module Nonlinear.Projective.Hom3 where
import Nonlinear.Internal (Lens')
import Nonlinear.Matrix
import Nonlinear.Quaternion
import Nonlinear.V3
import Nonlinear.V4
import Nonlinear.Vector
m43_to_m44 :: Num a => M43 a -> M44 a
m43_to_m44 :: M43 a -> M44 a
m43_to_m44
( V4
(V3 a
a a
b a
c)
(V3 a
d a
e a
f)
(V3 a
g a
h a
i)
(V3 a
j a
k a
l)
) =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
d a
e a
f a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
g a
h a
i a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
j a
k a
l a
1)
vector :: Num a => V3 a -> V4 a
vector :: V3 a -> V4 a
vector (V3 a
a a
b a
c) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
0
{-# INLINE vector #-}
point :: Num a => V3 a -> V4 a
point :: V3 a -> V4 a
point (V3 a
a a
b a
c) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c a
1
{-# INLINE point #-}
normalizePoint :: Fractional a => V4 a -> V3 a
normalizePoint :: V4 a -> V3 a
normalizePoint (V4 a
a a
b a
c a
w) = (a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
w) a -> V3 a -> V3 a
forall (f :: * -> *) a. (Vec f, Num a) => a -> f a -> f a
*^ a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a a
b a
c
{-# INLINE normalizePoint #-}
m33_to_m44 :: Num a => M33 a -> M44 a
m33_to_m44 :: M33 a -> M44 a
m33_to_m44 (V3 V3 a
r1 V3 a
r2 V3 a
r3) = V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4 (V3 a -> V4 a
forall a. Num a => V3 a -> V4 a
vector V3 a
r1) (V3 a -> V4 a
forall a. Num a => V3 a -> V4 a
vector V3 a
r2) (V3 a -> V4 a
forall a. Num a => V3 a -> V4 a
vector V3 a
r3) (V3 a -> V4 a
forall a. Num a => V3 a -> V4 a
point V3 a
0)
translation :: (Vec t, R3 t, R4 v) => Lens' (t (v a)) (V3 a)
translation :: Lens' (t (v a)) (V3 a)
translation = Lens' (v a) a -> Lens' (t (v a)) (t a)
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) a
forall (t :: * -> *) a. R4 t => Lens' (t a) a
_w ((t a -> m (t a)) -> t (v a) -> m (t (v a)))
-> ((V3 a -> m (V3 a)) -> t a -> m (t a))
-> (V3 a -> m (V3 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (V3 a -> m (V3 a)) -> t a -> m (t a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz
mkTransformationMat :: Num a => M33 a -> V3 a -> M44 a
mkTransformationMat :: M33 a -> V3 a -> M44 a
mkTransformationMat (V3 V3 a
r1 V3 a
r2 V3 a
r3) (V3 a
tx a
ty a
tz) =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4 (V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 V3 a
r1 a
tx) (V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 V3 a
r2 a
ty) (V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 V3 a
r3 a
tz) (a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 a
1)
where
snoc3 :: V3 a -> a -> V4 a
snoc3 (V3 a
x a
y a
z) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
y a
z
{-# INLINE mkTransformationMat #-}
mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a
mkTransformation :: Quaternion a -> V3 a -> M44 a
mkTransformation = M33 a -> V3 a -> M44 a
forall a. Num a => M33 a -> V3 a -> M44 a
mkTransformationMat (M33 a -> V3 a -> M44 a)
-> (Quaternion a -> M33 a) -> Quaternion a -> V3 a -> M44 a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Quaternion a -> M33 a
forall a. Num a => Quaternion a -> M33 a
fromQuaternion
{-# INLINE mkTransformation #-}
{-# SPECIALIZE lookAt :: V3 Float -> V3 Float -> V3 Float -> M44 Float #-}
{-# SPECIALIZE lookAt :: V3 Double -> V3 Double -> V3 Double -> M44 Double #-}
lookAt ::
(Floating a) =>
V3 a ->
V3 a ->
V3 a ->
M44 a
lookAt :: V3 a -> V3 a -> V3 a -> M44 a
lookAt V3 a
eye V3 a
center V3 a
up =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 V3 a
xa a
xd)
(V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 V3 a
ya a
yd)
(V3 a -> a -> V4 a
forall a. V3 a -> a -> V4 a
snoc3 (-V3 a
za) a
zd)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 a
1)
where
snoc3 :: V3 a -> a -> V4 a
snoc3 (V3 a
a a
b a
c) = a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
b a
c
za :: V3 a
za = V3 a -> V3 a
