, zero
+, fromList
+, vec2
+ -- * Operations
+, perp
+, dot
+, normSq
+, norm
+, scale
, neg
-, perp
-)
-where
-
-import Foreign.C.Types (CFloat)
-import Foreign.Storable
-
-
--- | Represents a vector in 2D.
-data Vector2 = Vector2 {-# UNPACK #-} !Float {-# UNPACK #-} !Float deriving (Eq, Show)
-
-
-instance Num Vector2 where
- Vector2 ax ay + Vector2 bx by = Vector2 (ax + bx) (ay + by)
- Vector2 ax ay - Vector2 bx by = Vector2 (ax - bx) (ay - by)
- Vector2 ax ay * Vector2 bx by = Vector2 (ax * bx) (ay * by)
- abs (Vector2 ax ay) = Vector2 (abs ax) (abs ay)
- signum (Vector2 ax ay) = Vector2 (signum ax) (signum ay)
- fromInteger i = Vector2 i' i' where i' = fromInteger i
-
-
-instance Fractional Vector2 where
- Vector2 ax ay / Vector2 bx by = Vector2 (ax / bx) (ay / by)
- fromRational r = Vector2 r' r' where r' = fromRational r
-
-
-instance Ord Vector2 where
- Vector2 ax ay <= Vector2 bx by = (ax <= bx) || (ax == bx && ay <= by)
- Vector2 ax ay >= Vector2 bx by = (ax >= bx) || (ax == bx && ay >= by)
- Vector2 ax ay < Vector2 bx by = (ax < bx) || (ax == bx && ay < by)
- Vector2 ax ay > Vector2 bx by = (ax > bx) || (ax == bx && ay > by)
-
-
-sizeFloat = sizeOf (undefined :: CFloat)
-
-
-instance Storable Vector2 where
- sizeOf _ = 2*sizeFloat
- alignment _ = alignment (undefined :: CFloat)
-
- peek ptr = do
- ax <- peekByteOff ptr 0
- ay <- peekByteOff ptr $ sizeFloat
- return (Vector2 ax ay)
-
- poke ptr (Vector2 ax ay) = do
- pokeByteOff ptr 0 ax
- pokeByteOff ptr sizeFloat ay
-
-
--- | Get the vector's x coordinate.
+, normalise
+)
+where
+
+
+import Foreign.C.Types (CFloat)
+import Foreign.Storable
+
+
+-- | Represents a vector in 2D.
+data Vector2 = Vector2 {-# UNPACK #-} !Float {-# UNPACK #-} !Float deriving (Eq, Show)
+
+
+instance Num Vector2 where
+ Vector2 ax ay + Vector2 bx by = Vector2 (ax + bx) (ay + by)
+ Vector2 ax ay - Vector2 bx by = Vector2 (ax - bx) (ay - by)
+ Vector2 ax ay * Vector2 bx by = Vector2 (ax * bx) (ay * by)
+ abs (Vector2 ax ay) = Vector2 (abs ax) (abs ay)
+ signum (Vector2 ax ay) = Vector2 (signum ax) (signum ay)
+ fromInteger i = Vector2 i' i' where i' = fromInteger i
+
+
+instance Fractional Vector2 where
+ Vector2 ax ay / Vector2 bx by = Vector2 (ax / bx) (ay / by)
+ fromRational r = Vector2 r' r' where r' = fromRational r
+
+
+instance Ord Vector2 where
+ Vector2 ax ay <= Vector2 bx by = (ax <= bx) || (ax == bx && ay <= by)
+ Vector2 ax ay >= Vector2 bx by = (ax >= bx) || (ax == bx && ay >= by)
+ Vector2 ax ay < Vector2 bx by = (ax < bx) || (ax == bx && ay < by)
+ Vector2 ax ay > Vector2 bx by = (ax > bx) || (ax == bx && ay > by)
+ max (Vector2 ax ay) (Vector2 bx by) = Vector2 (Prelude.max ax bx) (Prelude.max ay by)
+ min (Vector2 ax ay) (Vector2 bx by) = Vector2 (Prelude.min ax bx) (Prelude.min ay by)
+
+
+sizeFloat = sizeOf (undefined :: CFloat)
+
+
+instance Storable Vector2 where
+ sizeOf _ = 2*sizeFloat
+ alignment _ = alignment (undefined :: CFloat)
+
+ peek ptr = do
+ ax <- peekByteOff ptr 0
+ ay <- peekByteOff ptr $ sizeFloat
+ return (Vector2 ax ay)
+
+ poke ptr (Vector2 ax ay) = do
+ pokeByteOff ptr 0 ax
+ pokeByteOff ptr sizeFloat ay
+
+
+-- | Get the vector's x coordinate.
