: q- ( u v -- u-v )
v- ; inline
+<PRIVATE
+
+GENERIC: (q*sign) ( q -- q' )
+M: object (q*sign) { -1 1 1 1 } v* ; inline
+
+PRIVATE>
+
: q* ( u v -- u*v )
{
[ [ { 1 0 0 0 } vshuffle ] [ { 1 1 2 3 } vshuffle ] bi* v* ]
[ [ { 2 1 2 3 } vshuffle ] [ { 2 0 0 0 } vshuffle ] bi* v* v+ ]
[ [ { 3 2 3 1 } vshuffle ] [ { 3 3 1 2 } vshuffle ] bi* v* v+ ]
[ [ { 0 3 1 2 } vshuffle ] [ { 0 2 3 1 } vshuffle ] bi* v* v- ]
- } 2cleave { -1 1 1 1 } v* ; inline
+ } 2cleave (q*sign) ; inline
-: qconjugate ( u -- u' )
+GENERIC: qconjugate ( u -- u' )
+M: object qconjugate ( u -- u' )
{ 1 -1 -1 -1 } v* ; inline
: qrecip ( u -- 1/u )
: euler ( phi theta psi -- q )
{ } euler-like ; inline
-
float-4{ 0.5 0.5 0.5 1.0 } scale-matrix4 m4.
float-4{ 2.0 3.0 4.0 1.0 } m4.v
] unit-test
+
+[
+ S{ matrix4 f
+ float-4-array{
+ float-4{ 1.0 0.0 0.0 0.0 }
+ float-4{ 0.0 1.0 0.0 0.0 }
+ float-4{ 0.0 0.0 1.0 0.0 }
+ float-4{ 0.0 0.0 0.0 1.0 }
+ }
+ }
+] [
+ float-4{ 1.0 0.0 0.0 0.0 } q>matrix4
+] unit-test
+
+[ t ] [
+ pi 0.5 * 0.0 0.0 euler4 q>matrix4
+ S{ matrix4 f
+ float-4-array{
+ float-4{ 1.0 0.0 0.0 0.0 }
+ float-4{ 0.0 0.0 1.0 0.0 }
+ float-4{ 0.0 -1.0 0.0 0.0 }
+ float-4{ 0.0 0.0 0.0 1.0 }
+ }
+ }
+ 1.0e-7 m~
+] unit-test
+
+[ t ] [
+ 0.0 pi 0.25 * 0.0 euler4 q>matrix4
+ S{ matrix4 f
+ float-4-array{
+ float-4{ $[ 1/2. sqrt ] 0.0 $[ 1/2. sqrt neg ] 0.0 }
+ float-4{ 0.0 1.0 0.0 0.0 }
+ float-4{ $[ 1/2. sqrt ] 0.0 $[ 1/2. sqrt ] 0.0 }
+ float-4{ 0.0 0.0 0.0 1.0 }
+ }
+ }
+ 1.0e-7 m~
+] unit-test
! (c)Joe Groff bsd license
USING: accessors classes.struct fry generalizations kernel locals
math math.combinatorics math.functions math.matrices.simd math.vectors
-math.vectors.simd sequences sequences.private specialized-arrays
+math.vectors.simd math.quaternions sequences sequences.private specialized-arrays
typed ;
+FROM: sequences.private => nth-unsafe ;
+FROM: math.quaternions.private => (q*sign) ;
QUALIFIED-WITH: alien.c-types c
SPECIALIZED-ARRAY: float-4
IN: math.matrices.simd
:: set-columns ( c1 c2 c3 c4 c -- c )
c columns>> :> columns
- c1 columns set-first
- c2 columns set-second
- c3 columns set-third
- c4 columns set-fourth
+ c1 c2 c3 c4 columns 4 set-firstn-unsafe
c ; inline
: make-matrix4 ( quot: ( -- c1 c2 c3 c4 ) -- c )
] dip
] make-matrix4 ;
+:: (rotation-matrix4) ( diagonal triangle-hi triangle-lo -- matrix )
+ matrix4 (struct) :> triangle-m
+ diagonal scale-matrix4 :> diagonal-m
+
+ triangle-hi { 3 2 1 3 } vshuffle
+ triangle-hi { 3 3 0 3 } vshuffle triangle-lo { 2 3 3 3 } vshuffle vbitor
+ triangle-lo { 1 0 3 3 } vshuffle
+ float-4 new
+
+ triangle-m set-columns drop
+
+ diagonal-m triangle-m m4+ ; inline
+
TYPED:: rotation-matrix4 ( axis: float-4 theta: float -- matrix: matrix4 )
! x*x + c*(1.0 - x*x) x*y*(1.0 - c) + s*z x*z*(1.0 - c) - s*y 0
! x*y*(1.0 - c) - s*z y*y + c*(1.0 - y*y) y*z*(1.0 - c) + s*x 0
! x*z*(1.0 - c) + s*y y*z*(1.0 - c) - s*x z*z + c*(1.0 - z*z) 0
! 0 0 0 1
- matrix4 (struct) :> triangle-m
theta cos :> c
theta sin :> s
triangle-a triangle-b v+ :> triangle-lo
triangle-a triangle-b v- :> triangle-hi
- diagonal scale-matrix4 :> diagonal-m
-
- triangle-hi { 3 2 1 3 } vshuffle
- triangle-hi { 3 3 0 3 } vshuffle triangle-lo { 2 3 3 3 } vshuffle v+
- triangle-lo { 1 0 3 3 } vshuffle
- float-4 new
-
- triangle-m set-columns drop
-
- diagonal-m triangle-m m4+ ;
-
+ diagonal triangle-hi triangle-lo (rotation-matrix4) ;
+
TYPED:: frustum-matrix4 ( xy: float-4 near: float far: float -- matrix: matrix4 )
[
near near near far + 2 near far * * float-4-boa ! num
[ negone (vmerge) ] bi*
] make-matrix4 ;
+! interface with quaternions
+M: float-4 (q*sign)
+ float-4{ -0.0 0.0 0.0 0.0 } vbitxor ; inline
+M: float-4 qconjugate
+ float-4{ 0.0 -0.0 -0.0 -0.0 } vbitxor ; inline
+
+: euler4 ( phi theta psi -- q )
+ float-4{ 0 0 0 0 } euler-like ; inline
+
+TYPED:: q>matrix4 ( q: float-4 -- matrix: matrix4 )
+ ! a*a + b*b - c*c - d*d 2*b*c - 2*a*d 2*b*d + 2*a*c 0
+ ! 2*b*c + 2*a*d a*a - b*b + c*c - d*d 2*c*d - 2*a*b 0
+ ! 2*b*d - 2*a*c 2*c*d + 2*a*b a*a - b*b - c*c + d*d 0
+ ! 0 0 0 1
+ q { 2 1 1 3 } vshuffle q { 3 3 2 3 } vshuffle v* :> triangle-a
+ q { 0 0 0 3 } vshuffle q { 1 2 3 3 } vshuffle v* :> triangle-b
+
+ 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*
+ [ v- ] [ v+ ] 2bi :> ( triangle-hi triangle-lo )
+
+ q q v* first4 {
+ [ [ + ] [ - ] [ - ] tri* ]
+ [ [ - ] [ + ] [ - ] tri* ]
+ [ [ - ] [ - ] [ + ] tri* ]
+ } 4 ncleave 1.0 float-4-boa :> diagonal
+
+ diagonal triangle-hi triangle-lo (rotation-matrix4) ;