1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
|
{-# LANGUAGE MultiParamTypeClasses #-}
module Graphics.Glyph.Mat4 where
import Control.Monad
import Foreign.Marshal.Alloc
import Foreign.Marshal.Array
import Foreign.Ptr
import Foreign.Storable
import Graphics.Rendering.OpenGL (Uniform(..),uniform,UniformLocation(..),makeStateVar)
import Graphics.Rendering.OpenGL.Raw.Core31
data Mat4 a = Matrix4 (a,a,a,a,
a,a,a,a,
a,a,a,a,
a,a,a,a) | IdentityMatrix
data Mat3 a = Matrix3 ( a,a,a,
a,a,a,
a,a,a ) | IdentityMatrix3
class StorableMatrix t a where
fromList :: [t] -> a t
toPtr :: a t -> (Ptr t -> IO b) -> IO b
fromPtr :: Ptr t -> (a t -> IO b) -> IO b
class Mat a where
inverse :: a -> Maybe a
transpose :: a -> a
determinate :: a -> Double
scale :: (Real b) => b -> a -> a
instance (RealFloat a,Eq a) => Mat (Mat4 a) where
inverse = inv4
transpose = transpose4
determinate = det4
scale b = scale4 (realToFrac b)
instance (RealFloat a,Eq a) => Mat (Mat3 a) where
transpose
(Matrix3 (a00,a01,a02,
a10,a11,a12,
a20,a21,a22)) = Matrix3 (a00,a10,a20,a01,a11,a21,a02,a12,a22)
determinate
(Matrix3 (a11,a12,a13,a21,a22,a23,a31,a32,a33)) =
realToFrac $
a11*a22*a33+a21*a32*a13+a31*a12*a23-a11*a32*a23-a31*a22*a13-a21*a12*a33
scale n' (Matrix3 (m11,m12,m13,m21,m22,m23,m31,m32,m33)) =
let n = realToFrac n' in
Matrix3 (m11*n,m12*n,m13*n,m21*n,m22*n,m23*n,m31*n,m32*n,m33*n)
inverse
m@(Matrix3 (a11,a12,a13,a21,a22,a23,a31,a32,a33)) =
let det = determinate m in
if det == 0 then Nothing else Just $
(1 / determinate m) `scale` Matrix3 (
a22*a33 - a23*a32, a13*a32 - a12*a33, a12*a23 - a13*a22,
a23*a31 - a21*a33, a11*a33 - a13*a31, a13*a21 - a11*a23,
a21*a32 - a22*a31, a12*a31 - a11*a32, a11*a22 - a12*a21)
instance (Storable t) => StorableMatrix t Mat4 where
fromList (m1:m2:m3:m4:m5:m6:m7:m8:m9:m10:m11:m12:m13:m14:m15:m16:_) =
Matrix4 (m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15,m16)
toPtr (Matrix4 (m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15,m16)) fun =
allocaArray 16 $ \ptr -> do
pokeArray ptr [m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15,m16]
fun ptr
fromPtr ptr f = peekArray 16 ptr >>= f . fromList
instance (Storable t) => StorableMatrix t Mat3 where
fromList (m1:m2:m3:m4:m5:m6:m7:m8:m9:_) =
Matrix3 (m1,m2,m3,m4,m5,m6,m7,m8,m9)
toPtr (Matrix3 (m1,m2,m3,m4,m5,m6,m7,m8,m9)) fun =
allocaArray 9 $ \ptr -> do
pokeArray ptr [m1,m2,m3,m4,m5,m6,m7,m8,m9]
fun ptr
fromPtr ptr f = peekArray 9 ptr >>= f . fromList
instance Uniform (Mat4 GLfloat) where
uniform (UniformLocation loc) = makeStateVar getter setter
where setter mat = toPtr mat $ \ptr ->
glUniformMatrix4fv loc 1 (fromIntegral gl_FALSE) ptr
getter :: IO (Mat4 GLfloat)
getter = do
pid <- liftM fromIntegral getCurrentProgram
allocaArray 16 $ \buf -> do
glGetUniformfv pid loc buf
fromPtr buf return
uniformv _ = undefined
instance Uniform (Mat3 GLfloat) where
uniform (UniformLocation loc) = makeStateVar getter setter
where setter mat = toPtr mat $ \ptr ->
glUniformMatrix3fv loc 1 (fromIntegral gl_FALSE) ptr