x (Vector2 ax _) = ax
--- | Get the vector's y coordinate.
-y (Vector2 _ ay) = ay
-
-
--- | Unit vector along the X axis.
-unitx :: Vector2
-unitx = Vector2 1 0
-
-
--- | Unit vector along the Y axis.
-unity :: Vector2
-unity = Vector2 0 1
-
-
--- | Zero vector.
-zero :: Vector2
-zero = Vector2 0 0
-
-
--- | Create a vector from the given list.
-fromList :: [Float] -> Vector2
-fromList (ax:ay:_) = Vector2 ax ay
-
-
--- | Create a vector from the given values.
-vec2 :: Float -> Float -> Vector2
-vec2 ax ay = Vector2 ax ay
-
-
--- | Create a vector with components set to the minimum of each of the given vectors'.
-v2min :: Vector2 -> Vector2 -> Vector2
-v2min (Vector2 ax ay) (Vector2 bx by) = Vector2 (Prelude.min ax bx) (Prelude.min ay by)
-
-
--- | Create a vector with components set to the maximum of each of the given vectors'.
-v2max :: Vector2 -> Vector2 -> Vector2
-v2max (Vector2 ax ay) (Vector2 bx by) = Vector2 (Prelude.max ax bx) (Prelude.max ay by)
-
-
--- | Compute the given vectors' dot product.
-dot :: Vector2 -> Vector2 -> Float
-Vector2 ax ay `dot` Vector2 bx by = ax*bx + ay*by
-
-
--- | Compute the given vector's squared norm.
-normSq :: Vector2 -> Float
-normSq (Vector2 ax ay) = ax*ax + ay*ay
-
-
--- | Compute the given vector's norm.
-norm :: Vector2 -> Float
-norm = sqrt . normSq
-
-
--- | Multiply the given vector with the given scalar.
-scale :: Float -> Vector2 -> Vector2
-scale s (Vector2 ax ay) = Vector2 (s*ax) (s*ay)
-
-
--- | Normalise the given vector.
-normalise :: Vector2 -> Vector2
-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 :: Vector2 -> Vector2
-neg (Vector2 ax ay) = Vector2 (-ax) (-ay)
+-- | Get the vector's y coordinate.
+y (Vector2 _ ay) = ay
+
+
+-- | Unit vector along the X axis.
+unitx :: Vector2
+unitx = Vector2 1 0
+
+
+-- | Unit vector along the Y axis.
+unity :: Vector2
+unity = Vector2 0 1
+
+
+-- | Zero vector.
+zero :: Vector2
+zero = Vector2 0 0
+
+
+-- | Create a vector from the given list.
+fromList :: [Float] -> Vector2
+fromList (ax:ay:_) = Vector2 ax ay
+
+
+-- | Create a vector from the given values.
+vec2 :: Float -> Float -> Vector2
+vec2 ax ay = Vector2 ax ay
-- | Compute a vector perpendicular to the given one, satisfying:
---
+--
-- perp (Vector2 0 1) = Vector2 1 0
--
-- perp (Vector2 1 0) = Vector2 0 (-1)
perp :: Vector2 -> Vector2
-perp (Vector2 x y) = Vector2 y (-x)
+perp (Vector2 x y) = Vector2 y (-x)
+
+
+-- | Compute the given vectors' dot product.
