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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
module Graphics.Glyph.GLMath where
import Graphics.Glyph.Mat4
import qualified Graphics.Rendering.OpenGL as GL
import Graphics.Rendering.OpenGL (GLfloat,Uniform,Vertex3(..),uniform,UniformComponent)
import Data.Angle
import Data.Maybe
import Debug.Trace
data Vec2 a = Vec2 (a,a) deriving (Show,Eq)
data Vec3 a = Vec3 (a,a,a) deriving (Show,Eq)
data Vec4 a = Vec4 (a,a,a,a) deriving (Show,Eq)
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)
uniformv _ = undefined
instance UniformComponent a => Uniform (Vec4 a) where
uniform loc = GL.makeStateVar
(do
(GL.Vertex4 x y z w) <-
GL.get (uniform loc)
return (Vec4 (x,y,z,w)) )
(\(Vec4 (x,y,z,w)) -> uniform loc GL.$= GL.Vertex4 x y z w)
uniformv _ = undefined
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
vNegate :: 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)
vNegate (Vec2 (a,b)) = Vec2 (-a,-b)
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)
vNegate (Vec3 (a,b,c)) = Vec3 (-a,-b,-c)
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)
vNegate (Vec4 (a,b,c,d)) = Vec4 (-a,-b,-c,-d)
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 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
Matrix4 (sx, ux, -fx, 0,
sy, uy, -fy, 0,
sz, uz, -fz, 0,
-(s<.>e) , -(u'<.>e), f<.>e, 1 )
orthoMatrix :: GLfloat -> GLfloat -> GLfloat -> GLfloat -> GLfloat -> GLfloat -> Mat4 GLfloat
orthoMatrix top bot right left near far =
Matrix4 (2 / (right-left), 0, 0, - (right + left) / (right - left),
0, 2 / (top-bot), 0, - (top+bot) / (top-bot),
0, 0, -2 / (far-near), - (far+near) / (far - near),
0, 0, 0, 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) $
Matrix4 (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 (Matrix4 (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 )
glslModelViewToNormalMatrix :: Mat4 GLfloat -> Mat3 GLfloat
glslModelViewToNormalMatrix = fromJust.inverse.transpose.trunc4
(==>) :: (Num a) => Mat4 a -> Vec4 a -> Mat4 a
(==>) = glslMatTranslate
glslMatTranslate :: (Num a) => Mat4 a -> Vec4 a -> Mat4 a
glslMatTranslate
mat@(Matrix4 (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
Matrix4 (m00,m01,m02,m03,
m10,m11,m12,m13,
m20,m21,m22,m23,
m30+v0,m31+v1,m32+v2,m33+v3)
rotationMatrix :: GLfloat -> Vec3 GLfloat -> Mat3 GLfloat
rotationMatrix ang (Vec3 (u,v,w)) =
let l = (u*u + v*v + w*w)
u2 = u*u
v2 = v*v
w2 = w*w in
Matrix3 (
(u2 + (v2 + w2) * cos(ang)) / l,
(u * v * (1 - cos(ang)) - w * sqrt(l) * sin(ang)) / l,
(u * w * (1 - cos(ang)) + v * sqrt(l) * sin(ang)) / l,
(u * v * (1 - cos(ang)) + w * sqrt(l) * sin(ang)) / l,
(v2 + (u2 + w2) * cos(ang)) / l,
(v * w * (1 - cos(ang)) - u * sqrt(l) * sin(ang)) / l,
(u * w * (1 - cos(ang)) - v * sqrt(l) * sin(ang)) / l,
(v * w * (1 - cos(ang)) + u * sqrt(l) * sin(ang)) / l,
(w2 + (u2 + v2) * cos(ang)) / l
)
zRotationMatrix :: GLfloat -> Mat3 GLfloat
zRotationMatrix ang = rotationMatrix ang (Vec3 (0,0,1))
maybeNormalize :: (Vector f a, Eq f) => a f -> a f
maybeNormalize x = if norm x == 0 then x else normalize x
coordinateConvert :: Vec3 GLfloat -> Vec3 GLfloat -> Vec3 GLfloat -> Vec3 GLfloat
coordinateConvert forward up' vector =
if vector == Vec3 (0,0,0) then vector else
let right = forward × up'
up = right × forward in
case (normalize forward, normalize up, normalize right, vector) of
(za,ya,xa,Vec3 (x,y,z)) -> (x `vScale` xa) <+> (y `vScale` ya) <+> (z `vScale` za)
rotateFrom :: Vec3 GLfloat -> Vec3 GLfloat -> Vec3 GLfloat -> Vec3 GLfloat
rotateFrom vector relative newRelative =
if vector == Vec3 (0,0,0) then vector else
case (normalize relative, normalize newRelative) of
(r', n') ->
if r' == n' then vector else
let axis = r' × n'
ang = acos $ r' `vDot` n' in
rotationMatrix ang axis -*| vector
|
