Add documentation for math.quaternions
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USING: help.markup help.syntax math math.vectors vectors ;
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IN: math.quaternions
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HELP: q*
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{ $values { "u" "a quaternion" } { "v" "a quaternion" } { "u*v" "a quaternion" } }
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{ $description "Multiply quaternions." }
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{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q* ." "{ 0 C{ 0 1 } }" } } ;
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HELP: qconjugate
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{ $values { "u" "a quaternion" } { "u'" "a quaternion" } }
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{ $description "Quaternion conjugate." } ;
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HELP: qrecip
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{ $values { "u" "a quaternion" } { "1/u" "a quaternion" } }
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{ $description "Quaternion inverse." } ;
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HELP: q/
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{ $values { "u" "a quaternion" } { "v" "a quaternion" } { "u/v" "a quaternion" } }
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{ $description "Divide quaternions." }
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{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 C{ 0 1 } } { 0 1 } q/ ." "{ C{ 0 1 } 0 }" } } ;
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HELP: q*n
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{ $values { "q" "a quaternion" } { "n" number } { "q" "a quaternion" } }
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{ $description "Multiplies each element of " { $snippet "q" } " by " { $snippet "n" } "." }
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{ $notes "You will get the wrong result if you try to multiply a quaternion by a complex number on the right using " { $link v*n } ". Use this word instead."
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$nl "Note that " { $link v*n } " with a quaternion and a real is okay." } ;
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HELP: c>q
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{ $values { "c" number } { "q" "a quaternion" } }
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{ $description "Turn a complex number into a quaternion." }
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{ $examples { $example "USING: math.quaternions prettyprint ;" "C{ 0 1 } c>q ." "{ C{ 0 1 } 0 }" } } ;
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HELP: v>q
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{ $values { "v" vector } { "q" "a quaternion" } }
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{ $description "Turn a 3-vector into a quaternion with real part 0." }
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{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 1 0 0 } v>q ." "{ C{ 0 1 } 0 }" } } ;
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HELP: q>v
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{ $values { "q" "a quaternion" } { "v" vector } }
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{ $description "Get the vector part of a quaternion, discarding the real part." }
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{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } q>v ." "{ 1 0 0 }" } } ;
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HELP: euler
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{ $values { "phi" number } { "theta" number } { "psi" number } { "q" "a quaternion" } }
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{ $description "Convert a rotation given by Euler angles (phi, theta, and psi) to a quaternion." } ;
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! Copyright (C) 2005, 2007 Slava Pestov.
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! See http://factorcode.org/license.txt for BSD license.
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! Everybody's favorite non-commutative skew field, the
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! quaternions!
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! Quaternions are represented as pairs of complex numbers,
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! using the identity: (a+bi)+(c+di)j = a+bi+cj+dk.
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USING: arrays kernel math math.vectors math.functions
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arrays sequences ;
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USING: arrays kernel math math.functions math.vectors sequences ;
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IN: math.quaternions
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! Everybody's favorite non-commutative skew field, the quaternions!
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! Quaternions are represented as pairs of complex numbers, using the
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! identity: (a+bi)+(c+di)j = a+bi+cj+dk.
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<PRIVATE
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: ** conjugate * ; inline
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@ -23,39 +21,27 @@ IN: math.quaternions
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PRIVATE>
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: q* ( u v -- u*v )
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#! Multiply quaternions.
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[ q*a ] [ q*b ] 2bi 2array ;
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: qconjugate ( u -- u' )
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#! Quaternion conjugate.
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first2 [ conjugate ] [ neg ] bi* 2array ;
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: qrecip ( u -- 1/u )
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#! Quaternion inverse.
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qconjugate dup norm-sq v/n ;
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: q/ ( u v -- u/v )
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#! Divide quaternions.
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qrecip q* ;
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: q*n ( q n -- q )
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#! Note: you will get the wrong result if you try to
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#! multiply a quaternion by a complex number on the right
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#! using v*n. Use this word instead. Note that v*n with a
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#! quaternion and a real is okay.
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conjugate v*n ;
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: c>q ( c -- q )
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#! Turn a complex number into a quaternion.
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0 2array ;
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: v>q ( v -- q )
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#! Turn a 3-vector into a quaternion with real part 0.
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first3 rect> [ 0 swap rect> ] dip 2array ;
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: q>v ( q -- v )
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#! Get the vector part of a quaternion, discarding the real
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#! part.
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first2 [ imaginary-part ] dip >rect 3array ;
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! Zero
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@ -67,11 +53,14 @@ PRIVATE>
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: qj { 0 1 } ;
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: qk { 0 C{ 0 1 } } ;
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! Euler angles -- see
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! http://www.mathworks.com/access/helpdesk/help/toolbox/aeroblks/euleranglestoquaternions.html
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! Euler angles
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<PRIVATE
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: (euler) ( theta unit -- q )
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[ -0.5 * dup cos c>q swap sin ] dip n*v v- ;
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[ -0.5 * [ cos c>q ] [ sin ] bi ] dip n*v v- ;
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PRIVATE>
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: euler ( phi theta psi -- q )
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[ qi (euler) ] [ qj (euler) ] [ qk (euler) ] tri* q* q* ;
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