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	<title>1990Harauz Quaternions - Revision history</title>
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	<updated>2026-05-24T19:53:24Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://3demmethods.i2pc.es/index.php?title=1990Harauz_Quaternions&amp;diff=2196&amp;oldid=prev</id>
		<title>CoSS: Created page with &quot;== Citation ==  Harauz, G. Representation of rotations by unit quaternions Ultramicroscopy, 1990, 33, 209-213  == Abstract ==  A closed form solution by Horn of an absolute or...&quot;</title>
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		<updated>2012-08-02T06:52:37Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Citation ==  Harauz, G. Representation of rotations by unit quaternions Ultramicroscopy, 1990, 33, 209-213  == Abstract ==  A closed form solution by Horn of an absolute or...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== Citation ==&lt;br /&gt;
&lt;br /&gt;
Harauz, G. Representation of rotations by unit quaternions Ultramicroscopy, 1990, 33, 209-213&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
&lt;br /&gt;
A closed form solution by Horn of an absolute orientation problem in photogrammetry and robotics entails the equivalent&lt;br /&gt;
expression of rotation matrices by unit quaternions [B.K.P. Horn, J. Opt. Soc. Am. 4 (1987) 629]. Such representation by&lt;br /&gt;
quaternions offers practical advantages in electron microscopy of macromolecular structures, where rotation angles must also&lt;br /&gt;
be determined by optimisation techniques.&lt;br /&gt;
&lt;br /&gt;
== Keywords ==&lt;br /&gt;
&lt;br /&gt;
Angular representation, Euler angles, Rotation matrix&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
&lt;br /&gt;
== Related software ==&lt;br /&gt;
&lt;br /&gt;
== Related methods ==&lt;br /&gt;
&lt;br /&gt;
== Comments ==&lt;/div&gt;</summary>
		<author><name>CoSS</name></author>
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