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QuaternionOp.php
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QuaternionOp.php
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<?php
//
// +----------------------------------------------------------------------+
// | PHP Version 4 |
// +----------------------------------------------------------------------+
// | Copyright (c) 1997-2002 The PHP Group |
// +----------------------------------------------------------------------+
// | This source file is subject to version 2.0 of the PHP license, |
// | that is bundled with this package in the file LICENSE, and is |
// | available at through the world-wide-web at |
// | http://www.php.net/license/2_02.txt. |
// | If you did not receive a copy of the PHP license and are unable to |
// | obtain it through the world-wide-web, please send a note to |
// | license@php.net so we can mail you a copy immediately. |
// +----------------------------------------------------------------------+
// | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> |
// +----------------------------------------------------------------------+
//
// $Id$
//
include_once 'PEAR.php';
include_once 'Math/Quaternion.php';
/**
* Math_QuaternionOp: class that implements operations on quaternions
*
* Originally this class was part of NumPHP (Numeric PHP package)
*
* Example:
* <pre>
* require_once 'Math/QuaternionOp.php';
*
* $a = new Math_Quaternion(2,4,2,-0.5);
* $b = new Math_Quaternion(1,2,3,0.5);
*
* if (!Math_QuaternionOp::areEqual($a, Math_QuaternionOp::negative($a))) {
* echo "a and neg(a) are different\n";
* }
* $t=Math_QuaternionOp::negative($a);
* echo "Neg(a) is ".$t->toString()."\n";
* $t=Math_QuaternionOp::conjugate($a);
* echo "Conj(a) is ".$t->toString()."\n";
* $t=Math_QuaternionOp::inverse($a);
* echo "Inv(a) is ".$t->toString()."\n";
* $t=Math_QuaternionOp::multReal($a, 1.23);
* echo "MultReal(a, 1.23) is ".$t->toString()."\n";
*
* echo "====\n";
* $t=Math_QuaternionOp::mult($a,$b);
* echo "a*b: ".$t->toString()."\n";
* $t=Math_QuaternionOp::mult($b,$a);
* echo "b*a: ".$t->toString()."\n";
* $t=Math_QuaternionOp::mult($a,Math_QuaternionOp::conjugate($a));
* echo "a*a': ".$t->toString()."\n";
* echo "length(a*a'): ".$t->length()."\n";
* $t=Math_QuaternionOp::add($a,$b);
* echo "a+b: ".$t->toString()."\n";
* $t=Math_QuaternionOp::sub($a,$b);
* echo "a-b: ".$t->toString()."\n";
* $t=Math_QuaternionOp::sub($b,$a);
* echo "b-a: ".$t->toString()."\n";
* $t=Math_QuaternionOp::sub($b,Math_QuaternionOp::conjugate($a));
* echo "b-a': ".$t->toString()."\n";
* $t=Math_QuaternionOp::sub(Math_QuaternionOp::conjugate($b), $a);
* echo "b'-a: ".$t->toString()."\n";
* $t=Math_QuaternionOp::sub(Math_QuaternionOp::conjugate($b), Math_QuaternionOp::conjugate($a));
* echo "b'-a': ".$t->toString()."\n";
* $t = Math_QuaternionOp::div($a, $b);
* echo "a/b: ".$t->toString()."\n";
* $t = Math_QuaternionOp::div($b, $a);
* echo "b/a: ".$t->toString()."\n";
* </pre>
*
* Output from example:
* <pre>
* a and neg(a) are different
* Neg(a) is -2 + -4i + -2j + 0.5k
* Conj(a) is 2 + -4i + -2j + 0.5k
* Inv(a) is 0.40613846605345 + -0.8122769321069i + -0.40613846605345j + 0.10153461651336k
* MultReal(a, 1.23) is 2.46 + 4.92i + 2.46j + -0.615k
* ====
* a*b: -11.25 + 6i + 9j + 1.5k
* b*a: -18.25 + 12i + 6j + -1.5k
* a*a': -16.25 + -16i + -8j + 2k
* length(a*a'): 24.25
* a+b: 3 + 6i + 5j + 0k
* a-b: 1 + 2i + -1j + -1k
* b-a: -1 + -2i + 1j + 1k
* b-a': -1 + 6i + 5j + 0k
* b'-a: -1 + -6i + -5j + 0k
* b'-a': -1 + 2i + -1j + -1k
* a/b: -19.720187057174 + 9.059625885652i + 4.529812942826j + -1.1324532357065k
* b/a: -12.843861533947 + 2.8122769321069i + 4.2184153981603j + 0.70306923302672k
* </pre>
*
* @author Jesus M. Castagnetto <jmcastagnetto@php.net>
* @version 0.7
* @access public
* @package Math_Quaternion
*/
class Math_QuaternionOp {/*{{{*/
/**
* Whether the object is a Math_Quaternion instance
*
* @param object Math_Quaternion $q1
* @return boolean TRUE if object is a Math_Quaternion, FALSE otherwise
* @access public
*/
function isQuaternion (&$q1) {/*{{{*/
if (function_exists('is_a')) {
return is_a($q1, 'math_quaternion');
} else {
return (get_class($q1) == 'math_quaternion'
|| is_subclass_of($q1, 'math_quaternion'));
}
}/*}}}*/
/**
* Calculate the conjugate of a quaternion
*
* @param object Math_Quaternion $q1
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &conjugate (&$q1) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1)) {
return PEAR::raiseError("Parameter needs to be a Math_Quaternion object");
}
$q2 = $q1->clone();
