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|
{-# LANGUAGE MultiParamTypeClasses #-}
module Graphics.Glyph.GLMath where
import Data.Angle
import Debug.Trace
import Graphics.Glyph.Mat4
import Graphics.Rendering.OpenGL (GLfloat, Uniform, UniformComponent, Vertex3 (..), uniform)
import qualified Graphics.Rendering.OpenGL as GL
data Vec2 a = Vec2 (a, a) deriving (Show)
data Vec3 a = Vec3 (a, a, a) deriving (Show)
data Vec4 a = Vec4 (a, a, a, a) deriving (Show)
instance UniformComponent a => Uniform (Vec3 a) where
uniform loc =
GL.makeStateVar
( do
(Vertex3 x y z) <-
GL.get (uniform loc)
return (Vec3 (x, y, z))
)
(\(Vec3 (x, y, z)) -> uniform loc GL.$= Vertex3 x y z)
class (Floating flT) => Vector flT b where
(<+>) :: b flT -> b flT -> b flT
(<->) :: b flT -> b flT -> b flT
norm :: b flT -> flT
normalize :: b flT -> b flT
vDot :: b flT -> b flT -> flT
vScale :: flT -> b flT -> b flT
(<.>) :: (Vector a b) => b a -> b a -> a
(<.>) = vDot
(|||) :: (Vector a b) => b a -> a
(|||) = norm
instance (Floating flT) => Vector flT Vec2 where
(<+>) (Vec2 (a, b)) (Vec2 (c, d)) = Vec2 (a + c, b + d)
(<->) (Vec2 (a, b)) (Vec2 (c, d)) = Vec2 (a - c, b - d)
vDot (Vec2 (a, b)) (Vec2 (c, d)) = a * c + b * d
vScale c (Vec2 (a, b)) = Vec2 (a * c, b * c)
norm (Vec2 (a, b)) = sqrt (a * a + b * b)
normalize vec@(Vec2 (a, b)) =
let n = norm vec in Vec2 (a / n, b / n)
instance (Floating flT) => Vector flT Vec3 where
(<+>) (Vec3 (a, b, c)) (Vec3 (d, e, f)) = Vec3 (a + d, b + e, c + f)
(<->) (Vec3 (a, b, c)) (Vec3 (d, e, f)) = Vec3 (a - d, b - e, c - f)
vDot (Vec3 (a, b, c)) (Vec3 (d, e, f)) = a * d + b * e + c * f
vScale x (Vec3 (a, b, c)) = Vec3 (a * x, b * x, c * x)
norm (Vec3 (a, b, c)) = sqrt (a * a + b * b + c * c)
normalize vec@(Vec3 (a, b, c)) =
let n = norm vec in Vec3 (a / n, b / n, c / n)
instance (Floating flT) => Vector flT Vec4 where
(<+>) (Vec4 (a, b, c, g)) (Vec4 (d, e, f, h)) = Vec4 (a + d, b + e, c + f, g + h)
(<->) (Vec4 (a, b, c, g)) (Vec4 (d, e, f, h)) = Vec4 (a - d, b - e, c - f, g - h)
vDot (Vec4 (a, b, c, g)) (Vec4 (d, e, f, h)) = a * d + b * e + c * f + g * h
vScale x (Vec4 (a, b, c, d)) = Vec4 (a * x, b * x, c * x, d * x)
norm (Vec4 (a, b, c, d)) = sqrt (a * a + b * b + c * c + d * d)
normalize vec@(Vec4 (a, b, c, d)) =
let n = norm vec in Vec4 (a / n, b / n, c / n, d / n)
cross :: (Num a) => Vec3 a -> Vec3 a -> Vec3 a
