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<h1>1D Meshing Hypotheses</h1>

<ul type="disc" class="whs1">
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#arithmetic_1D"><span 
 style="font-weight: bold;"><B>Arithmetic 1D</B></span></a></p></li>
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Average_length"><span 
 style="font-weight: bold;"><B>Average Length</B></span></a></p></li>
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#deflection_1D"><span 
 style="font-weight: bold;"><B>Deflection 1D </B></span></a></p></li>
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Number_of_elements"><span 
 style="font-weight: bold;"><B>Number of segments</B></span></a></p></li>
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#start_and_end_length"><span 
 style="font-weight: bold;"><B>Start and end length</B></span></a></p></li>
	
	<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
		class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#automatic_length"><span 
 style="font-weight: bold;"><B>Automatic Length</B></span></a></p></li>
</ul>

<h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3>

<p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows 
 to split edges into segments with a length that changes in arithmetic 
 progression (Lk = Lk-1 + d) beginning from a given starting length and 
 up to a given end length.</p>

<p>&nbsp;</p>

<p class="whs3"><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs5"></p>

<p>&nbsp;</p>

<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> 
 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining 
 Arithmetic 1D hypothesis</a> operation. &nbsp;</p>

<h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3>

<p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can 
 be applied for meshing curvilinear edges composing your geometrical object. 
 It uses only one parameter: the value of deflection. &nbsp;</p>

<p>A geometrical edge is divided into equal segments. The maximum distance 
 between a point on the edge within a segment and the line connecting the 
 ends of the segment should not exceed the specified value of deflection 
 . Then mesh nodes are constructed at end segment locations and 1D mesh 
 elements are constructed on segments.</p>

<p>&nbsp;</p>

<p class="whs3"><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs8"></p>

<p>&nbsp;</p>

<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> 
 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining 
 Deflection 1D hypothesis</a> operation. &nbsp;</p>

<p>&nbsp;</p>

<p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p>

<h3><a name=Average_length>Average Length hypothesis</a></h3>

<p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can 
 be applied for meshing of edges composing your geometrical object. Definition 
 of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span> 
 of segments, which will split these edges. The points on the edges generated 
 by these segments will represent nodes of your mesh. Later these nodes 
 will be used for meshing of the faces abutting to these edges.</p>

<p>&nbsp;</p>

<p class="whs3"><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs11"></p>

<p>&nbsp;</p>

<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> 
 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining 
 Average Length hypothesis</a> operation. &nbsp;</p>

<p>&nbsp;</p>

<p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p>

<h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3>

<p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis 
 can be applied for meshing of edges composing your geometrical object. 
 Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span> 
 of segments, which will split these edges. In other words your edges will 
 be split into a definite number of segments with approximately the same 
 length. The points on the edges generated by these segments will represent 
 nodes of your mesh. Later these nodes will be used for meshing of the 
 faces abutting to these edges.</p>

<p>&nbsp;</p>

<p class="whs6">You can set the type of distribution for this 
 hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span> 
 dialog bog : </p>

<p class="whs6">&nbsp;</p>

<p class="whs6"><span style="font-weight: bold;"><B>Equidistant 
 Distribution</B></span> - all segments will have the same length, you define 
 only the <span style="font-weight: bold;"><B>Number of Segments</B></span>.</p>

<p class="whs6">&nbsp;</p>

<p class="whs3"><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs14"></p>

<p>&nbsp;</p>

<p class="whs9">Scale Distribution - <span style="font-weight: normal;">each 
 next segment differs from the previous according to the formula:</span> 
 A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i 
 </span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is 
 a</span> Scale Factor. </p>

<p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p>

<p class="whs9">&nbsp;</p>

<p class="whs9">Distribution with Table Density - <span style="font-weight: normal;">you 
 input a number of pairs</span> t - F(t),<span style="font-weight: normal;"> 
 where </span>t<span style="font-weight: normal;"> ranges from 0 to 1,</span> 
 &nbsp;<span style="font-weight: normal;">and 
 the module computes the formula, which will rule the change of length 
 of segments and shows the curve in the plot. You can select the </span>Conversion 
 mode<span style="font-weight: normal;"> from </span>Exponent<span style="font-weight: normal;"> 
 and </span>Cut negative<span style="font-weight: normal;">. </span></p>

<p class="whs9">&nbsp;</p>

<p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p>

<p class="whs9">&nbsp;</p>

<p class="whs9">Distribution with Analytic Density - <span 
 style="font-weight: normal;">you input the formula, which will rule the 
 change of length of segments and the module shows the curve in the plot.</span></p>

<h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3>

<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> 
 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining 
 Number of Segments hypothesis</a> operation. &nbsp;</p>

<h3>&nbsp;</h3>

<h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3>

<p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis 
 allows to divide a geometrical edge into segments so that the first and 
 the last segments have a specified length. The length of each but the 
 first segment differs from length of the previous one by a constant factor. 
 Then mesh nodes are constructed at segment ends location and 1D mesh elements 
 are constructed on them.</p>

<p>&nbsp;</p>

<p class="whs3"><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs19"></p>

<p class="whs6">&nbsp;</p>

<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> 
 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining 
 Start and End Length &nbsp;hypothesis</a> 
 operation. &nbsp;</p>

<p class="whs6">&nbsp;</p>

<h3><a name=automatic_length>Automatic Length</a></h3>

<p>This hypothesis is automatically applied when you select <span style="font-weight: bold;"><B>Assign 
 a set of hypotheses</B></span> option in Create Mesh menu. </p>

<p>&nbsp;</p>

<p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p>

<p>&nbsp;</p>

<p>The dialog box prompts you to define the quality of the future mesh 
 by only one parameter, which is <span style="font-weight: bold;"><B>Fineness</B></span>, 
 ranging from 0 (coarse mesh, low number of elements) to 1 (extremely fine 
 mesh, great number of elements). Compare one and the same object (sphere) 
 meshed with minimum and maximum value of this parameter. </p>

<p>&nbsp;</p>

<p class="whs3"><img src="../image147.gif" width="195px" height="192px" border="0" class="img_whs21"> &nbsp;&nbsp;&nbsp;<img src="../image148.gif" width="206px" height="195px" border="0" class="img_whs22"></p>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p>&nbsp;</p>

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