getter :: IO (Mat3 GLfloat)
getter = do
pid <- liftM fromIntegral getCurrentProgram
allocaArray 9 $ \buf -> do
glGetUniformfv pid loc buf
fromPtr buf return
uniformv _ = undefined
getCurrentProgram :: IO GLint
getCurrentProgram = alloca $ glGetIntegerv gl_CURRENT_PROGRAM >> peek
instance (Show a) => Show (Mat4 a) where
show IdentityMatrix =
"[ 1 0 0 0\n" ++
" 0 1 0 0\n" ++
" 0 0 1 0\n" ++
" 0 0 0 1 ]\n"
show (Matrix4 (m00,m01,m02,m03,m10,m11,m12,m13,m20,m21,m22,m23,m30,m31,m32,m33)) =
"["++! m00 ++ " " ++! m01 ++ " " ++! m02 ++ " " ++! m03 ++ "\n" ++
" "++! m10 ++ " " ++! m11 ++ " " ++! m12 ++ " " ++! m13 ++ "\n" ++
" "++! m20 ++ " " ++! m21 ++ " " ++! m22 ++ " " ++! m23 ++ "\n" ++
" "++! m30 ++ " " ++! m31 ++ " " ++! m32 ++ " " ++! m33 ++ "]"
where (++!) a = (a++) . show
translateMat4 :: (Num a) => Mat4 a -> (a,a,a,a) -> Mat4 a
translateMat4 IdentityMatrix x = translateMat4 (Matrix4 (1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1)) x
translateMat4 (Matrix4 (m00,m01,m02,m03,
m10,m11,m12,m13,
m20,m21,m22,m23,
m30,m31,m32,m33)) (v0,v1,v2,v3) =
Matrix4 (m00,m01,m02,m03+v0,
m10,m11,m12,m13+v1,
m20,m21,m22,m23+v2,
m30,m31,m32,m33+v3)
applyMatrix :: (Num a) => Mat4 a -> (a,a,a,a) -> (a,a,a,a)
applyMatrix (Matrix4 (m00,m01,m02,m03,
m10,m11,m12,m13,
m20,m21,m22,m23,
m30,m31,m32,m33)) (v0,v1,v2,v3) =
( v0 * m00 + v1 * m01 + v2 * m02 + v3 * m03,
v0 * m10 + v1 * m11 + v2 * m12 + v3 * m13,
v0 * m20 + v1 * m21 + v2 * m22 + v3 * m23,
v0 * m30 + v1 * m31 + v2 * m32 + v3 * m33 )
applyMatrix IdentityMatrix v = v
scaleMatrix :: (Num a) => Mat4 a -> (a,a,a) -> Mat4 a
scaleMatrix IdentityMatrix (a,b,c) = Matrix4 ( a,0,0,0,
0,b,0,0,
0,0,c,0,
0,0,0,1)
scaleMatrix (Matrix4 (m00,m01,m02,m03,m10,m11,m12,m13,m20,m21,m22,m23,m30,m31,m32,m33)) (a,b,c)
= Matrix4 ( m00*a,m01,m02,m03,
m10,m11*b,m12,m13,
m20,m21,m22*c,m23,
m30,m31,m32,m33)
applyMatrixToList :: (Num a) => Mat4 a -> [a] -> [a]
applyMatrixToList IdentityMatrix t = t
applyMatrixToList mat (a:b:c:xs) =
let (a',b',c',_) = applyMatrix mat (a,b,c,1) in
(a':b':c':applyMatrixToList mat xs)
applyMatrixToList _ _ = []
mulMatrix4 :: (Num a) => Mat4 a -> Mat4 a -> Mat4 a
mulMatrix4 IdentityMatrix a = a
mulMatrix4 a IdentityMatrix = a
mulMatrix4
(Matrix4 (a00,a01,a02,a03,
a10,a11,a12,a13,
a20,a21,a22,a23,
a30,a31,a32,a33 ))
(Matrix4 (b00,b01,b02,b03,
b10,b11,b12,b13,
b20,b21,b22,b23,
b30,b31,b32,b33 )) =
Matrix4 (b00*a00+b10*a01+b20*a02+b30*a03,
b01*a00+b11*a01+b21*a02+b31*a03,
b02*a00+b12*a01+b22*a02+b32*a03,
b03*a00+b13*a01+b23*a02+b33*a03,
b00*a10+b10*a11+b20*a12+b30*a13,
b01*a10+b11*a11+b21*a12+b31*a13,
b02*a10+b12*a11+b22*a12+b32*a13,
b03*a10+b13*a11+b23*a12+b33*a13,
b00*a20+b10*a21+b20*a22+b30*a23,
b01*a20+b11*a21+b21*a22+b31*a23,
b02*a20+b12*a21+b22*a22+b32*a23,
b03*a20+b13*a21+b23*a22+b33*a23,
b00*a30+b10*a31+b20*a32+b30*a33,
b01*a30+b11*a31+b21*a32+b31*a33,
b02*a30+b12*a31+b22*a32+b32*a33,
b03*a30+b13*a31+b23*a32+b33*a33 )
(|*|) :: (Num a) => Mat4 a -> Mat4 a -> Mat4 a