+dot :: Vector2 -> Vector2 -> Float
+Vector2 ax ay `dot` Vector2 bx by = ax*bx + ay*by
+
+
+-- | Compute the given vector's squared norm.
+normSq :: Vector2 -> Float
+normSq (Vector2 ax ay) = ax*ax + ay*ay
+
+
+-- | Compute the given vector's norm.
+norm :: Vector2 -> Float
+norm = sqrt . normSq
+
+
+-- | Multiply the given vector with the given scalar.
+scale :: Float -> Vector2 -> Vector2
+scale s (Vector2 ax ay) = Vector2 (s*ax) (s*ay)
+
+
+-- | Negate the given vector.
+neg :: Vector2 -> Vector2
+neg (Vector2 ax ay) = Vector2 (-ax) (-ay)
+
+
+-- | Normalise the given vector.
+normalise :: Vector2 -> Vector2
+normalise v =
+ let n' = norm v
+ n = if n' == 0 then 1 else n'
+ in scale (1.0 / n) v
diff --git a/Spear/Math/Vector3.hs b/Spear/Math/Vector3.hs
index 7ac0f7a..d280811 100644
--- a/Spear/Math/Vector3.hs
+++ b/Spear/Math/Vector3.hs
@@ -14,18 +14,17 @@ module Spear.Math.Vector3
, vec3
, orbit
-- * Operations
-, Spear.Math.Vector3.min
-, Spear.Math.Vector3.max
, dot
, cross
, normSq
, norm
, scale
-, normalise
, neg
+, normalise
)
where
+
import Foreign.C.Types (CFloat)
import Foreign.Storable
@@ -73,6 +72,10 @@ instance Ord Vector3 where
|| (ax == bx && ay > by)
|| (ax == bx && ay == by && az > bz)
+ max (Vector3 ax ay az) (Vector3 bx by bz) = Vector3 (Prelude.max ax bx) (Prelude.max ay by) (Prelude.max az bz)
+
+ min (Vector3 ax ay az) (Vector3 bx by bz) = Vector3 (Prelude.min ax bx) (Prelude.min ay by) (Prelude.min az bz)
+
sizeFloat = sizeOf (undefined :: CFloat)
@@ -149,16 +152,6 @@ orbit center radius anglex angley =
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)
-
-
-- | 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
@@ -169,31 +162,26 @@ 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)
+-- | Negate the given vector.
+neg (Vector3 ax ay az) = Vector3 (-ax) (-ay) (-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
-
+ 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)
diff --git a/Spear/Math/Vector4.hs b/Spear/Math/Vector4.hs
index 9ba35bc..554fb27 100644
--- a/Spear/Math/Vector4.hs
+++ b/Spear/Math/Vector4.hs
@@ -1,183 +1,176 @@
-module Spear.Math.Vector4
-(
- Vector4
- -- * Accessors
-, x
-, y
-, z
-, w
- -- * Construction
-, unitX
-, unitY
-, unitZ
-, fromList
-, vec4
- -- * Operations
-, Spear.Math.Vector4.min
-, Spear.Math.Vector4.max
-, dot
-, normSq
-, norm
-, scale
-, normalise
-, neg
-)
-where
-
-
-import Foreign.C.Types (CFloat)
-import Foreign.Storable
-
-
--- | Represents a vector in 3D.
+module Spear.Math.Vector4
+(
+ Vector4
+ -- * Accessors
+, x
+, y
+, z
+, w
+ -- * Construction
+, unitX
+, unitY
+, unitZ
+, fromList
+, vec4
+ -- * Operations
+, dot
+, normSq
+, norm
+, scale
+, neg
+, normalise
+)
+where
+
+
+import Foreign.C.Types (CFloat)
+import Foreign.Storable
+
+
+-- | Represents a vector in 3D.
