-! (c)Joe Groff bsd license
-USING: accessors classes.struct generalizations kernel locals
-math math.combinatorics math.functions math.matrices.simd math.vectors
-math.vectors.simd sequences sequences.private specialized-arrays
+! Copyright (C) 2009, 2011 Joe Groff.
+! See http://factorcode.org/license.txt for BSD license.
+USING: accessors classes.struct generalizations kernel
+math math.functions math.matrices.simd math.vectors
+math.vectors.simd math.quaternions sequences
+sequences.generalizations sequences.private specialized-arrays
typed ;
+FROM: sequences.private => nth-unsafe ;
+FROM: math.quaternions.private => (q*sign) ;
QUALIFIED-WITH: alien.c-types c
-SIMD: c:float
SPECIALIZED-ARRAY: float-4
IN: math.matrices.simd
STRUCT: matrix4
- { rows float-4[4] } ;
+ { columns float-4[4] } ;
INSTANCE: matrix4 immutable-sequence
M: matrix4 length drop 4 ; inline
-M: matrix4 nth-unsafe rows>> nth-unsafe ; inline
+M: matrix4 nth-unsafe columns>> nth-unsafe ; inline
M: matrix4 new-sequence 2drop matrix4 (struct) ; inline
<PRIVATE
-: rows ( a -- a1 a2 a3 a4 )
- rows>> 4 firstn ; inline
+: columns ( a -- a1 a2 a3 a4 )
+ columns>> first4 ; inline
-:: set-rows ( c1 c2 c3 c4 c -- c )
- c rows>> :> rows
- c1 rows set-first
- c2 rows set-second
- c3 rows set-third
- c4 rows set-fourth
+:: set-columns ( c1 c2 c3 c4 c -- c )
+ c columns>> :> columns
+ c1 c2 c3 c4 columns 4 set-firstn-unsafe
c ; inline
-:: 2map-rows ( a b quot -- c )
- matrix4 (struct) :> c
+: make-matrix4 ( ..a quot: ( ..a -- ..b c1 c2 c3 c4 ) -- ..b c )
+ matrix4 (struct) swap dip set-columns ; inline
- a rows :> a4 :> a3 :> a2 :> a1
- b rows :> b4 :> b3 :> b2 :> b1
+:: 2map-columns ( a b quot -- c )
+ [
+ a columns :> ( a1 a2 a3 a4 )
+ b columns :> ( b1 b2 b3 b4 )
- a1 b1 quot call
- a2 b2 quot call
- a3 b3 quot call
- a4 b4 quot call
+ a1 b1 quot call
+ a2 b2 quot call
+ a3 b3 quot call
+ a4 b4 quot call
+ ] make-matrix4 ; inline
- c set-rows ; inline
+: map-columns ( ... a quot: ( ... col -- ... newcol ) -- ... c )
+ '[ columns _ 4 napply ] make-matrix4 ; inline
-:: map-rows ( a quot -- c )
- matrix4 (struct) :> c
-
- a rows :> a4 :> a3 :> a2 :> a1
-
- a1 quot call
- a2 quot call
- a3 quot call
- a4 quot call
-
- c set-rows ; inline
-
PRIVATE>
-TYPED: m4+ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v+ ] 2map-rows ;
-TYPED: m4- ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v- ] 2map-rows ;
-TYPED: m4* ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v* ] 2map-rows ;
-TYPED: m4/ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v/ ] 2map-rows ;
+TYPED: m4+ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v+ ] 2map-columns ;
+TYPED: m4- ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v- ] 2map-columns ;
