1 ! (c)Joe Groff bsd license
2 USING: accessors classes.struct fry generalizations kernel
3 locals math math.combinatorics math.functions math.matrices.simd
4 math.vectors math.vectors.simd math.quaternions sequences
5 sequences.generalizations sequences.private specialized-arrays
7 FROM: sequences.private => nth-unsafe ;
8 FROM: math.quaternions.private => (q*sign) ;
9 QUALIFIED-WITH: alien.c-types c
10 SPECIALIZED-ARRAY: float-4
11 IN: math.matrices.simd
14 { columns float-4[4] } ;
16 INSTANCE: matrix4 immutable-sequence
18 M: matrix4 length drop 4 ; inline
19 M: matrix4 nth-unsafe columns>> nth-unsafe ; inline
20 M: matrix4 new-sequence 2drop matrix4 (struct) ; inline
24 : columns ( a -- a1 a2 a3 a4 )
25 columns>> first4 ; inline
27 :: set-columns ( c1 c2 c3 c4 c -- c )
28 c columns>> :> columns
29 c1 c2 c3 c4 columns 4 set-firstn-unsafe
32 : make-matrix4 ( ..a quot: ( ..a -- ..b c1 c2 c3 c4 ) -- ..b c )
33 matrix4 (struct) swap dip set-columns ; inline
35 :: 2map-columns ( a b quot -- c )
37 a columns :> ( a1 a2 a3 a4 )
38 b columns :> ( b1 b2 b3 b4 )
44 ] make-matrix4 ; inline
46 : map-columns ( ... a quot: ( ... col -- ... newcol ) -- ... c )
47 '[ columns _ 4 napply ] make-matrix4 ; inline
51 TYPED: m4+ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v+ ] 2map-columns ;
52 TYPED: m4- ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v- ] 2map-columns ;
53 TYPED: m4* ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v* ] 2map-columns ;
54 TYPED: m4/ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v/ ] 2map-columns ;
56 TYPED: m4*n ( a: matrix4 b: float -- c: matrix4 ) [ v*n ] curry map-columns ;
57 TYPED: m4/n ( a: matrix4 b: float -- c: matrix4 ) [ v/n ] curry map-columns ;
58 TYPED: n*m4 ( a: float b: matrix4 -- c: matrix4 ) [ n*v ] with map-columns ;
59 TYPED: n/m4 ( a: float b: matrix4 -- c: matrix4 ) [ n/v ] with map-columns ;
61 TYPED:: m4. ( a: matrix4 b: matrix4 -- c: matrix4 )
63 a columns :> ( a1 a2 a3 a4 )
64 b columns :> ( b1 b2 b3 b4 )
66 b1 first a1 n*v :> c1a
67 b2 first a1 n*v :> c2a
68 b3 first a1 n*v :> c3a
69 b4 first a1 n*v :> c4a
71 b1 second a2 n*v c1a v+ :> c1b
72 b2 second a2 n*v c2a v+ :> c2b
73 b3 second a2 n*v c3a v+ :> c3b
74 b4 second a2 n*v c4a v+ :> c4b
76 b1 third a3 n*v c1b v+ :> c1c
77 b2 third a3 n*v c2b v+ :> c2c
78 b3 third a3 n*v c3b v+ :> c3c
79 b4 third a3 n*v c4b v+ :> c4c
81 b1 fourth a4 n*v c1c v+
82 b2 fourth a4 n*v c2c v+
83 b3 fourth a4 n*v c3c v+
84 b4 fourth a4 n*v c4c v+
87 TYPED:: m4.v ( m: matrix4 v: float-4 -- v': float-4 )
88 m columns :> ( m1 m2 m3 m4 )
95 TYPED:: v.m4 ( v: float-4 m: matrix4 -- c: float-4 )
96 m columns [ v v. ] 4 napply float-4-boa ;
98 CONSTANT: identity-matrix4
101 float-4{ 1.0 0.0 0.0 0.0 }
102 float-4{ 0.0 1.0 0.0 0.0 }
103 float-4{ 0.0 0.0 1.0 0.0 }
104 float-4{ 0.0 0.0 0.0 1.0 }
108 CONSTANT: zero-matrix4
111 float-4{ 0.0 0.0 0.0 0.0 }
112 float-4{ 0.0 0.0 0.0 0.0 }
113 float-4{ 0.0 0.0 0.0 0.0 }
114 float-4{ 0.0 0.0 0.0 0.0 }
118 TYPED:: m4^n ( m: matrix4 n: fixnum -- m^n: matrix4 )
119 identity-matrix4 n [ m m4. ] times ;
121 : vmerge-diagonal* ( x y -- h t )
122 [ (vmerge-head) ] [ swap (vmerge-tail) ] 2bi ; inline
123 : vmerge-diagonal ( x -- h t )
