quaterion to matrix4 conversion
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4ba8c6e0b5
commit
2381e9bf24
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@ -9,15 +9,23 @@ IN: math.quaternions
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: q- ( u v -- u-v )
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v- ; inline
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<PRIVATE
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GENERIC: (q*sign) ( q -- q' )
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M: object (q*sign) { -1 1 1 1 } v* ; inline
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PRIVATE>
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: q* ( u v -- u*v )
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{
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[ [ { 1 0 0 0 } vshuffle ] [ { 1 1 2 3 } vshuffle ] bi* v* ]
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[ [ { 2 1 2 3 } vshuffle ] [ { 2 0 0 0 } vshuffle ] bi* v* v+ ]
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[ [ { 3 2 3 1 } vshuffle ] [ { 3 3 1 2 } vshuffle ] bi* v* v+ ]
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[ [ { 0 3 1 2 } vshuffle ] [ { 0 2 3 1 } vshuffle ] bi* v* v- ]
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} 2cleave { -1 1 1 1 } v* ; inline
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} 2cleave (q*sign) ; inline
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: qconjugate ( u -- u' )
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GENERIC: qconjugate ( u -- u' )
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M: object qconjugate ( u -- u' )
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{ 1 -1 -1 -1 } v* ; inline
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: qrecip ( u -- 1/u )
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@ -59,4 +67,3 @@ PRIVATE>
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: euler ( phi theta psi -- q )
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{ } euler-like ; inline
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@ -238,3 +238,42 @@ IN: math.matrices.simd.tests
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float-4{ 0.5 0.5 0.5 1.0 } scale-matrix4 m4.
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float-4{ 2.0 3.0 4.0 1.0 } m4.v
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] unit-test
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[
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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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] [
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float-4{ 1.0 0.0 0.0 0.0 } q>matrix4
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] unit-test
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[ t ] [
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pi 0.5 * 0.0 0.0 euler4 q>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 0.0 1.0 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 0.0 1.0 }
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}
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}
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1.0e-7 m~
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] unit-test
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[ t ] [
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0.0 pi 0.25 * 0.0 euler4 q>matrix4
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S{ matrix4 f
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float-4-array{
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float-4{ $[ 1/2. sqrt ] 0.0 $[ 1/2. sqrt neg ] 0.0 }
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float-4{ 0.0 1.0 0.0 0.0 }
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float-4{ $[ 1/2. sqrt ] 0.0 $[ 1/2. sqrt ] 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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1.0e-7 m~
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] unit-test
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@ -1,8 +1,10 @@
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! (c)Joe Groff bsd license
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USING: accessors classes.struct fry generalizations kernel locals
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math math.combinatorics math.functions math.matrices.simd math.vectors
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math.vectors.simd sequences sequences.private specialized-arrays
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math.vectors.simd math.quaternions sequences 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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@ -23,10 +25,7 @@ M: matrix4 new-sequence 2drop matrix4 (struct) ; 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 columns set-first
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c2 columns set-second
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c3 columns set-third
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c4 columns set-fourth
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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 ( quot: ( -- c1 c2 c3 c4 ) -- c )
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@ -151,12 +150,24 @@ TYPED: translation-matrix4 ( offset: float-4 -- matrix: matrix4 )
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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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matrix4 (struct) :> triangle-m
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theta cos :> c
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theta sin :> s
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@ -176,17 +187,8 @@ TYPED:: rotation-matrix4 ( axis: float-4 theta: float -- matrix: matrix4 )
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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 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 v+
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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+ ;
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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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@ -200,3 +202,30 @@ TYPED:: frustum-matrix4 ( xy: float-4 near: float far: float -- matrix: matrix4
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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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