+TYPED: m4* ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v* ] 2map-columns ;
+TYPED: m4/ ( a: matrix4 b: matrix4 -- c: matrix4 ) [ v/ ] 2map-columns ;
-TYPED: m4*n ( a: matrix4 b: float -- c: matrix4 ) [ v*n ] curry map-rows ;
-TYPED: m4/n ( a: matrix4 b: float -- c: matrix4 ) [ v/n ] curry map-rows ;
-TYPED: n*m4 ( a: float b: matrix4 -- c: matrix4 ) [ n*v ] with map-rows ;
-TYPED: n/m4 ( a: float b: matrix4 -- c: matrix4 ) [ n/v ] with map-rows ;
+TYPED: m4*n ( a: matrix4 b: float -- c: matrix4 ) [ v*n ] curry map-columns ;
+TYPED: m4/n ( a: matrix4 b: float -- c: matrix4 ) [ v/n ] curry map-columns ;
+TYPED: n*m4 ( a: float b: matrix4 -- c: matrix4 ) [ n*v ] with map-columns ;
+TYPED: n/m4 ( a: float b: matrix4 -- c: matrix4 ) [ n/v ] with map-columns ;
TYPED:: m4. ( a: matrix4 b: matrix4 -- c: matrix4 )
- matrix4 (struct) :> c
-
- a rows :> a4 :> a3 :> a2 :> a1
- b rows :> b4 :> b3 :> b2 :> b1
-
- a1 first b1 n*v :> c1a
- a2 first b1 n*v :> c2a
- a3 first b1 n*v :> c3a
- a4 first b1 n*v :> c4a
-
- a1 second b2 n*v c1a v+ :> c1b
- a2 second b2 n*v c2a v+ :> c2b
- a3 second b2 n*v c3a v+ :> c3b
- a4 second b2 n*v c4a v+ :> c4b
-
- a1 third b3 n*v c1b v+ :> c1c
- a2 third b3 n*v c2b v+ :> c2c
- a3 third b3 n*v c3b v+ :> c3c
- a4 third b3 n*v c4b v+ :> c4c
-
- a1 fourth b4 n*v c1c v+
- a2 fourth b4 n*v c2c v+
- a3 fourth b4 n*v c3c v+
- a4 fourth b4 n*v c4c v+
-
- c set-rows ;
-
-TYPED:: v.m4 ( a: float-4 b: matrix4 -- c: float-4 )
- b rows :> b4 :> b3 :> b2 :> b1
-
- a first b1 n*v
- a second b2 n*v v+
- a third b3 n*v v+
- a fourth b4 n*v v+ ;
-
-TYPED:: m4.v ( a: matrix4 b: float-4 -- c: float-4 )
- a rows [ b v. ] 4 napply float-4-boa ;
+ [
+ a columns :> ( a1 a2 a3 a4 )
+ b columns :> ( b1 b2 b3 b4 )
+
+ b1 first a1 n*v :> c1a
+ b2 first a1 n*v :> c2a
+ b3 first a1 n*v :> c3a
+ b4 first a1 n*v :> c4a
+
+ b1 second a2 n*v c1a v+ :> c1b
+ b2 second a2 n*v c2a v+ :> c2b
+ b3 second a2 n*v c3a v+ :> c3b
+ b4 second a2 n*v c4a v+ :> c4b
+
+ b1 third a3 n*v c1b v+ :> c1c
+ b2 third a3 n*v c2b v+ :> c2c
+ b3 third a3 n*v c3b v+ :> c3c
+ b4 third a3 n*v c4b v+ :> c4c
+
+ b1 fourth a4 n*v c1c v+
+ b2 fourth a4 n*v c2c v+
+ b3 fourth a4 n*v c3c v+
+ b4 fourth a4 n*v c4c v+
+ ] make-matrix4 ;
+
+TYPED:: m4.v ( m: matrix4 v: float-4 -- v': float-4 )
+ m columns :> ( m1 m2 m3 m4 )
+
+ v first m1 n*v
+ v second m2 n*v v+
+ v third m3 n*v v+
+ v fourth m4 n*v v+ ;
+
+TYPED:: v.m4 ( v: float-4 m: matrix4 -- c: float-4 )
+ m columns [ v vdot ] 4 napply float-4-boa ;
CONSTANT: identity-matrix4
S{ matrix4 f
TYPED:: m4^n ( m: matrix4 n: fixnum -- m^n: matrix4 )
identity-matrix4 n [ m m4. ] times ;
-TYPED:: scale-matrix4 ( factors: float-4 -- matrix: matrix4 )
- matrix4 (struct) :> c
+: vmerge-diagonal* ( x y -- h t )
+ [ (vmerge-head) ] [ swap (vmerge-tail) ] 2bi ; inline
