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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">	<html>		<head>			<title>page_30</title>			<link rel="stylesheet" href="reset.css" type="text/css" media="all">			<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />		</head>		<body>		<table summary="top nav" border="0" width="100%">			<tr>				<td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_29.html">&lt;&nbsp;previous page</a></td>				<td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_30</strong></td>				<td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_31.html">next page&nbsp;&gt;</a></td>			</tr>					<tr>				<td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;">    <table border="0" width="100%" cellpadding="0"><tr><td align="center">  <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td>  <td align="right"></td>  </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 30</font></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="200" cellpadding="4"><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="1">TABLE</font><font face="Times New Roman, Times, Serif" size="2"> 2.2 Approximate Closed-Form Solution for the ECEF Rectangular-to-Geodetic Coordinate Transformation</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="c0b2861858ab5426173d23fbcf2be231.gif" border="0" alt="0030-01.GIF" width="157" height="177" /></font></td></tr></table></td></tr></table><br /><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><i>2.3.1<br />Points</i></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">Given a right-handed orthogonal coordinate system </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, the coordinates</font><font face="Times New Roman, Times, Serif" size="2"><sup>**</sup></font><font face="Times New Roman, Times, Serif" size="3"> (<i>x</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">) represent the location of a point <i>P</i> relative to the origin of the </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> coordinate system, as shown in Fig. 2.6. The coordinates can be interpreted as the projections of the vector V</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, from the coordinate system origin to the point <i>P</i>, onto the coordinate system axes:</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="be9829dc0e4cd75bbb9f70c2b1371a17.gif" border="0" alt="0030-02.GIF" width="323" height="21" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="b661985bc524149484fa1b7470fa2bef.gif" border="0" alt="0030-03.GIF" width="319" height="21" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="ebcd3cf04b74eb862f1374ef7f06c45d.gif" border="0" alt="0030-04.GIF" width="318" height="22" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="e9bd48e25ea7e1e217cebda7c30414bb.gif" border="0" alt="0030-05.GIF" width="318" height="21" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">where I</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, J</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, and K</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> are unit vectors along the </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> axes.</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="787d829ca11568b4cb20345b169f7058.gif" border="0" alt="0030-06.GIF" width="130" height="131" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽2.6<br />Points聽and聽vectors聽in聽an<br />orthogonal聽coordinate<br />system.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3" height="1"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="2"><sup>** </sup>Here a three space is used throughout the discussion; however, the discussion is equally valid for <i>R<sup>n</sup></i><sup></sup>.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>  </td>			</tr>				<tr>				<td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_29.html">&lt;&nbsp;previous page</a></td>				<td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_30</strong></td>				<td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_31.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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