forall (f :: * -> *) a. (Vec f, Floating a) => f a -> f a
normalize (V3 a -> V3 a) -> V3 a -> V3 a
forall a b. (a -> b) -> a -> b
$ V3 a
center V3 a -> V3 a -> V3 a
forall a. Num a => a -> a -> a
- V3 a
eye
xa :: V3 a
xa = V3 a -> V3 a
forall (f :: * -> *) a. (Vec f, Floating a) => f a -> f a
normalize (V3 a -> V3 a) -> V3 a -> V3 a
forall a b. (a -> b) -> a -> b
$ V3 a -> V3 a -> V3 a
forall a. Num a => V3 a -> V3 a -> V3 a
cross V3 a
za V3 a
up
ya :: V3 a
ya = V3 a -> V3 a -> V3 a
forall a. Num a => V3 a -> V3 a -> V3 a
cross V3 a
xa V3 a
za
xd :: a
xd = -V3 a -> V3 a -> a
forall (f :: * -> *) a. (Vec f, Num a) => f a -> f a -> a
dot V3 a
xa V3 a
eye
yd :: a
yd = -V3 a -> V3 a -> a
forall (f :: * -> *) a. (Vec f, Num a) => f a -> f a -> a
dot V3 a
ya V3 a
eye
zd :: a
zd = V3 a -> V3 a -> a
forall (f :: * -> *) a. (Vec f, Num a) => f a -> f a -> a
dot V3 a
za V3 a
eye
{-# SPECIALIZE perspective :: Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE perspective :: Double -> Double -> Double -> Double -> M44 Double #-}
perspective ::
Floating a =>
a ->
a ->
a ->
a ->
M44 a
perspective :: a -> a -> a -> a -> M44 a
perspective a
fovy a
aspect a
near a
far =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
0 a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
y a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
z a
w)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 (-a
1) a
0)
where
tanHalfFovy :: a
tanHalfFovy = a -> a
forall a. Floating a => a -> a
tan (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ a
fovy a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
2
x :: a
x = a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ (a
aspect a -> a -> a
forall a. Num a => a -> a -> a
* a
tanHalfFovy)
y :: a
y = a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
tanHalfFovy
fpn :: a
fpn = a
far a -> a -> a
forall a. Num a => a -> a -> a
+ a
near
fmn :: a
fmn = a
far a -> a -> a
forall a. Num a => a -> a -> a
- a
near
oon :: a
oon = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
near
oof :: a
oof = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
far
z :: a
z = -a
fpn a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
fmn
w :: a
w = a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ (a
oof a -> a -> a
forall a. Num a => a -> a -> a
- a
oon)
{-# SPECIALIZE inversePerspective :: Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE inversePerspective :: Double -> Double -> Double -> Double -> M44 Double #-}
inversePerspective ::
Floating a =>
a ->
a ->
a ->
a ->
M44 a
inversePerspective :: a -> a -> a -> a -> M44 a
inversePerspective a
fovy a
aspect a
near a
far =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
a a
0 a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
b a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 (-a
1))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
c a
d)
where
tanHalfFovy :: a
tanHalfFovy = a -> a
forall a. Floating a => a -> a
tan (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ a
fovy a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
2
a :: a
a = a
aspect a -> a -> a
forall a. Num a => a -> a -> a
* a
tanHalfFovy
b :: a
b = a
tanHalfFovy
c :: a
c = a
oon a -> a -> a
forall a. Num a => a -> a -> a
- a
oof
d :: a
d = a
oon a -> a -> a
forall a. Num a => a -> a -> a
+ a
oof
oon :: a
oon = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
near
oof :: a
oof = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
far
{-# SPECIALIZE frustum :: Float -> Float -> Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE frustum :: Double -> Double -> Double -> Double -> Double -> Double -> M44 Double #-}
frustum ::
Floating a =>
a ->
a ->
a ->
a ->
a ->
a ->
M44 a
frustum :: a -> a -> a -> a -> a -> a -> M44 a
frustum a
l a
r a
b a
t a
n a
f =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
0 a
a a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
y a
e a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