data Vector4 = Vector4
{-# UNPACK #-} !Float
{-# UNPACK #-} !Float
{-# UNPACK #-} !Float
{-# UNPACK #-} !Float
- deriving (Eq, Show)
-
-
-instance Num Vector4 where
- Vector4 ax ay az aw + Vector4 bx by bz bw = Vector4 (ax + bx) (ay + by) (az + bz) (aw + bw)
- Vector4 ax ay az aw - Vector4 bx by bz bw = Vector4 (ax - bx) (ay - by) (az - bz) (aw - bw)
- Vector4 ax ay az aw * Vector4 bx by bz bw = Vector4 (ax * bx) (ay * by) (az * bz) (aw * bw)
- abs (Vector4 ax ay az aw) = Vector4 (abs ax) (abs ay) (abs az) (abs aw)
- signum (Vector4 ax ay az aw) = Vector4 (signum ax) (signum ay) (signum az) (signum aw)
- fromInteger i = Vector4 i' i' i' i' where i' = fromInteger i
-
-
-instance Fractional Vector4 where
- Vector4 ax ay az aw / Vector4 bx by bz bw = Vector4 (ax / bx) (ay / by) (az / bz) (aw / bw)
- fromRational r = Vector4 r' r' r' r' where r' = fromRational r
-
-
-instance Ord Vector4 where
- Vector4 ax ay az aw <= Vector4 bx by bz bw
- = (ax <= bx)
- || (az == bx && ay <= by)
- || (ax == bx && ay == by && az <= bz)
- || (ax == bx && ay == by && az == bz && aw <= bw)
-
- Vector4 ax ay az aw >= Vector4 bx by bz bw
- = (ax >= bx)
- || (ax == bx && ay >= by)
- || (ax == bx && ay == by && az >= bz)
- || (ax == bx && ay == by && az == bz && aw >= bw)
-
- Vector4 ax ay az aw < Vector4 bx by bz bw
- = (ax < bx)
- || (az == bx && ay < by)
- || (ax == bx && ay == by && az < bz)
- || (ax == bx && ay == by && az == bz && aw < bw)
-
- Vector4 ax ay az aw > Vector4 bx by bz bw
- = (ax > bx)
- || (ax == bx && ay > by)
- || (ax == bx && ay == by && az > bz)
- || (ax == bx && ay == by && az == bz && aw > bw)
-
-
-sizeFloat = sizeOf (undefined :: CFloat)
-
-
-instance Storable Vector4 where
- sizeOf _ = 4*sizeFloat
- alignment _ = alignment (undefined :: CFloat)
-
- peek ptr = do
- ax <- peekByteOff ptr 0
- ay <- peekByteOff ptr $ 1 * sizeFloat
- az <- peekByteOff ptr $ 2 * sizeFloat
- aw <- peekByteOff ptr $ 3 * sizeFloat
- return (Vector4 ax ay az aw)
-
- poke ptr (Vector4 ax ay az aw) = do
- pokeByteOff ptr 0 ax
- pokeByteOff ptr (1 * sizeFloat) ay
- pokeByteOff ptr (2 * sizeFloat) az
- pokeByteOff ptr (3 * sizeFloat) aw
-
-
-x (Vector4 ax _ _ _ ) = ax
-y (Vector4 _ ay _ _ ) = ay
-z (Vector4 _ _ az _ ) = az
-w (Vector4 _ _ _ aw) = aw
-
-
--- | Unit vector along the X axis.
-unitX :: Vector4
-unitX = Vector4 1 0 0 0
-
-
--- | Unit vector along the Y axis.
-unitY :: Vector4
-unitY = Vector4 0 1 0 0
-
-
--- | Unit vector along the Z axis.
-unitZ :: Vector4
-unitZ = Vector4 0 0 1 0
-
-
--- | Create a vector from the given list.
-fromList :: [Float] -> Vector4
-fromList (ax:ay:az:aw:_) = Vector4 ax ay az aw
-
-
--- | Create a 4D vector from the given values.
-vec4 :: Float -> Float -> Float -> Float -> Vector4
-vec4 ax ay az aw = Vector4 ax ay az aw
-
-
--- | Create a vector whose components are the minimum of each of the given vectors'.
