--- /dev/null
+USING: help.markup help.syntax math math.vectors vectors ;
+IN: math.quaternions
+
+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 } }" } } ;
+
+HELP: qconjugate
+{ $values { "u" "a quaternion" } { "u'" "a quaternion" } }
+{ $description "Quaternion conjugate." } ;
+
+HELP: qrecip
+{ $values { "u" "a quaternion" } { "1/u" "a quaternion" } }
+{ $description "Quaternion inverse." } ;
+
+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 }" } } ;
+
+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." } ;
+
+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 }" } } ;
+
+HELP: euler
+{ $values { "phi" number } { "theta" number } { "psi" number } { "q" "a quaternion" } }
+{ $description "Convert a rotation given by Euler angles (phi, theta, and psi) to a quaternion." } ;
+
! Copyright (C) 2005, 2007 Slava Pestov.
! See http://factorcode.org/license.txt for BSD license.
+USING: arrays kernel math math.functions math.vectors sequences ;
+IN: math.quaternions
-! Everybody's favorite non-commutative skew field, the
-! 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.
-USING: arrays kernel math math.vectors math.functions
-arrays sequences ;
-IN: math.quaternions
+! Quaternions are represented as pairs of complex numbers, using the
+! identity: (a+bi)+(c+di)j = a+bi+cj+dk.
<PRIVATE
PRIVATE>
: q* ( u v -- u*v )
- #! Multiply quaternions.
[ q*a ] [ q*b ] 2bi 2array ;
: qconjugate ( u -- u' )
- #! Quaternion conjugate.
first2 [ conjugate ] [ neg ] bi* 2array ;
: qrecip ( u -- 1/u )
- #! Quaternion inverse.
qconjugate dup norm-sq v/n ;
: q/ ( u v -- u/v )
- #! Divide quaternions.
qrecip q* ;
: q*n ( q n -- q )
- #! Note: you will get the wrong result if you try to
- #! multiply a quaternion by a complex number on the right
- #! using v*n. Use this word instead. Note that v*n with a
- #! quaternion and a real is okay.
conjugate v*n ;
: c>q ( c -- q )
- #! Turn a complex number into a quaternion.
0 2array ;
: v>q ( v -- q )
- #! Turn a 3-vector into a quaternion with real part 0.
first3 rect> [ 0 swap rect> ] dip 2array ;
: q>v ( q -- v )
- #! Get the vector part of a quaternion, discarding the real
- #! part.
first2 [ imaginary-part ] dip >rect 3array ;
! Zero
: qj { 0 1 } ;
: qk { 0 C{ 0 1 } } ;
-! Euler angles -- see
-! http://www.mathworks.com/access/helpdesk/help/toolbox/aeroblks/euleranglestoquaternions.html
+! Euler angles
+
+<PRIVATE
: (euler) ( theta unit -- q )
- [ -0.5 * dup cos c>q swap sin ] dip n*v v- ;
+ [ -0.5 * [ cos c>q ] [ sin ] bi ] dip n*v v- ;
+
+PRIVATE>
: euler ( phi theta psi -- q )
[ qi (euler) ] [ qj (euler) ] [ qk (euler) ] tri* q* q* ;