+: vmerge-diagonal ( x -- h t )
+ 0.0 float-4-with vmerge-diagonal* ; inline
+
+TYPED: diagonal-matrix4 ( diagonal: float-4 -- matrix: matrix4 )
+ [ vmerge-diagonal [ vmerge-diagonal ] bi@ ] make-matrix4 ;
- factors float-4{ t t t f } vbitand :> factors'
+: vmerge-transpose ( a b c d -- a' b' c' d' )
+ [ (vmerge) ] bi-curry@ bi* ; inline
- factors' { 0 3 3 3 } vshuffle
- factors' { 3 1 3 3 } vshuffle
- factors' { 3 3 2 3 } vshuffle
- float-4{ 0.0 0.0 0.0 1.0 }
+TYPED: transpose-matrix4 ( matrix: matrix4 -- matrix: matrix4 )
+ [ columns vmerge-transpose vmerge-transpose ] make-matrix4 ;
- c set-rows ;
+: linear>homogeneous ( v -- v' )
+ [ float-4{ t t t f } ] dip float-4{ 0.0 0.0 0.0 1.0 } v? ; inline
+
+: scale-matrix4 ( factors -- matrix )
+ linear>homogeneous diagonal-matrix4 ; inline
: ortho-matrix4 ( factors -- matrix )
float-4{ 1.0 1.0 1.0 1.0 } swap v/ scale-matrix4 ; inline
-TYPED:: translation-matrix4 ( offset: float-4 -- matrix: matrix4 )
- matrix4 (struct) :> c
+TYPED: translation-matrix4 ( offset: float-4 -- matrix: matrix4 )
+ [
+ linear>homogeneous
+ [
+ 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 }
+ ] dip
+ ] make-matrix4 ;
+
+:: (rotation-matrix4) ( diagonal triangle-hi triangle-lo -- matrix )
+ matrix4 (struct) :> triangle-m
+ diagonal scale-matrix4 :> diagonal-m
- float-4{ 0.0 0.0 0.0 1.0 } :> c4
- float-4{ t t t f } offset c4 v? :> offset'
+ 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
- offset' { 3 3 3 0 } vshuffle float-4{ t f f t } vbitand
- offset' { 3 3 3 1 } vshuffle float-4{ f t f t } vbitand
- offset' { 3 3 3 2 } vshuffle float-4{ f f t t } vbitand
- c4
+ triangle-m set-columns drop
- c set-rows ;
+ 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
+ ! 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
- float-4{ 1.0 -1.0 1.0 0.0 } :> triangle-sign
+ float-4{ -1.0 1.0 -1.0 0.0 } :> triangle-sign
c float-4-with :> cc
s float-4-with :> ss
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-rows 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 )
- matrix4 (struct) :> c
-
- near near near far + 2 near far * * float-4-boa :> num
- float-4{ t t f f } xy near far - float-4-with v? :> denom
- num denom v/ :> fov
-
- fov { 0 0 0 0 } vshuffle float-4{ t f f f } vbitand
- fov { 1 1 1 1 } vshuffle float-4{ f t f f } vbitand
- fov { 2 2 2 3 } vshuffle float-4{ f f t t } vbitand
- float-4{ 0.0 0.0 -1.0 0.0 }
-
- c set-rows ;
-
+ [
+ near near near far + 2 near far * * float-4-boa ! num
+ float-4{ t t f f } xy near far - float-4-with v? ! denom
+ v/ :> fov
+
+ float-4{ 0.0 -1.0 0.0 0.0 } :> negone
+
+ fov vmerge-diagonal
+ [ vmerge-diagonal ]
+ [ 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) ;
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