<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=utf-8"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Hi Maris,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>The transformation matrix contains the rotation, scaling (so to say, the upper-left 3x3 matrix) and other components, e.g. a translational component (the 4<sup>th</sup> column). You can think of the fourth row as a sort of a mathematical trick to end up with a square matrix, making a lot of operations easier and computationally more efficient. This 4x4 transformation matrix is actually called a projection matrix (widely used in 3D programming), and there the 4<sup>th</sup> row actually plays a big role in perspective mapping (e.g. being able to make objects farther away seem smaller). <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>This explanation should be roughly correct - I am not a mathematician though ;) <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Best regards,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Jörn<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:9.0pt;font-family:"Verdana",sans-serif;color:#1F497D;mso-fareast-language:NL'>--</span></b><b><span style='font-size:9.0pt;font-family:"Verdana",sans-serif;color:#255A9E;mso-fareast-language:NL'><br>Jörn M. Horschig, PhD</span></b><span style='font-size:9.0pt;font-family:"Verdana",sans-serif;color:#626264;mso-fareast-language:NL'>, Software Engineer<br><a href="http://www.artinis.com/" target="_blank"><span style='color:#626264'>Artinis Medical Systems</span></a> | +31 481 350 980 </span><b><span style='font-size:9.0pt;font-family:"Verdana",sans-serif;color:#255A9E;mso-fareast-language:NL'><o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> fieldtrip-bounces@science.ru.nl [mailto:fieldtrip-bounces@science.ru.nl] <b>On Behalf Of </b>Maris Skujevskis<br><b>Sent:</b> Monday, April 25, 2016 23:52<br><b>To:</b> fieldtrip@science.ru.nl<br><b>Subject:</b> [FieldTrip] transformation matrix<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Dear Fieldtrip users,<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>A quick simple question (maybe it's been answered somewhere already but really I cannot find it...)<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Functions like ft_read_mri and ft_volumerealign attach the field 'transform' (a 4 x 4 matrix) to the data structure ( <a href="http://www.fieldtriptoolbox.org/faq/how_to_coregister_an_anatomical_mri_with_the_gradiometer_or_electrode_positions" target="_blank">http://www.fieldtriptoolbox.org/faq/how_to_coregister_an_anatomical_mri_with_the_gradiometer_or_electrode_positions</a> )<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>My question is: what operations do each of the values in this transformation matrix correspond to?<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Thanks for your help!<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Maris<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div></div></body></html>