233 lines
7.3 KiB
Factor
233 lines
7.3 KiB
Factor
! (c)Joe Groff bsd license
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USING: accessors classes.struct fry generalizations kernel
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locals math math.combinatorics math.functions math.matrices.simd
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math.vectors math.vectors.simd math.quaternions sequences
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sequences.generalizations sequences.private specialized-arrays
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typed ;
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FROM: sequences.private => nth-unsafe ;
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FROM: math.quaternions.private => (q*sign) ;
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QUALIFIED-WITH: alien.c-types c
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SPECIALIZED-ARRAY: float-4
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IN: math.matrices.simd
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STRUCT: matrix4
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{ columns float-4[4] } ;
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INSTANCE: matrix4 immutable-sequence
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M: matrix4 length drop 4 ; inline
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M: matrix4 nth-unsafe columns>> nth-unsafe ; inline
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M: matrix4 new-sequence 2drop matrix4 (struct) ; inline
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<PRIVATE
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: columns ( a -- a1 a2 a3 a4 )
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columns>> first4 ; inline
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:: set-columns ( c1 c2 c3 c4 c -- c )
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c columns>> :> columns
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c1 c2 c3 c4 columns 4 set-firstn-unsafe
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c ; inline
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: make-matrix4 ( ..a quot: ( ..a -- ..b c1 c2 c3 c4 ) -- ..b c )
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matrix4 (struct) swap dip set-columns ; inline
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:: 2map-columns ( a b quot -- c )
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[
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a columns :> ( a1 a2 a3 a4 )
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b columns :> ( b1 b2 b3 b4 )
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a1 b1 quot call
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a2 b2 quot call
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a3 b3 quot call
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a4 b4 quot call
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] make-matrix4 ; inline
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: map-columns ( ... a quot: ( ... col -- ... newcol ) -- ... c )
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'[ columns _ 4 napply ] make-matrix4 ; inline
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PRIVATE>
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TYPED: m4+ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v+ ] 2map-columns ;
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TYPED: m4- ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v- ] 2map-columns ;
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TYPED: m4* ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v* ] 2map-columns ;
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TYPED: m4/ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v/ ] 2map-columns ;
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TYPED: m4*n ( a: matrix4 b: float -- c: matrix4 ) [ v*n ] curry map-columns ;
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TYPED: m4/n ( a: matrix4 b: float -- c: matrix4 ) [ v/n ] curry map-columns ;
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TYPED: n*m4 ( a: float b: matrix4 -- c: matrix4 ) [ n*v ] with map-columns ;
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TYPED: n/m4 ( a: float b: matrix4 -- c: matrix4 ) [ n/v ] with map-columns ;
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TYPED:: m4. ( a: matrix4 b: matrix4 -- c: matrix4 )
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[
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a columns :> ( a1 a2 a3 a4 )
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b columns :> ( b1 b2 b3 b4 )
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b1 first a1 n*v :> c1a
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b2 first a1 n*v :> c2a
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b3 first a1 n*v :> c3a
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b4 first a1 n*v :> c4a
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b1 second a2 n*v c1a v+ :> c1b
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b2 second a2 n*v c2a v+ :> c2b
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b3 second a2 n*v c3a v+ :> c3b
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b4 second a2 n*v c4a v+ :> c4b
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b1 third a3 n*v c1b v+ :> c1c
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b2 third a3 n*v c2b v+ :> c2c
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b3 third a3 n*v c3b v+ :> c3c
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b4 third a3 n*v c4b v+ :> c4c
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b1 fourth a4 n*v c1c v+
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b2 fourth a4 n*v c2c v+
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b3 fourth a4 n*v c3c v+
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b4 fourth a4 n*v c4c v+
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] make-matrix4 ;
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TYPED:: m4.v ( m: matrix4 v: float-4 -- v': float-4 )
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m columns :> ( m1 m2 m3 m4 )
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v first m1 n*v
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v second m2 n*v v+
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v third m3 n*v v+
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v fourth m4 n*v v+ ;
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TYPED:: v.m4 ( v: float-4 m: matrix4 -- c: float-4 )
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m columns [ v v. ] 4 napply float-4-boa ;
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CONSTANT: identity-matrix4
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S{ matrix4 f
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float-4-array{
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float-4{ 1.0 0.0 0.0 0.0 }
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float-4{ 0.0 1.0 0.0 0.0 }
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float-4{ 0.0 0.0 1.0 0.0 }
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float-4{ 0.0 0.0 0.0 1.0 }
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}
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}
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CONSTANT: zero-matrix4
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S{ matrix4 f
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float-4-array{
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float-4{ 0.0 0.0 0.0 0.0 }
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float-4{ 0.0 0.0 0.0 0.0 }
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float-4{ 0.0 0.0 0.0 0.0 }
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float-4{ 0.0 0.0 0.0 0.0 }
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}
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}
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TYPED:: m4^n ( m: matrix4 n: fixnum -- m^n: matrix4 )