124 0.0 float-4-with vmerge-diagonal* ; inline
126 TYPED: diagonal-matrix4 ( diagonal: float-4 -- matrix: matrix4 )
127 [ vmerge-diagonal [ vmerge-diagonal ] bi@ ] make-matrix4 ;
129 : vmerge-transpose ( a b c d -- a' b' c' d' )
130 [ (vmerge) ] bi-curry@ bi* ; inline
132 TYPED: transpose-matrix4 ( matrix: matrix4 -- matrix: matrix4 )
133 [ columns vmerge-transpose vmerge-transpose ] make-matrix4 ;
135 : linear>homogeneous ( v -- v' )
136 [ float-4{ t t t f } ] dip float-4{ 0.0 0.0 0.0 1.0 } v? ; inline
138 : scale-matrix4 ( factors -- matrix )
139 linear>homogeneous diagonal-matrix4 ; inline
141 : ortho-matrix4 ( factors -- matrix )
142 float-4{ 1.0 1.0 1.0 1.0 } swap v/ scale-matrix4 ; inline
144 TYPED: translation-matrix4 ( offset: float-4 -- matrix: matrix4 )
148 float-4{ 1.0 0.0 0.0 0.0 }
149 float-4{ 0.0 1.0 0.0 0.0 }
150 float-4{ 0.0 0.0 1.0 0.0 }
154 :: (rotation-matrix4) ( diagonal triangle-hi triangle-lo -- matrix )
155 matrix4 (struct) :> triangle-m
156 diagonal scale-matrix4 :> diagonal-m
158 triangle-hi { 3 2 1 3 } vshuffle
159 triangle-hi { 3 3 0 3 } vshuffle triangle-lo { 2 3 3 3 } vshuffle vbitor
160 triangle-lo { 1 0 3 3 } vshuffle
163 triangle-m set-columns drop
165 diagonal-m triangle-m m4+ ; inline
167 TYPED:: rotation-matrix4 ( axis: float-4 theta: float -- matrix: matrix4 )
168 ! x*x + c*(1.0 - x*x) x*y*(1.0 - c) + s*z x*z*(1.0 - c) - s*y 0
169 ! x*y*(1.0 - c) - s*z y*y + c*(1.0 - y*y) y*z*(1.0 - c) + s*x 0
170 ! x*z*(1.0 - c) + s*y y*z*(1.0 - c) - s*x z*z + c*(1.0 - z*z) 0
175 float-4{ -1.0 1.0 -1.0 0.0 } :> triangle-sign
179 1.0 float-4-with :> ones
181 axis axis v* :> axis2
183 axis2 cc ones axis2 v- v* v+ :> diagonal
185 axis { 1 0 0 3 } vshuffle axis { 2 2 1 3 } vshuffle v* 1-c v*
186 float-4{ t t t f } vbitand :> triangle-a
187 ss axis v* triangle-sign v* :> triangle-b
188 triangle-a triangle-b v+ :> triangle-lo
189 triangle-a triangle-b v- :> triangle-hi
191 diagonal triangle-hi triangle-lo (rotation-matrix4) ;
193 TYPED:: frustum-matrix4 ( xy: float-4 near: float far: float -- matrix: matrix4 )
195 near near near far + 2 near far * * float-4-boa ! num
196 float-4{ t t f f } xy near far - float-4-with v? ! denom
199 float-4{ 0.0 -1.0 0.0 0.0 } :> negone
203 [ negone (vmerge) ] bi*
206 ! interface with quaternions
208 float-4{ -0.0 0.0 0.0 0.0 } vbitxor ; inline
209 M: float-4 qconjugate
210 float-4{ 0.0 -0.0 -0.0 -0.0 } vbitxor ; inline
212 : euler4 ( phi theta psi -- q )
213 float-4{ 0 0 0 0 } euler-like ; inline
215 TYPED:: q>matrix4 ( q: float-4 -- matrix: matrix4 )
216 ! a*a + b*b - c*c - d*d 2*b*c - 2*a*d 2*b*d + 2*a*c 0
217 ! 2*b*c + 2*a*d a*a - b*b + c*c - d*d 2*c*d - 2*a*b 0
218 ! 2*b*d - 2*a*c 2*c*d + 2*a*b a*a - b*b - c*c + d*d 0
220 q { 2 1 1 3 } vshuffle q { 3 3 2 3 } vshuffle v* :> triangle-a
221 q { 0 0 0 3 } vshuffle q { 1 2 3 3 } vshuffle v* :> triangle-b
223 triangle-a float-4{ 2.0 2.0 2.0 0.0 } v* triangle-b float-4{ -2.0 2.0 -2.0 0.0 } v*
224 [ v- ] [ v+ ] 2bi :> ( triangle-hi triangle-lo )
227 [ [ + ] [ - ] [ - ] tri* ]
228 [ [ - ] [ + ] [ - ] tri* ]
229 [ [ - ] [ - ] [ + ] tri* ]
230 } 4 ncleave 1.0 float-4-boa :> diagonal
232 diagonal triangle-hi triangle-lo (rotation-matrix4) ;