(|*|) = mulMatrix4
transpose4 :: Mat4 a -> Mat4 a
transpose4 (Matrix4
(m00,m01,m02,m03,
m10,m11,m12,m13,
m20,m21,m22,m23,
m30,m31,m32,m33 )) = Matrix4 (m00, m10, m20, m30,
m01, m11, m21, m31,
m02, m12, m22, m32,
m03, m13, m23, m33)
scale4 :: (Num a) => a -> Mat4 a -> Mat4 a
scale4 n (Matrix4 (m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44)) =
Matrix4 (m11*n,m12*n,m13*n,m14*n,m21*n,m22*n,m23*n,m24*n,m31*n,m32*n,m33*n,m34*n,m41*n,m42*n,m43*n,m44*n)
det4 :: (Real a,Fractional b) => Mat4 a -> b
det4 (Matrix4 (m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44)) =
realToFrac $
m11*m22*m33*m44 + m11*m23*m34*m42 + m11*m24*m32*m43
+ m12*m21*m34*m43 + m12*m23*m31*m44 + m12*m24*m33*m41
+ m13*m21*m32*m44 + m13*m22*m34*m41 + m13*m24*m31*m42
+ m14*m21*m33*m42 + m14*m22*m31*m43 + m14*m23*m32*m41
- m11*m22*m34*m43 - m11*m23*m32*m44 - m11*m24*m33*m42
- m12*m21*m33*m44 - m12*m23*m34*m41 - m12*m24*m31*m43
- m13*m21*m34*m42 - m13*m22*m31*m44 - m13*m24*m32*m41
- m14*m21*m32*m43 - m14*m22*m33*m41 - m14*m23*m31*m42
inv4 :: (RealFloat a,Eq a) => Mat4 a -> Maybe (Mat4 a)
inv4 mat@(Matrix4 (m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44)) =
let b11 = m22*m33*m44 + m23*m34*m42 + m24*m32*m43 - m22*m34*m43 - m23*m32*m44 - m24*m33*m42
b12 = m12*m34*m43 + m13*m32*m44 + m14*m33*m42 - m12*m33*m44 - m13*m34*m42 - m14*m32*m43
b13 = m12*m23*m44 + m13*m24*m42 + m14*m22*m43 - m12*m24*m43 - m13*m22*m44 - m14*m23*m42
b14 = m12*m24*m33 + m13*m22*m34 + m14*m23*m32 - m12*m23*m34 - m13*m24*m32 - m14*m22*m33
b21 = m21*m34*m43 + m23*m31*m44 + m24*m33*m41 - m21*m33*m44 - m23*m34*m41 - m24*m31*m43
b22 = m11*m33*m44 + m13*m34*m41 + m14*m31*m43 - m11*m34*m43 - m13*m31*m44 - m14*m33*m41
b23 = m11*m24*m43 + m13*m21*m44 + m14*m23*m41 - m11*m23*m44 - m13*m24*m41 - m14*m21*m43
b24 = m11*m23*m34 + m13*m24*m31 + m14*m21*m33 - m11*m24*m33 - m13*m21*m34 - m14*m23*m31
b31 = m21*m32*m44 + m22*m34*m41 + m24*m31*m42 - m21*m34*m42 - m22*m31*m44 - m24*m32*m41
b32 = m11*m34*m42 + m12*m31*m44 + m14*m32*m41 - m11*m32*m44 - m12*m34*m41 - m14*m31*m42
b33 = m11*m22*m44 + m12*m24*m41 + m14*m21*m42 - m11*m24*m42 - m12*m21*m44 - m14*m22*m41
b34 = m11*m24*m32 + m12*m21*m34 + m14*m22*m31 - m11*m22*m34 - m12*m24*m31 - m14*m21*m32
b41 = m21*m33*m42 + m22*m31*m43 + m23*m32*m41 - m21*m32*m43 - m22*m33*m41 - m23*m31*m42
b42 = m11*m32*m43 + m12*m33*m41 + m13*m31*m42 - m11*m33*m42 - m12*m31*m43 - m13*m32*m41
b43 = m11*m23*m42 + m12*m21*m43 + m13*m22*m41 - m11*m22*m43 - m12*m23*m41 - m13*m21*m42
b44 = m11*m22*m33 + m12*m23*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 - m13*m22*m31 in
case det4 mat of
0 -> Nothing
det -> Just $ (1 / det) `scale4` Matrix4 (b11,b12,b13,b14,b21,b22,b23,b24,b31,b32,b33,b34,b41,b42,b43,b44)
trunc4 :: Mat4 a -> Mat3 a
trunc4 (Matrix4
(m11,m12,m13,_,
m21,m22,m23,_,
m31,m32,m33,_,
_ , _ , _ ,_)) = Matrix3 (m11,m12,m13,m21,m22,m23,m31,m32,m33)
toNormalMatrix :: (RealFloat a,Eq a) => Mat4 a -> Maybe (Mat3 a)
toNormalMatrix mat = liftM (trunc4 . transpose4) $ inv4 mat
|
