1 ! (c)Joe Groff bsd license
2 USING: accessors classes.struct fry generalizations kernel locals
3 math math.combinatorics math.functions math.matrices.simd math.vectors
4 math.vectors.simd sequences sequences.private specialized-arrays
6 QUALIFIED-WITH: alien.c-types c
7 SPECIALIZED-ARRAY: float-4
11 { columns float-4[4] } ;
13 INSTANCE: matrix4 immutable-sequence
15 M: matrix4 length drop 4 ; inline
16 M: matrix4 nth-unsafe columns>> nth-unsafe ; inline
17 M: matrix4 new-sequence 2drop matrix4 (struct) ; inline
21 : columns ( a -- a1 a2 a3 a4 )
22 columns>> first4 ; inline
24 :: set-columns ( c1 c2 c3 c4 c -- c )
25 c columns>> :> columns
32 : make-matrix4 ( quot: ( -- c1 c2 c3 c4 ) -- 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 -- 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 TYPED:: rotation-matrix4 ( axis: float-4 theta: float -- matrix: matrix4 )
155 ! x*x + c*(1.0 - x*x) x*y*(1.0 - c) + s*z x*z*(1.0 - c) - s*y 0
156 ! x*y*(1.0 - c) - s*z y*y + c*(1.0 - y*y) y*z*(1.0 - c) + s*x 0
157 ! x*z*(1.0 - c) + s*y y*z*(1.0 - c) - s*x z*z + c*(1.0 - z*z) 0
159 matrix4 (struct) :> triangle-m
163 float-4{ -1.0 1.0 -1.0 0.0 } :> triangle-sign
167 1.0 float-4-with :> ones
169 axis axis v* :> axis2
171 axis2 cc ones axis2 v- v* v+ :> diagonal
173 axis { 1 0 0 3 } vshuffle axis { 2 2 1 3 } vshuffle v* 1-c v*
174 float-4{ t t t f } vbitand :> triangle-a
175 ss axis v* triangle-sign v* :> triangle-b
176 triangle-a triangle-b v+ :> triangle-lo
177 triangle-a triangle-b v- :> triangle-hi
179 diagonal scale-matrix4 :> diagonal-m
181 triangle-hi { 3 2 1 3 } vshuffle
182 triangle-hi { 3 3 0 3 } vshuffle triangle-lo { 2 3 3 3 } vshuffle v+
183 triangle-lo { 1 0 3 3 } vshuffle
186 triangle-m set-columns drop
188 diagonal-m triangle-m m4+ ;
190 TYPED:: frustum-matrix4 ( xy: float-4 near: float far: float -- matrix: matrix4 )
192 near near near far + 2 near far * * float-4-boa ! num
193 float-4{ t t f f } xy near far - float-4-with v? ! denom
196 float-4{ 0.0 -1.0 0.0 0.0 } :> negone
200 [ negone (vmerge) ] bi*