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	<title>LiveDocs Comments - flash - 9.0 - ActionScriptLangRefV3 - flash/geom/Matrix.html</title>	
		<link>http://livedocs.adobe.com/</link>
		<description>Macromedia LiveDocs - online documentation with user feedback.</description>
		<copyright>Copyright 2009, Macromedia, Inc.</copyright>
		<dc:date>2009-11-25T11:09:10</dc:date>
		<dc:language>en-us</dc:language>
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		<title>flash/9.0/ActionScriptLangRefV3/flash/geom/Matrix.html</title>
		<link>http://livedocs.adobe.com/flash/9.0/ActionScriptLangRefV3/flash/geom/Matrix.html#79516</link>
		<description>I submitted my previous remarks too quickly.  It's mathematically equivalent to think of the matrix elements as&lt;br /&gt;&lt;br /&gt;a    b    0&lt;br /&gt;c    d    0&lt;br /&gt;t(x) t(y) 1&lt;br /&gt;&lt;br /&gt;as long as you use pre-multiplied row vectors and treat concatenation as a post-multiply operation.  So take your pick; just be consistent.&lt;br /&gt;&lt;br /&gt;The important point is that the b and c elements are transposed in Adobe's documentation.&lt;br /&gt;&lt;br /&gt;Also, I wrote that this error had persisted since AS 2.0.  What I meant to say was that it had persisted since Flash 8.&lt;br /&gt;&lt;br /&gt;Happy hacking!</description>
		<dc:creator>mmcaulay</dc:creator>
		<dc:type>0 0</dc:type>
		<dc:date>2008-01-15T10:28:51</dc:date>
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		<title>flash/9.0/ActionScriptLangRefV3/flash/geom/Matrix.html</title>
		<link>http://livedocs.adobe.com/flash/9.0/ActionScriptLangRefV3/flash/geom/Matrix.html#79199</link>
		<description>BaconTastesGood is right: the Matrix documentation is incorrect regarding the order of the elements.  The correct order is:&lt;br /&gt;&lt;br /&gt;a c t(x)&lt;br /&gt;b d t(y)&lt;br /&gt;0 0 1&lt;br /&gt;&lt;br /&gt;There is a nice interactive tutorial here: http://imm.sheridanc.on.ca/imm2006/macgillm/tutorial/&lt;br /&gt;&lt;br /&gt;It's not stated explicitly anywhere in the documentation but flash uses column vectors (not row vectors).  So the transformation of a vector by a matrix is a post-multiply operation: x' = Ax.&lt;br /&gt;&lt;br /&gt;A consequence is that the operation A concat B is equivalent to premultiplying A by B:  A' = BA, *not* A' = AB.&lt;br /&gt;&lt;br /&gt;For casual use this may not matter.  But for anyone else out there playing tricksy matrix games, I hope this saves you a little time.&lt;br /&gt;&lt;br /&gt;Adobe, it's time to update the Matrix docs!  This error has persisted since AS2.0.</description>
		<dc:creator>mmcaulay</dc:creator>
		<dc:type>0 0</dc:type>
		<dc:date>2008-01-04T16:34:07</dc:date>
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