<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html
  SYSTEM "about:legacy-compat">
<html xmlns:mml = "http://www.w3.org/1998/Math/MathML" lang = "en"><head><meta charset = "UTF-8"/><meta name = "copyright" content = "(C) Copyright 2020"/><meta name = "DC.rights.owner" content = "(C) Copyright 2020"/><meta name = "DC.type" content = "concept"/><meta name = "abstract" content = "A third possibility to define a coordinate system is by an origin and rotation angles."/><meta name = "description" content = "A third possibility to define a coordinate system is by an origin and rotation angles."/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-usr-model-csDefOrigAngle"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Definition by Origin and Rotation Angles</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script></head><body onLoad = "highlightSearchTerms();" id = "tso-c-usr-model-csDefOrigAngle">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Definition by Origin and Rotation Angles</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">A third possibility to define a coordinate system is by an origin and rotation angles.</span>

</p>
<ul><li><a href = "#tso-c-usr-model-csDefOrigAngle__tso-c-usr-model-csDefOrigAngle-expl" id = "toc_rg" title = "">Examples</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>In <span class = "ph">Tosca Structure.gui</span>,
   instead of using three points with given coordinates, the origin and
   the rotation angles around the three axes are used in order to define
   a coordinate system. This is done using <code class = "ph codeph">Local</code> radio
   button as shown in the following figure (this is equivalent to setting
<code class = "ph codeph">DEF_TYPE = LOCAL</code> in <code class = "ph codeph">CS_DEF</code> command):</p>

<br/><img class = "image" src = "../TsoUserImages/model_coordinate_system15.png" width = "362" height = "156"/><br/>

<p>Then, the coordinates of the origin (with respect to the coordinate
   system specified in Reference CS field) and the three rotation angles
   are to be chosen. The directions of the axes of the coordinate system
   are constructed in the following manner:</p>
<ul class = "ul">
<li class = "li">first, the axes X, Y, Z of the reference coordinate system are taken.</li>
<li class = "li">then, the axes are rotated around z-axis by the first angle in <code class = "ph codeph">Rotation</code>
fields (labeled with 3): axes X’, Y’, Z’ = Z are produced.</li>
<li class = "li">the resulting axes are rotated around Y’ by the second angle (field
labeled with 2): axes X’’, Y’’ = Y’, Z’’ are produced.</li>
<li class = "li">finally, these axes are rotated around X’’ by the third angle
(field labeled with 1): axes X’’’ = X’’, Y’’’, Z’’’
are produced that give the directions for the coordinate system axes.</li>
</ul>
<p>All rotations are performed in positive (counter-clockwise) directions.
   the values of the angles are in degrees.</p>
<div class = "section" id = "tso-c-usr-model-csDefOrigAngle__tso-c-usr-model-csDefOrigAngle-expl"><h2 class = "title sectiontitle">Examples</h2>

<p>As shown in the following figure, a Cartesian coordinate system with
   the name CS_14 should be defined relative to the global Cartesian coordinate
   system CS_0. The point of origin of the new coordinate system should
   have the coordinates (30, 20, 0). Then, a cylindrical coordinate system
   CS_15 should be defined relative to CS_14 with the origin at the point
   (60, 5, 0). CS_15 should be rotated 15° around Z axis: The result coordinate
   system CS_15 defines a cylindrical coordinate system with origin (90,25,0)
   with respect to the global Cartesian coordinate system CS_0. The polar
   axis through the new origin is rotated by 15° around the z-axis. The
   longitudinal axis is parallel to the original z-axis through the new origin:</p>

<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME      = CS_14
  CS_TYPE      = RECTANGULAR
  DEF_TYPE     = LOCAL
  CS_REF       = CS_0
  ORIGIN_123   = 30,20,0
  ROTATION_321 = 0,0,0
END_
</code>
</pre>

<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME      = CS_15
  CS_TYPE      = CYLINDRICAL
  DEF_TYPE     = LOCAL
  CS_REF       = CS_14
  ORIGIN_123   = 60,5,0
  ROTATION_321 = 15,0,0
END_
</code>
</pre>

<br/><img class = "image" src = "../TsoUserImages/model_csDefOrigAngles.png" width = "443" height = "173"/><br/>
</div>

</div>

</td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