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identity-matrix4 n [ m m4. ] times ;
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: vmerge-diagonal* ( x y -- h t )
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[ (vmerge-head) ] [ swap (vmerge-tail) ] 2bi ; inline
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: vmerge-diagonal ( x -- h t )
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0.0 float-4-with vmerge-diagonal* ; inline
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TYPED: diagonal-matrix4 ( diagonal: float-4 -- matrix: matrix4 )
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[ vmerge-diagonal [ vmerge-diagonal ] bi@ ] make-matrix4 ;
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: vmerge-transpose ( a b c d -- a' b' c' d' )
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[ (vmerge) ] bi-curry@ bi* ; inline
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TYPED: transpose-matrix4 ( matrix: matrix4 -- matrix: matrix4 )
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[ columns vmerge-transpose vmerge-transpose ] make-matrix4 ;
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: linear>homogeneous ( v -- v' )
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[ float-4{ t t t f } ] dip float-4{ 0.0 0.0 0.0 1.0 } v? ; inline
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: scale-matrix4 ( factors -- matrix )
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linear>homogeneous diagonal-matrix4 ; inline
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: ortho-matrix4 ( factors -- matrix )
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float-4{ 1.0 1.0 1.0 1.0 } swap v/ scale-matrix4 ; inline
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TYPED: translation-matrix4 ( offset: float-4 -- matrix: matrix4 )
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[
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linear>homogeneous
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[
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float-4{ 1.0 0.0 0.0 0.0 }
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float-4{ 0.0 1.0 0.0 0.0 }
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float-4{ 0.0 0.0 1.0 0.0 }
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] dip
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] make-matrix4 ;
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:: (rotation-matrix4) ( diagonal triangle-hi triangle-lo -- matrix )
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matrix4 (struct) :> triangle-m
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diagonal scale-matrix4 :> diagonal-m
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triangle-hi { 3 2 1 3 } vshuffle
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triangle-hi { 3 3 0 3 } vshuffle triangle-lo { 2 3 3 3 } vshuffle vbitor
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triangle-lo { 1 0 3 3 } vshuffle
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float-4 new
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triangle-m set-columns drop
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diagonal-m triangle-m m4+ ; inline
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TYPED:: rotation-matrix4 ( axis: float-4 theta: float -- matrix: matrix4 )
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! x*x + c*(1.0 - x*x) x*y*(1.0 - c) + s*z x*z*(1.0 - c) - s*y 0
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! x*y*(1.0 - c) - s*z y*y + c*(1.0 - y*y) y*z*(1.0 - c) + s*x 0
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! x*z*(1.0 - c) + s*y y*z*(1.0 - c) - s*x z*z + c*(1.0 - z*z) 0
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! 0 0 0 1
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theta cos :> c
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theta sin :> s
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float-4{ -1.0 1.0 -1.0 0.0 } :> triangle-sign
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c float-4-with :> cc
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s float-4-with :> ss
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1.0 float-4-with :> ones
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ones cc v- :> 1-c
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axis axis v* :> axis2
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axis2 cc ones axis2 v- v* v+ :> diagonal
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axis { 1 0 0 3 } vshuffle axis { 2 2 1 3 } vshuffle v* 1-c v*
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float-4{ t t t f } vbitand :> triangle-a
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ss axis v* triangle-sign v* :> triangle-b
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triangle-a triangle-b v+ :> triangle-lo
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triangle-a triangle-b v- :> triangle-hi
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diagonal triangle-hi triangle-lo (rotation-matrix4) ;
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TYPED:: frustum-matrix4 ( xy: float-4 near: float far: float -- matrix: matrix4 )
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[
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near near near far + 2 near far * * float-4-boa ! num
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float-4{ t t f f } xy near far - float-4-with v? ! denom
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v/ :> fov
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float-4{ 0.0 -1.0 0.0 0.0 } :> negone
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fov vmerge-diagonal
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[ vmerge-diagonal ]
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[ negone (vmerge) ] bi*
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] make-matrix4 ;
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! interface with quaternions
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M: float-4 (q*sign)
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float-4{ -0.0 0.0 0.0 0.0 } vbitxor ; inline
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M: float-4 qconjugate
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float-4{ 0.0 -0.0 -0.0 -0.0 } vbitxor ; inline
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: euler4 ( phi theta psi -- q )
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float-4{ 0 0 0 0 } euler-like ; inline
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TYPED:: q>matrix4 ( q: float-4 -- matrix: matrix4 )
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! a*a + b*b - c*c - d*d 2*b*c - 2*a*d 2*b*d + 2*a*c 0
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! 2*b*c + 2*a*d a*a - b*b + c*c - d*d 2*c*d - 2*a*b 0
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! 2*b*d - 2*a*c 2*c*d + 2*a*b a*a - b*b - c*c + d*d 0
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! 0 0 0 1
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q { 2 1 1 3 } vshuffle q { 3 3 2 3 } vshuffle v* :> triangle-a
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q { 0 0 0 3 } vshuffle q { 1 2 3 3 } vshuffle v* :> triangle-b
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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*
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[ v- ] [ v+ ] 2bi :> ( triangle-hi triangle-lo )
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q q v* first4 {
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[ [ + ] [ - ] [ - ] tri* ]
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[ [ - ] [ + ] [ - ] tri* ]
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[ [ - ] [ - ] [ + ] tri* ]
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} 4 ncleave 1.0 float-4-boa :> diagonal
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diagonal triangle-hi triangle-lo (rotation-matrix4) ;
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