cross (Vec3 (u1, u2, u3)) (Vec3 (v1, v2, v3)) =
Vec3
( u2 * v3 - u3 * v2,
u3 * v1 - u1 * v3,
u1 * v2 - u2 * v1
)
(×) :: (Num a) => Vec3 a -> Vec3 a -> Vec3 a
(×) = cross
lookAtMatrix :: Vec3 GLfloat -> Vec3 GLfloat -> Vec3 GLfloat -> Mat4 GLfloat
lookAtMatrix e@(Vec3 (ex, ey, ez)) c u =
let f@(Vec3 (fx, fy, fz)) = normalize (c <-> e)
s@(Vec3 (sx, sy, sz)) = normalize (f × u)
u'@(Vec3 (ux, uy, uz)) = s × f
in Matrix
( sx,
ux,
- fx,
0,
sy,
uy,
- fy,
0,
sz,
uz,
- fz,
0,
- (s <.> e),
- (u' <.> e),
(f <.> e),
1
)
perspectiveMatrix :: GLfloat -> GLfloat -> GLfloat -> GLfloat -> Mat4 GLfloat
{- as close to copied from glm as possible -}
perspectiveMatrix fov asp zn zf =
let tanHalfFovy = tangent (Degrees fov / 2)
res00 = 1 / (asp * tanHalfFovy)
res11 = 1 / tanHalfFovy
res22 = - (zf + zn) / (zf - zn)
res23 = - 1
res32 = - (2 * zf * zn) / (zf - zn)
in trace ("res22=" ++ (show res22)) $
Matrix
( res00,
0,
0,
0,
0,
res11,
0,
0,
0,
0,
res22,
res23,
0,
0,
res32,
0
)
class VectorMatrix vecT matT where
vTranslate :: matT -> vecT -> matT
(-*|) :: matT -> vecT -> vecT
instance (Num a) => VectorMatrix (Vec3 a) (Mat3 a) where
vTranslate
( Matrix3
( a00,
a01,
a02,
a10,
a11,
a12,
a20,
a21,
a22
)
)
(Vec3 (a, b, c)) =
Matrix3
( a00,
a01,
a02 + a,
a10,
a11,
a12 + b,
a20,
a21,
a22 + c
)
( Matrix3
( a00,
a01,
a02,
a10,
a11,
a12,
a20,
a21,
a22
)
)
-*| (Vec3 (a, b, c)) =
Vec3
( a00 * a + a01 * b + a02 * c,
a10 * a + a11 * b + a12 * c,
a20 * a + a21 * b + a22 * c
)
instance (Num a) => VectorMatrix (Vec4 a) (Mat4 a) where
vTranslate mat (Vec4 tmp) = translateMat4 mat tmp
mat -*| tmp = glslMatMul mat tmp
glslMatMul :: (Num a) => Mat4 a -> Vec4 a -> Vec4 a
glslMatMul
( Matrix
( m00,
m01,
m02,
m03,
m10,
m11,
m12,
m13,
m20,
m21,
m22,
m23,
m30,
m31,
m32,
m33
)
)
(Vec4 (v0, v1, v2, v3)) =
Vec4
( v0 * m00 + v1 * m10 + v2 * m20 + v3 * m30,
v0 * m01 + v1 * m11 + v2 * m21 + v3 * m31,
v0 * m02 + v1 * m12 + v2 * m22 + v3 * m32,
v0 * m03 + v1 * m13 + v2 * m23 + v3 * m33
)
(==>) :: (Num a) => Mat4 a -> Vec4 a -> Mat4 a
(==>) = glslMatTranslate
glslMatTranslate :: (Num a) => Mat4 a -> Vec4 a -> Mat4 a
glslMatTranslate
mat@( Matrix
( m00,
m01,
m02,
m03,
m10,
m11,
m12,
m13,
m20,
m21,
m22,
m23,
m30,
m31,
m32,
m33
)
)
vec =
let (Vec4 (v0, v1, v2, v3)) = mat -*| vec
in ( Matrix
( m00,
m01,
m02,
m03,
m10,
m11,
m12,
m13,
m20,
m21,
m22,
m23,
m30 + v0,
m31 + v1,
m32 + v2,
m33 + v3
)
)
|