$q2->conjugate();
return $q2;
}/*}}}*/
/**
* Negates the given quaternion
*
* @param object Math_Quaternion $q1
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &negate (&$q1) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1)) {
return PEAR::raiseError("Parameter needs to be a Math_Quaternion object");
}
$q2 = $q1->clone();
$q2->negate();
return $q2;
}/*}}}*/
/**
* Inverts the given quaternion
*
* @param object Math_Quaternion $q1
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
* @see Math_QuaternionOp::multReal
*/
function &inverse (&$q1) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1)) {
return PEAR::raiseError("Parameter needs to be a Math_Quaternion object");
}
$c = Math_QuaternionOp::conjugate($q1);
$norm = $q1->norm();
if ($norm == 0) {
return PEAR::raiseError('Quaternion norm is zero, cannot calculate inverse');
}
$invmult = 1/$norm;
return Math_QuaternionOp::multReal($c, $invmult);
}/*}}}*/
/**
* Checks if two quaternions represent the same number
*
* @param object Math_Quaternion $q1
* @param object Math_Quaternion $q2
* @return mixed PEAR_Error on error, TRUE if q1 == q2, FALSE otherwise
* @access public
*/
function areEqual (&$q1, &$q2) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !Math_QuaternionOp::isQuaternion($q2)) {
return PEAR::raiseError("Parameters need to be Math_Quaternion objects");
}
return ( $q1->getReal() == $q2->getReal() && $q1->getI() == $q2->getI() &&
$q1->getJ() == $q2->getJ() && $q1->getK() == $q2->getK() );
}/*}}}*/
/**
* Adds two quaternions: q1 + q2
*
* @param object Math_Quaternion $q1
* @param object Math_Quaternion $q2
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &add (&$q1, &$q2) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !Math_QuaternionOp::isQuaternion($q2)) {
return PEAR::raiseError("Parameters need to be Math_Quaternion objects");
}
return new Math_Quaternion( $q1->getReal() + $q2->getReal(), $q1->getI() + $q2->getI(),
$q1->getJ() + $q2->getJ(), $q1->getK() + $q2->getK() );
}/*}}}*/
/**
* Substracts two quaternions: q1 - q2
*
* @param object Math_Quaternion $q1
* @param object Math_Quaternion $q2
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &sub (&$q1, &$q2) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !Math_QuaternionOp::isQuaternion($q2)) {
return PEAR::raiseError("Parameters need to be Math_Quaternion objects");
}
return Math_QuaternionOp::add($q1, Math_QuaternionOp::negate($q2));
}/*}}}*/
/**
* Multiplies two quaternions: q1 * q2
* It uses a fast multiplication algorithm.
*
* @param object Math_Quaternion $q1
* @param object Math_Quaternion $q2
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &mult (&$q1, &$q2) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !Math_QuaternionOp::isQuaternion($q2)) {
return PEAR::raiseError("Parameters need to be Math_Quaternion objects");
}
// uses the fast multiplication algorithm
$a = $q1->getReal(); $q1im = $q1->getAllIm();
$b = $q1im["i"]; $c = $q1im["j"]; $d = $q1im["k"];
$x = $q2->getReal(); $q2im = $q2->getAllIm();
$y = $q2im["i"]; $z = $q2im["j"]; $w = $q2im["k"];
$t0 = ($d - $c) * ($z - $w);
$t1 = ($a + $b) * ($x + $y);
$t2 = ($a - $b) * ($z + $w);
$t3 = ($c + $d) * ($x - $y);
$t4 = ($d - $b) * ($y - $z);
$t5 = ($d + $b) * ($y + $z);
$t6 = ($a + $c) * ($x - $w);
$t7 = ($a - $c) * ($x + $w);
$t8 = $t5 + $t6 + $t7;
$t9 = 0.5 * ($t4 + $t8);
$r = $t0 + $t9 - $t5;
$i = $t1 + $t9 - $t8;
$j = $t2 + $t9 - $t7;
$k = $t3 + $t9 - $t6;
return new Math_Quaternion($r, $i , $j, $k);
}/*}}}*/
/**
* Divides two quaternions: q1 / q2
*
* @param object Math_Quaternion $q1
* @param object Math_Quaternion $q2
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &div (&$q1, &$q2) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !Math_QuaternionOp::isQuaternion($q2)) {
return PEAR::raiseError("Parameters need to be Math_Quaternion objects");
}
$i2 = Math_QuaternionOp::inverse($q2);
if (PEAR::isError($i2)) {
return $i2;
}
return Math_QuaternionOp::mult($i2, $q1);
}/*}}}*/
/**
* Multiplies a quaternion by a real number: q1 * realnum
*
* @param object Math_Quaternion $q1
* @param float $realnum
* @return object a Math_Quaternion on success, PEAR_Error otherwise
* @access public
*/
function &multReal (&$q1, $realnum) {/*{{{*/
if (!Math_QuaternionOp::isQuaternion($q1) || !is_numeric($realnum)) {
return PEAR::raiseError("A Math_Quaternion object and a real number are needed");
}
return new Math_Quaternion ( $realnum * $q1->getReal(), $realnum * $q1->getI(),
$realnum * $q1->getJ(), $realnum * $q1->getK() );
}/*}}}*/
}/*}}} end of Math_QuaternionOp */
?>