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<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 Vectors</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">Another possibility to define a coordinate system is by an origin and three vectors.</span>

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<ul><li><a href = "#tso-c-usr-model-csDefVector__tso-c-usr-model-csDefVector-expl" id = "toc_rg" title = "">Examples</a></li></ul>
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<div class = "body conbody">
<p>In <span class = "ph">Tosca Structure.gui</span>,
   the origin and three vectors are used in order to define
   a coordinate system. This is done using <code class = "ph codeph">VECTOR</code> radio
   button as shown in the following figure (this is equivalent to setting
<code class = "ph codeph">DEF_TYPE = VECTOR</code> in <code class = "ph codeph">CS_DEF</code> command):</p>

<br/><img class = "image" src = "../TsoUserImages/model_coordinate_system16.png" width = "362"/><br/>

<p>Then, the coordinates of the origin (with respect to the coordinate
   system CS_0) and the three vectors
   are to be chosen. The directions of the axes of the coordinate system
   are constructed by setting the X,Y, Z axes to the <code class = "ph codeph">VECTOR_X</code>, <code class = "ph codeph">VECTOR_Y</code>
   and <code class = "ph codeph">VECTOR_Z</code> entries, respectively.</p>
<p>The rotation matrix given by <code class = "ph codeph">VECTOR_X</code>, <code class = "ph codeph">VECTOR_Y</code>, <code class = "ph codeph">VECTOR_Z</code>
	must have a determinant of 1, ie:</p>
<p><span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "17" altimg-width = "22" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">abs</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">det</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "[" close = "]" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced><mi class = "- topic/foreign ">=</mi><mi class = "- topic/foreign ">abs</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">det</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "[" close = "]" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">VECTOR_X, VECTOR_Y, VECTOR_Z</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced><mi class = "- topic/foreign ">=</mi><mi class = "- topic/foreign ">1</mi></mrow></math></span></p>

<div class = "section" id = "tso-c-usr-model-csDefVector__tso-c-usr-model-csDefVector-expl"><h2 class = "title sectiontitle">Examples</h2>

<p> As shown in the following figure, a Cartesian coordinate system with
	the name CS_16 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 (10, 10, 10). The x-axis is defined by the vector (-1,0,0), 
	y-axis with the vector (0,-1,0) and the z-axis with (0,0,-1).:</p>

<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME  = CS_16
  CS_TYPE  = RECTANGULAR
  DEF_TYPE = VECTOR
  ORIGIN   = 10,10,10
  VECTOR_X = -1,0,0
  VECTOR_Y = 0,-1,0
  VECTOR_Z = 0,0,-1
END_
</code>
</pre>

<br/><img class = "image" src = "../TsoUserImages/model_csDefOrigVector.png" width = "250"/><br/>
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