-min :: Vector4 -> Vector4 -> Vector4
-min (Vector4 ax ay az aw) (Vector4 bx by bz bw) =
- Vector4 (Prelude.min ax bx) (Prelude.min ay by) (Prelude.min az bz) (Prelude.min aw bw)
-
-
--- | Create a vector whose components are the maximum of each of the given vectors'.
-max :: Vector4 -> Vector4 -> Vector4
-max (Vector4 ax ay az aw) (Vector4 bx by bz bw) =
- Vector4 (Prelude.max ax bx) (Prelude.max ay by) (Prelude.max az bz) (Prelude.min aw bw)
-
-
--- | Compute the given vectors' dot product.
-dot :: Vector4 -> Vector4 -> Float
-Vector4 ax ay az aw `dot` Vector4 bx by bz bw = ax*bx + ay*by + az*bz + aw*bw
-
-
--- | Compute the given vectors' cross product.
--- The vectors are projected to 3D space. The resulting vector is the cross product of the vectors' projections with w=0.
-cross :: Vector4 -> Vector4 -> Vector4
-(Vector4 ax ay az _) `cross` (Vector4 bx by bz _) =
- Vector4 (ay * bz - az * by) (az * bx - ax * bz) (ax * by - ay * bx) 0
-
-
--- | Compute the given vector's squared norm.
-normSq :: Vector4 -> Float
-normSq (Vector4 ax ay az aw) = ax*ax + ay*ay + az*az + aw*aw
-
-
--- | Compute the given vector's norm.
-norm :: Vector4 -> Float
-norm = sqrt . normSq
-
-
--- | Multiply the given vector with the given scalar.
-scale :: Float -> Vector4 -> Vector4
-scale s (Vector4 ax ay az aw) = Vector4 (s*ax) (s*ay) (s*az) (s*aw)
-
-
--- | Normalise the given vector.
-normalise :: Vector4 -> Vector4
-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 :: Vector4 -> Vector4
-neg (Vector4 ax ay az aw) = Vector4 (-ax) (-ay) (-az) (-aw)
+ deriving (Eq, Show)
+
+
+instance Num Vector4 where
+ Vector4 ax ay az aw + Vector4 bx by bz bw = Vector4 (ax + bx) (ay + by) (az + bz) (aw + bw)
+ Vector4 ax ay az aw - Vector4 bx by bz bw = Vector4 (ax - bx) (ay - by) (az - bz) (aw - bw)
+ Vector4 ax ay az aw * Vector4 bx by bz bw = Vector4 (ax * bx) (ay * by) (az * bz) (aw * bw)
+ abs (Vector4 ax ay az aw) = Vector4 (abs ax) (abs ay) (abs az) (abs aw)
+ signum (Vector4 ax ay az aw) = Vector4 (signum ax) (signum ay) (signum az) (signum aw)
+ fromInteger i = Vector4 i' i' i' i' where i' = fromInteger i
+
+
+instance Fractional Vector4 where
+ Vector4 ax ay az aw / Vector4 bx by bz bw = Vector4 (ax / bx) (ay / by) (az / bz) (aw / bw)
+ fromRational r = Vector4 r' r' r' r' where r' = fromRational r
+
+
+instance Ord Vector4 where
+ Vector4 ax ay az aw <= Vector4 bx by bz bw
+ = (ax <= bx)
+ || (az == bx && ay <= by)
+ || (ax == bx && ay == by && az <= bz)
+ || (ax == bx && ay == by && az == bz && aw <= bw)
+
+ Vector4 ax ay az aw >= Vector4 bx by bz bw
+ = (ax >= bx)
+ || (ax == bx && ay >= by)
+ || (ax == bx && ay == by && az >= bz)
+ || (ax == bx && ay == by && az == bz && aw >= bw)
+
+ Vector4 ax ay az aw < Vector4 bx by bz bw
+ = (ax < bx)
+ || (az == bx && ay < by)
+ || (ax == bx && ay == by && az < bz)
