vector-friendlier math.quaternions

basis/math/quaternions/quaternions-docs.factor

@@ -4,17 +4,17 @@ IN: math.quaternions
 HELP: q+
 { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u+v" "a quaternion" } }
 { $description "Add quaternions." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q+ ." "{ C{ 0 1 } 1 }" } } ;
+{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q+ ." "{ 0 1 1 0 }" } } ;
 
 HELP: q-
 { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u-v" "a quaternion" } }
 { $description "Subtract quaternions." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q- ." "{ C{ 0 1 } -1 }" } } ;
+{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q- ." "{ 0 1 -1 0 }" } } ;
 
 HELP: q*
 { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u*v" "a quaternion" } }
 { $description "Multiply quaternions." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q* ." "{ 0 C{ 0 1 } }" } } ;
+{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q* ." "{ 0 0 0 1 }" } } ;
 
 HELP: qconjugate
 { $values { "u" "a quaternion" } { "u'" "a quaternion" } }
@@ -27,28 +27,17 @@ HELP: qrecip
 HELP: q/
 { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u/v" "a quaternion" } }
 { $description "Divide quaternions." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 C{ 0 1 } } { 0 1 } q/ ." "{ C{ 0 1 } 0 }" } } ;
+{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 0 0 1 } { 0 0 1 0 } q/ ." "{ 0 1 0 0 }" } } ;
 
 HELP: q*n
-{ $values { "q" "a quaternion" } { "n" number } { "q" "a quaternion" } }
-{ $description "Multiplies each element of " { $snippet "q" } " by " { $snippet "n" } "." }
-{ $notes "You will get the wrong result if you try to multiply a quaternion by a complex number on the right using " { $link v*n } ". Use this word instead."
-    $nl "Note that " { $link v*n } " with a quaternion and a real is okay." } ;
+{ $values { "q" "a quaternion" } { "n" real } { "q" "a quaternion" } }
+{ $description "Multiplies each element of " { $snippet "q" } " by real value " { $snippet "n" } "." }
+{ $notes "To multiply a quaternion with a complex value, use " { $link c>q } " " { $link q* } "." } ;
 
 HELP: c>q
 { $values { "c" number } { "q" "a quaternion" } }
 { $description "Turn a complex number into a quaternion." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "C{ 0 1 } c>q ." "{ C{ 0 1 } 0 }" } } ;
-
-HELP: v>q
-{ $values { "v" vector } { "q" "a quaternion" } }
-{ $description "Turn a 3-vector into a quaternion with real part 0." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 1 0 0 } v>q ." "{ C{ 0 1 } 0 }" } } ;
-
-HELP: q>v
-{ $values { "q" "a quaternion" } { "v" vector } }
-{ $description "Get the vector part of a quaternion, discarding the real part." }
-{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } q>v ." "{ 1 0 0 }" } } ;
+{ $examples { $example "USING: math.quaternions prettyprint ;" "C{ 0 1 } c>q ." "{ 0 1 0 0 }" } } ;
 
 HELP: euler
 { $values { "phi" number } { "theta" number } { "psi" number } { "q" "a quaternion" } }

basis/math/quaternions/quaternions-tests.factor

@@ -2,6 +2,12 @@ IN: math.quaternions.tests
 USING: tools.test math.quaternions kernel math.vectors
 math.constants ;
 
+CONSTANT: q0 { 0 0 0 0 }
+CONSTANT: q1 { 1 0 0 0 }
+CONSTANT: qi { 0 1 0 0 }
+CONSTANT: qj { 0 0 1 0 }
+CONSTANT: qk { 0 0 0 1 }
+
 [ 1.0 ] [ qi norm ] unit-test
 [ 1.0 ] [ qj norm ] unit-test
 [ 1.0 ] [ qk norm ] unit-test
@@ -10,18 +16,13 @@ math.constants ;
 [ t ] [ qi qj q* qk = ] unit-test
 [ t ] [ qj qk q* qi = ] unit-test
 [ t ] [ qk qi q* qj = ] unit-test
-[ t ] [ qi qi q* q1 v+ q0 = ] unit-test
-[ t ] [ qj qj q* q1 v+ q0 = ] unit-test
-[ t ] [ qk qk q* q1 v+ q0 = ] unit-test
-[ t ] [ qi qj qk q* q* q1 v+ q0 = ] unit-test
-[ t ] [ C{ 0 1 } qj n*v qk = ] unit-test
-[ t ] [ qj C{ 0 1 } q*n qk v+ q0 = ] unit-test
+[ t ] [ qi qi q* q1 q+ q0 = ] unit-test
+[ t ] [ qj qj q* q1 q+ q0 = ] unit-test
+[ t ] [ qk qk q* q1 q+ q0 = ] unit-test
+[ t ] [ qi qj qk q* q* q1 q+ q0 = ] unit-test
 [ t ] [ qk qj q/ qi = ] unit-test
 [ t ] [ qi qk q/ qj = ] unit-test
 [ t ] [ qj qi q/ qk = ] unit-test
-[ t ] [ qi q>v v>q qi = ] unit-test
-[ t ] [ qj q>v v>q qj = ] unit-test
-[ t ] [ qk q>v v>q qk = ] unit-test
 [ t ] [ 1 c>q q1 = ] unit-test
 [ t ] [ C{ 0 1 } c>q qi = ] unit-test
 [ t ] [ qi qi q+ qi 2 q*n = ] unit-test