c a
d)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 (-a
1) a
0)
where
rml :: a
rml = a
r a -> a -> a
forall a. Num a => a -> a -> a
- a
l
tmb :: a
tmb = a
t a -> a -> a
forall a. Num a => a -> a -> a
- a
b
fmn :: a
fmn = a
f a -> a -> a
forall a. Num a => a -> a -> a
- a
n
x :: a
x = a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
n a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
rml
y :: a
y = a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
n a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
tmb
a :: a
a = (a
r a -> a -> a
forall a. Num a => a -> a -> a
+ a
l) a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
rml
e :: a
e = (a
t a -> a -> a
forall a. Num a => a -> a -> a
+ a
b) a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
tmb
c :: a
c = a -> a
forall a. Num a => a -> a
negate (a
f a -> a -> a
forall a. Num a => a -> a -> a
+ a
n) a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
fmn
d :: a
d = (-a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
f a -> a -> a
forall a. Num a => a -> a -> a
* a
n) a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
fmn
{-# SPECIALIZE inverseFrustum :: Float -> Float -> Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE inverseFrustum :: Double -> Double -> Double -> Double -> Double -> Double -> M44 Double #-}
inverseFrustum ::
Floating a =>
a ->
a ->
a ->
a ->
a ->
a ->
M44 a
inverseFrustum :: a -> a -> a -> a -> a -> a -> M44 a
inverseFrustum a
l a
r a
b a
t a
n a
f =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
rx a
0 a
0 a
ax)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
ry a
0 a
by)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 (-a
1))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
rd a
cd)
where
hrn :: a
hrn = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
n
hrnf :: a
hrnf = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ (a
n a -> a -> a
forall a. Num a => a -> a -> a
* a
f)
rx :: a
rx = (a
r a -> a -> a
forall a. Num a => a -> a -> a
- a
l) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
ry :: a
ry = (a
t a -> a -> a
forall a. Num a => a -> a -> a
- a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
ax :: a
ax = (a
r a -> a -> a
forall a. Num a => a -> a -> a
+ a
l) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
by :: a
by = (a
t a -> a -> a
forall a. Num a => a -> a -> a
+ a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
cd :: a
cd = (a
f a -> a -> a
forall a. Num a => a -> a -> a
+ a
n) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrnf
rd :: a
rd = (a
n a -> a -> a
forall a. Num a => a -> a -> a
- a
f) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrnf
{-# SPECIALIZE infinitePerspective :: Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE infinitePerspective :: Double -> Double -> Double -> M44 Double #-}
infinitePerspective ::
Floating a =>
a ->
a ->
a ->
M44 a
infinitePerspective :: a -> a -> a -> M44 a
infinitePerspective a
fovy a
a a
n =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
0 a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
y a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 (-a
1) a
w)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 (-a
1) a
0)
where
t :: a
t = a
n a -> a -> a
forall a. Num a => a -> a -> a
* a -> a
forall a. Floating a => a -> a
tan (a
fovy a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
2)
b :: a
b = -a
t
l :: a
l = a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
a
r :: a
r = a
t a -> a -> a
forall a. Num a => a -> a -> a
* a
a
x :: a
x = (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
n) a -> a -> a
forall a. Fractional a => a -> a -> a
/ (a
r a -> a -> a
forall a. Num a => a -> a -> a
- a
l)
y :: a
y = (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
n) a -> a -> a
forall a. Fractional a => a -> a -> a
/ (a
t a -> a -> a
forall a. Num a => a -> a -> a
- a
b)
w :: a
w = -a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
