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<h1>1D Meshing Hypotheses</h1>
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<ul type="disc" class="whs1">
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#arithmetic_1D"><span
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style="font-weight: bold;"><B>Arithmetic 1D</B></span></a></p></li>
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Average_length"><span
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style="font-weight: bold;"><B>Average Length</B></span></a></p></li>
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#deflection_1D"><span
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style="font-weight: bold;"><B>Deflection 1D </B></span></a></p></li>
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Number_of_elements"><span
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style="font-weight: bold;"><B>Number of segments</B></span></a></p></li>
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#start_and_end_length"><span
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style="font-weight: bold;"><B>Start and end length</B></span></a></p></li>
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<li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
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class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#automatic_length"><span
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style="font-weight: bold;"><B>Automatic Length</B></span></a></p></li>
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</ul>
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<h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3>
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<p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows
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to split edges into segments with a length that changes in arithmetic
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progression (Lk = Lk-1 + d) beginning from a given starting length and
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up to a given end length.</p>
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<p> </p>
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<p class="whs3"><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs5"></p>
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<p> </p>
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<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining
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Arithmetic 1D hypothesis</a> operation. </p>
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<h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3>
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<p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can
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be applied for meshing curvilinear edges composing your geometrical object.
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It uses only one parameter: the value of deflection. </p>
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<p>A geometrical edge is divided into equal segments. The maximum distance
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between a point on the edge within a segment and the line connecting the
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ends of the segment should not exceed the specified value of deflection
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. Then mesh nodes are constructed at end segment locations and 1D mesh
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elements are constructed on segments.</p>
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<p> </p>
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<p class="whs3"><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> <img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs8"></p>
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<p> </p>
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<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
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Deflection 1D hypothesis</a> operation. </p>
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<p> </p>
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<p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p>
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<h3><a name=Average_length>Average Length hypothesis</a></h3>
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<p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can
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be applied for meshing of edges composing your geometrical object. Definition
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of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span>
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of segments, which will split these edges. The points on the edges generated
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by these segments will represent nodes of your mesh. Later these nodes
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will be used for meshing of the faces abutting to these edges.</p>
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<p> </p>
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<p class="whs3"><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> <img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs11"></p>
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<p> </p>
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<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
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Average Length hypothesis</a> operation. </p>
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<p> </p>
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<p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p>
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<h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3>
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<p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis
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can be applied for meshing of edges composing your geometrical object.
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Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span>
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of segments, which will split these edges. In other words your edges will
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be split into a definite number of segments with approximately the same
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length. The points on the edges generated by these segments will represent
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nodes of your mesh. Later these nodes will be used for meshing of the
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faces abutting to these edges.</p>
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<p> </p>
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<p class="whs6">You can set the type of distribution for this
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hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span>
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dialog bog : </p>
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<p class="whs6"> </p>
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<p class="whs6"><span style="font-weight: bold;"><B>Equidistant
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Distribution</B></span> - all segments will have the same length, you define
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only the <span style="font-weight: bold;"><B>Number of Segments</B></span>.</p>
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<p class="whs6"> </p>
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<p class="whs3"><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs14"></p>
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<p> </p>
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<p class="whs9">Scale Distribution - <span style="font-weight: normal;">each
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next segment differs from the previous according to the formula:</span>
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A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i
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</span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is
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a</span> Scale Factor. </p>
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<p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p>
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<p class="whs9"> </p>
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<p class="whs9">Distribution with Table Density - <span style="font-weight: normal;">you
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input a number of pairs</span> t - F(t),<span style="font-weight: normal;">
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where </span>t<span style="font-weight: normal;"> ranges from 0 to 1,</span>
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<span style="font-weight: normal;">and
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the module computes the formula, which will rule the change of length
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of segments and shows the curve in the plot. You can select the </span>Conversion
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mode<span style="font-weight: normal;"> from </span>Exponent<span style="font-weight: normal;">
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and </span>Cut negative<span style="font-weight: normal;">. </span></p>
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<p class="whs9"> </p>
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<p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p>
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<p class="whs9"> </p>
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<p class="whs9">Distribution with Analytic Density - <span
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style="font-weight: normal;">you input the formula, which will rule the
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change of length of segments and the module shows the curve in the plot.</span></p>
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<h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3>
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<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
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Number of Segments hypothesis</a> operation. </p>
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<h3> </h3>
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<h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3>
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<p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis
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allows to divide a geometrical edge into segments so that the first and
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the last segments have a specified length. The length of each but the
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first segment differs from length of the previous one by a constant factor.
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Then mesh nodes are constructed at segment ends location and 1D mesh elements
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are constructed on them.</p>
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<p> </p>
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<p class="whs3"><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs19"></p>
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<p class="whs6"> </p>
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<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
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Start and End Length hypothesis</a>
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operation. </p>
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<p class="whs6"> </p>
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<h3><a name=automatic_length>Automatic Length</a></h3>
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<p>This hypothesis is automatically applied when you select <span style="font-weight: bold;"><B>Assign
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a set of hypotheses</B></span> option in Create Mesh menu. </p>
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<p> </p>
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<p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p>
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<p> </p>
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<p>The dialog box prompts you to define the quality of the future mesh
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by only one parameter, which is <span style="font-weight: bold;"><B>Fineness</B></span>,
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ranging from 0 (coarse mesh, low number of elements) to 1 (extremely fine
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mesh, great number of elements). Compare one and the same object (sphere)
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meshed with minimum and maximum value of this parameter. </p>
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<p> </p>
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<p class="whs3"><img src="../image147.gif" width="195px" height="192px" border="0" class="img_whs21"> <img src="../image148.gif" width="206px" height="195px" border="0" class="img_whs22"></p>
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<p> </p>
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<p> </p>
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<p> </p>
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<p> </p>
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