Class: Math_Quaternion

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Math_Quaternion: class to represent an manipulate quaternions (q = a + b*i + c*j + d*k)

A quaternion is an extension of the idea of complex numbers In 1844 Hamilton described a system in which numbers were composed of a real part and 3 imaginary and independent parts (i,j,k), such that:

i^2 = j^2 = k^2 = -1 and ij = k, jk = i, ki = j and ji = -k, kj = -i, ik = -j

The above are known as "Hamilton's rules"

Interesting references on quaternions:

• Sir William Rowan Hamilton "On Quaternions", Proceedings of the Royal Irish Academy, Nov. 11, 1844, vol. 3 (1847), 1-16 (http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Quatern2/Quatern2.html)

• Quaternion (from MathWorld): http://mathworld.wolfram.com/Quaternion.html

Originally this class was part of NumPHP (Numeric PHP package)

Example:

 require_once 'Math/Quaternion.php';

 $a = new Math_Quaternion(2,4,2,-0.5);
 $b = new Math_Quaternion(1,2,3,0.5);

 echo "a: ".$a->toString()."\n";
 echo "b: ".$b->toString()."\n";
 $t = Math_QuaternionOp::conjugate($a);
 echo "a': ".$t->toString()."\n";
 $t = Math_QuaternionOp::conjugate($b);
 echo "b': ".$t->toString()."\n";
 echo "length(a): ".$a->length()."  length2(a): ".$a->length2()."\n";
 echo "real(a): ".$a->getReal()."\nimag(a): ";

 print_r($a->getAllIm());

Output from example:

 a: 2 + 4i + 2j + -0.5k
 b: 1 + 2i + 3j + 0.5k
 a': 2 + -4i + -2j + 0.5k
 b': 1 + -2i + -3j + -0.5k
 length(a): 4.9244289008981  length2(a): 24.25
 real(a): 2
 imag(a): Array
 (
     [i] => 4
     [j] => 2
     [k] => -0.5
 )

Math_Quaternion (Constructor)   [line 131]

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conjugate   [line 217]

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getAllIm   [line 348]

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getI   [line 285]

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getJ   [line 306]

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getK   [line 327]

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getReal   [line 264]

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length   [line 184]

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length2   [line 160]

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makeClone   [line 242]

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negate   [line 229]

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norm   [line 174]

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normalize   [line 194]

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setAllIm   [line 336]

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setI   [line 275]

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setJ   [line 296]

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setK   [line 317]

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setReal   [line 254]

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toString   [line 144]

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