+ || (ax == bx && ay == by && az == bz && aw < bw)
+
+ Vector4 ax ay az aw > Vector4 bx by bz bw
+ = (ax > bx)
+ || (ax == bx && ay > by)
+ || (ax == bx && ay == by && az > bz)
+ || (ax == bx && ay == by && az == bz && aw > bw)
+
+ min (Vector4 ax ay az aw) (Vector4 bx by bz bw) =
+ Vector4 (Prelude.min ax bx) (Prelude.min ay by) (Prelude.min az bz) (Prelude.min aw bw)
+
+ max (Vector4 ax ay az aw) (Vector4 bx by bz bw) =
+ Vector4 (Prelude.max ax bx) (Prelude.max ay by) (Prelude.max az bz) (Prelude.min aw bw)
+
+
+sizeFloat = sizeOf (undefined :: CFloat)
+
+
+instance Storable Vector4 where
+ sizeOf _ = 4*sizeFloat
+ alignment _ = alignment (undefined :: CFloat)
+
+ peek ptr = do
+ ax <- peekByteOff ptr 0
+ ay <- peekByteOff ptr $ 1 * sizeFloat
+ az <- peekByteOff ptr $ 2 * sizeFloat
+ aw <- peekByteOff ptr $ 3 * sizeFloat
+ return (Vector4 ax ay az aw)
+
+ poke ptr (Vector4 ax ay az aw) = do
+ pokeByteOff ptr 0 ax
+ pokeByteOff ptr (1 * sizeFloat) ay
+ pokeByteOff ptr (2 * sizeFloat) az
+ pokeByteOff ptr (3 * sizeFloat) aw
+
+
+x (Vector4 ax _ _ _ ) = ax
+y (Vector4 _ ay _ _ ) = ay
+z (Vector4 _ _ az _ ) = az
+w (Vector4 _ _ _ aw) = aw
+
+
+-- | Unit vector along the X axis.
+unitX :: Vector4
+unitX = Vector4 1 0 0 0
+
+
+-- | Unit vector along the Y axis.
+unitY :: Vector4
+unitY = Vector4 0 1 0 0
+
+
+-- | Unit vector along the Z axis.
+unitZ :: Vector4
+unitZ = Vector4 0 0 1 0
+
+
+-- | Create a vector from the given list.
+fromList :: [Float] -> Vector4
+fromList (ax:ay:az:aw:_) = Vector4 ax ay az aw
+
+
+-- | Create a 4D vector from the given values.
+vec4 :: Float -> Float -> Float -> Float -> Vector4
+vec4 ax ay az aw = Vector4 ax ay az aw
+
+
+-- | Compute the given vectors' dot product.
+dot :: Vector4 -> Vector4 -> Float
+Vector4 ax ay az aw `dot` Vector4 bx by bz bw = ax*bx + ay*by + az*bz + aw*bw
+
+
+-- | Compute the given vectors' cross product.
+-- The vectors are projected to 3D space. The resulting vector is the cross product of the vectors' projections with w=0.
+cross :: Vector4 -> Vector4 -> Vector4
+(Vector4 ax ay az _) `cross` (Vector4 bx by bz _) =
+ Vector4 (ay * bz - az * by) (az * bx - ax * bz) (ax * by - ay * bx) 0
+
+
+-- | Compute the given vector's squared norm.
+normSq :: Vector4 -> Float
+normSq (Vector4 ax ay az aw) = ax*ax + ay*ay + az*az + aw*aw
+
+
+-- | Compute the given vector's norm.
+norm :: Vector4 -> Float
+norm = sqrt . normSq
+
+
+-- | Multiply the given vector with the given scalar.
+scale :: Float -> Vector4 -> Vector4
+scale s (Vector4 ax ay az aw) = Vector4 (s*ax) (s*ay) (s*az) (s*aw)
+
+
+-- | Negate the given vector.
+neg :: Vector4 -> Vector4
+neg (Vector4 ax ay az aw) = Vector4 (-ax) (-ay) (-az) (-aw)
+
+
+-- | Normalise the given vector.
+normalise :: Vector4 -> Vector4
+normalise v =
+ let n' = norm v
+ n = if n' == 0 then 1 else n'
+ in
+ scale (1.0 / n) v
+
--
cgit v1.2.3