<html> <head> <title>Struct AffineMatrix2D</title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <link rel="stylesheet" type="text/css" href="../../../../idl.css"> </head> <body> <div id="adc-idlref"> <a name="_top_"> </a><table class="navimain" border="0" cellpadding="3"> <tr> <td class="navimain"><a href="../module-ix.html" class="navimain">Overview</a></td> <td class="navimain"><a href="module-ix.html" class="navimain">Module</a></td> <td class="navimain"><a href="AffineMatrix2D-xref.html" class="navimain">Use</a></td> <td class="navimainnone">Devguide</td> <td class="navimain"><a href="../../../../index-files/index-1.html" class="navimain">Index</a></td> </tr> </table> <table class="navisub" border="0" cellpadding="0"> <tr> <td class="navisub"><a href="#Elements" class="navisub">Elements' Summary</a></td> <td class="navisub"><a href="#ElementDetails" class="navisub">Elements' Details</a></td> </tr> </table> <hr> <table border="0" width="100%" cellpadding="5" cellspacing="3" class="title-table" style="margin-bottom:6pt;"> <tr> <td><p class="namechain"><a href="../../../../module-ix.html" class="namechain">::</a> <a href="../../../module-ix.html" class="namechain">com</a> :: <a href="../../module-ix.html" class="namechain">sun</a> :: <a href="../module-ix.html" class="namechain">star</a> :: <a href="module-ix.html" class="namechain">geometry</a> :: </p> </td> </tr> <tr> <td class="title"><table class="title-table" width="99%"> <tr> <td width="25%" class="title2">unpublished </td> <td width="50%" class="title">struct AffineMatrix2D</td> <td width="*"/></tr> </table> </td> </tr> <tr> <td/></tr> <tr> <td><dl> <dt><b>Usage Restrictions</b></dt> <dd><i>not published</i></dd> <dt><b>Description</b></dt> <dd>This structure defines a 2 by 3 affine matrix.</dd> <dd><p> The matrix defined by this structure constitutes an affine mapping of a point in 2D to another point in 2D. The last line of a complete 3 by 3 matrix is omitted, since it is implicitly assumed to be [0,0,1].<p> An affine mapping, as performed by this matrix, can be written out as follows, where <code>xs</code> and <code>ys</code> are the source, and <code>xd</code> and <code>yd</code> the corresponding result coordinates: <code> xd = m00*xs + m01*ys + m02; yd = m10*xs + m11*ys + m12; </code><p> Thus, in common matrix language, with M being the <a href="AffineMatrix2D.html">AffineMatrix2D</a> and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D vectors, the affine transformation is written as vd=M*vs. Concatenation of transformations amounts to multiplication of matrices, i.e. a translation, given by T, followed by a rotation, given by R, is expressed as vd=R*(T*vs) in the above notation. Since matrix multiplication is associative, this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of consecutive transformations can be accumulated into a single AffineMatrix2D, by multiplying the current transformation with the additional transformation from the left.<p> Due to this transformational approach, all geometry data types are points in abstract integer or real coordinate spaces, without any physical dimensions attached to them. This physical measurement units are typically only added when using these data types to render something onto a physical output device, like a screen or a printer, Then, the total transformation matrix and the device resolution determine the actual measurement unit.<p> </dd> <dt><b>Since </b></dt> <dd>OOo 2.0 </dd> </dl> </td> </tr> </table> <hr> <a name="Elements"/><table border="1" width="100%" cellpadding="5" cellspacing="0" class="subtitle"> <tr> <td class="subtitle" colspan="2">Elements' Summary</td> </tr> <tr> <td class="imsum_left"><a href="#m00">m00</a></td> <td class="imsum_right">The top, left matrix entry. </td> </tr> <tr> <td class="imsum_left"><a href="#m01">m01</a></td> <td class="imsum_right">The top, middle matrix entry. </td> </tr> <tr> <td class="imsum_left"><a href="#m02">m02</a></td> <td class="imsum_right">The top, right matrix entry. </td> </tr> <tr> <td class="imsum_left"><a href="#m10">m10</a></td> <td class="imsum_right">The bottom, left matrix entry. </td> </tr> <tr> <td class="imsum_left"><a href="#m11">m11</a></td> <td class="imsum_right">The bottom, middle matrix entry. </td> </tr> <tr> <td class="imsum_left"><a href="#m12">m12</a></td> <td class="imsum_right">The bottom, right matrix entry. </td> </tr> </table> <a name="ElementDetails"/><table border="1" width="100%" cellpadding="5" cellspacing="0" class="subtitle"> <tr> <td class="subtitle">Elements' Details</td> </tr> <tr> <td class="imdetail"><a name="m00" class="membertitle">m00</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m00</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The top, left matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> <tr> <td class="imdetail"><a name="m01" class="membertitle">m01</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m01</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The top, middle matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> <tr> <td class="imdetail"><a name="m02" class="membertitle">m02</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m02</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The top, right matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> <tr> <td class="imdetail"><a name="m10" class="membertitle">m10</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m10</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The bottom, left matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> <tr> <td class="imdetail"><a name="m11" class="membertitle">m11</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m11</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The bottom, middle matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> <tr> <td class="imdetail"><a name="m12" class="membertitle">m12</a><table border="0" width="96%" cellpadding="5" cellspacing="0" class="table-in-data" bgcolor="#ffffff" align="center"> <tr> <td>double <b>m12</b>;<hr> <dl> <dt><b>Description</b></dt> <dd>The bottom, right matrix entry.</dd> </dl> </td> </tr> </table> </td> </tr> </table> <a href="#_top_">Top of Page</a><hr size="3"><p class="copyright" align="center">Copyright © 2000, 2012 LibreOffice contributors and/or their affiliates. 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