Quaternion type: Difference between revisions
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'a1*d2 + b1*c2 − c1*b2 + d1*a2' EVAL |
'a1*d2 + b1*c2 − c1*b2 + d1*a2' EVAL |
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{ 4 } →ARRY |
{ 4 } →ARRY |
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≫ ≫ '''' |
≫ ≫ ''''QMULT'''' STO |
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'''QNORM''' ''( [ a b c d ] -- √(a²+b²+c²+d²) )'' |
'''QNORM''' ''( [ a b c d ] -- √(a²+b²+c²+d²) )'' |
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''' |
'''QMULT''' ''( [Q1] [Q2] -- [Q1 x Q2] )'' |
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put the 2 quaternions in local variables |
put the 2 quaternions in local variables |
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do the math in stack |
do the math in stack |
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[2 3 4 5] [3 4 5 6] + |
[2 3 4 5] [3 4 5 6] + |
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[1 2 3 4] 7 * |
[1 2 3 4] 7 * |
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[2 3 4 5] [3 4 5 6] |
[2 3 4 5] [3 4 5 6] QMULT |
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[3 4 5 6] [2 3 4 5] |
[3 4 5 6] [2 3 4 5] QMULT |
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</pre> |
</pre> |
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1: [ -56 18 20 28 ] |
1: [ -56 18 20 28 ] |
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</pre> |
</pre> |
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=== Quaternion multiplication through Cayley-Dickson construction=== |
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This is a shorter and faster version of the <code>QMULT</code> word. {{trans|Ruby}} |
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{| class="wikitable" |
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! RPL code |
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! Comment |
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|- |
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| |
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≪ |
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ARRY→ DROP R→C ROT ROT R→C ROT |
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ARRY→ DROP R→C ROT ROT R→C → d c b a |
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≪ a c * d CONJ b * - C→R |
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d a * b c CONJ * + C→R |
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{ 4 } →ARRY |
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≫ ≫ ''''QMULT'''' STO |
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'''QMULT''' ''( [Q1] [Q2] -- [Q1 x Q2] )'' |
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convert the 2 quaternions into complex numbers |
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and store them locally |
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(a,b)(c,d) = (ac - conj(d).b, // (a,b) and (c,d) are pairs |
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da + b.conj(c)) // of complex numbers |
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convert stack to a quaternion |
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|} |
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Output is the same. |
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=={{header|Ruby}}== |
=={{header|Ruby}}== |
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