basis/math/quaternions/quaternions.factor

@@ -1,72 +1,62 @@
 ! Copyright (C) 2005, 2007 Slava Pestov.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: arrays kernel math math.functions math.vectors sequences ;
+USING: arrays combinators kernel math math.functions math.libm math.vectors sequences ;
 IN: math.quaternions
 
-! Everybody's favorite non-commutative skew field, the quaternions!
-
-! Quaternions are represented as pairs of complex numbers, using the
-! identity: (a+bi)+(c+di)j = a+bi+cj+dk.
-
-<PRIVATE
-
-: ** ( x y -- z ) conjugate * ; inline
-
-: 2q ( u v -- u' u'' v' v'' ) [ first2 ] bi@ ; inline
-
-: q*a ( u v -- a ) 2q swapd ** [ * ] dip - ; inline
-
-: q*b ( u v -- b ) 2q [ ** swap ] dip * + ; inline
-
-PRIVATE>
-
 : q+ ( u v -- u+v )
-    v+ ;
+    v+ ; inline
 
 : q- ( u v -- u-v )
-    v- ;
+    v- ; inline
 
 : q* ( u v -- u*v )
-    [ q*a ] [ q*b ] 2bi 2array ;
+    {
+        [ [ { 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
 
 : qconjugate ( u -- u' )
-    first2 [ conjugate ] [ neg  ] bi* 2array ;
+    { 1 -1 -1 -1 } v* ; inline
 
 : qrecip ( u -- 1/u )
-    qconjugate dup norm-sq v/n ;
+    qconjugate dup norm-sq v/n ; inline
 
 : q/ ( u v -- u/v )
-    qrecip q* ;
+    qrecip q* ; inline
+
+: n*q ( q n -- q )
+    v*n ; inline
 
 : q*n ( q n -- q )
-    conjugate v*n ;
+    v*n ; inline
+
+: n>q ( n -- q )
+    0 0 0 4array ; inline
+
+: n>q-like ( c exemplar -- q )
+    [ 0 0 0 ] dip 4sequence ; inline
 
 : c>q ( c -- q )
-    0 2array ;
+    >rect 0 0 4array ; inline
 
-: v>q ( v -- q )
-    first3 rect> [ 0 swap rect> ] dip 2array ;
-
-: q>v ( q -- v )
-    first2 [ imaginary-part ] dip >rect 3array ;
-
-! Zero
-CONSTANT: q0 { 0 0 }
-
-! Units
-CONSTANT: q1 { 1 0 }
-CONSTANT: qi { C{ 0 1 } 0 }
-CONSTANT: qj { 0 1 }
-CONSTANT: qk { 0 C{ 0 1 } }
+: c>q-like ( c exemplar -- q )
+    [ >rect 0 0 ] dip 4sequence ; inline
 
 ! Euler angles
 
 <PRIVATE
 
-: (euler) ( theta unit -- q )
-    [ -0.5 * [ cos c>q ] [ sin ] bi ] dip n*v v- ;
+: (euler) ( theta exemplar shuffle -- q )
+    swap
+    [ 0.5 * [ fcos ] [ fsin ] bi 0.0 0.0 ] [ call ] [ 4sequence ] tri* ; inline
 
 PRIVATE>
 
+: euler-like ( phi theta psi exemplar -- q )
+    [ [ ] (euler) ] [ [ swapd ] (euler) ] [ [ rot ] (euler) ] tri-curry tri* q* q* ; inline
+
 : euler ( phi theta psi -- q )
-  [ qi (euler) ] [ qj (euler) ] [ qk (euler) ] tri* q* q* ;
+    { } euler-like ; inline
+