n
{-# SPECIALIZE inverseInfinitePerspective :: Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE inverseInfinitePerspective :: Double -> Double -> Double -> M44 Double #-}
inverseInfinitePerspective ::
Floating a =>
a ->
a ->
a ->
M44 a
inverseInfinitePerspective :: a -> a -> a -> M44 a
inverseInfinitePerspective a
fovy a
a a
n =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
rx a
0 a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
ry a
0 a
0)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 (-a
1))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
rw (-a
rw))
where
t :: a
t = a
n a -> a -> a
forall a. Num a => a -> a -> a
* a -> a
forall a. Floating a => a -> a
tan (a
fovy a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
2)
b :: a
b = -a
t
l :: a
l = a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
a
r :: a
r = a
t a -> a -> a
forall a. Num a => a -> a -> a
* a
a
hrn :: a
hrn = a
0.5 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
n
rx :: a
rx = (a
r a -> a -> a
forall a. Num a => a -> a -> a
- a
l) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
ry :: a
ry = (a
t a -> a -> a
forall a. Num a => a -> a -> a
- a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
hrn
rw :: a
rw = -a
hrn
{-# SPECIALIZE ortho :: Float -> Float -> Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE ortho :: Double -> Double -> Double -> Double -> Double -> Double -> M44 Double #-}
ortho ::
Fractional a =>
a ->
a ->
a ->
a ->
a ->
a ->
M44 a
ortho :: a -> a -> a -> a -> a -> a -> M44 a
ortho a
l a
r a
b a
t a
n a
f =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 (-a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
x) a
0 a
0 ((a
r a -> a -> a
forall a. Num a => a -> a -> a
+ a
l) a -> a -> a
forall a. Num a => a -> a -> a
* a
x))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 (-a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
y) a
0 ((a
t a -> a -> a
forall a. Num a => a -> a -> a
+ a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
y))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* a
z) ((a
f a -> a -> a
forall a. Num a => a -> a -> a
+ a
n) a -> a -> a
forall a. Num a => a -> a -> a
* a
z))
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 a
1)
where
x :: a
x = a -> a
forall a. Fractional a => a -> a
recip (a
l a -> a -> a
forall a. Num a => a -> a -> a
- a
r)
y :: a
y = a -> a
forall a. Fractional a => a -> a
recip (a
b a -> a -> a
forall a. Num a => a -> a -> a
- a
t)
z :: a
z = a -> a
forall a. Fractional a => a -> a
recip (a
n a -> a -> a
forall a. Num a => a -> a -> a
- a
f)
{-# SPECIALIZE inverseOrtho :: Float -> Float -> Float -> Float -> Float -> Float -> M44 Float #-}
{-# SPECIALIZE inverseOrtho :: Double -> Double -> Double -> Double -> Double -> Double -> M44 Double #-}
inverseOrtho ::
Fractional a =>
a ->
a ->
a ->
a ->
a ->
a ->
M44 a
inverseOrtho :: a -> a -> a -> a -> a -> a -> M44 a
inverseOrtho a
l a
r a
b a
t a
n a
f =
V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
x a
0 a
0 a
c)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
y a
0 a
d)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
z a
e)
(a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4 a
0 a
0 a
0 a
1)
where
x :: a
x = a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
r a -> a -> a
forall a. Num a => a -> a -> a
- a
l)
y :: a
y = a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
t a -> a -> a
forall a. Num a => a -> a -> a
- a
b)
z :: a
z = a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
n a -> a -> a
forall a. Num a => a -> a -> a
- a
f)
c :: a
c = a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
l a -> a -> a
forall a. Num a => a -> a -> a
+ a
r)
d :: a
d = a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
b a -> a -> a
forall a. Num a => a -> a -> a
+ a
t)
e :: a
e = -a
0.5 a -> a -> a
forall a. Num a => a -> a -> a
* (a
n a -> a -> a
forall a. Num a => a -> a -> a
+ a
f)