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-<h1>Arithmetic 1D hypothesis</h1>\r
+<h1>1D Meshing Hypotheses</h1>\r
+\r
+<h3>Arithmetic 1D hypothesis</h3>\r
+\r
+<p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows \r
+ to split edges into segments with a length that changes in arithmetic \r
+ progression (Lk = Lk-1 + d) beginning from a given starting length and \r
+ up to a given end length.</p>\r
+\r
+<p> </p>\r
+\r
+<p><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs2"></p>\r
+\r
+<p> </p>\r
\r
-<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> <span style="font-weight: bold;"><B>Arithmetic 1D</B></span> \r
- - hypothesis for the Regular 1D algorithm. It allows to split edges into \r
- segments with a length that changes in arithmetic progression (Lk = Lk-1 \r
- + d) beginning from a given starting length and up to a given end length.</p>\r
+<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> \r
+ a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining \r
+ Arithmetic 1D hypothesis</a> operation. </p>\r
+\r
+<h3><span style="font-weight: bold;"><B>Deflection</B></span> 1D hypothesis</h3>\r
+\r
+<p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can \r
+ be applied for meshing curvilinear edges composing your geometrical object. \r
+ It uses only one parameter: the value of deflection. </p>\r
+\r
+<p>A geometrical edge is divided into equal segments. The maximum distance \r
+ between a point on the edge within a segment and the line connecting the \r
+ ends of the segment should not exceed the specified value of deflection \r
+ . Then mesh nodes are constructed at end segment locations and 1D mesh \r
+ elements are constructed on segments.</p>\r
\r
<p> </p>\r
\r
-<p>Similar to Start and End Length.</p>\r
+<p><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs4"> <img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs5"></p>\r
\r
<p> </p>\r
\r
-<p class=TODO>To define the Arithmetic 1D hypothesis:</p>\r
+<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> \r
+ a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining \r
+ Deflection 1D hypothesis</a> operation. </p>\r
\r
-<p class=TODO> </p>\r
+<p> </p>\r
\r
-<p class="whs2">Select this hypothesis in <a href="about_hypotheses.htm#CreateHyp">the \r
- <span style="font-weight: bold;"><B>Create Hypotheses </B></span>dialog box</a> \r
- click <span style="font-weight: bold;"><B>Create</B></span>. The following dialog \r
- box will appear:</p>\r
+<p class="whs6"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs7"></p>\r
\r
-<p class="whs2"> </p>\r
+<h3>Average Length hypothesis</h3>\r
\r
-<p class="whs2"><img src="../image16.jpg" width="319px" height="222px" border="0" class="img_whs3"></p>\r
+<p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can \r
+ be applied for meshing of edges composing your geometrical object. Definition \r
+ of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span> \r
+ of segments, which will split these edges. The points on the edges generated \r
+ by these segments will represent nodes of your mesh. Later these nodes \r
+ will be used for meshing of the faces abutting to these edges.</p>\r
\r
-<p class="whs4"> </p>\r
+<p> </p>\r
+\r
+<p><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs4"> <img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs8"></p>\r
+\r
+<p> </p>\r
+\r
+<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> \r
+ a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining \r
+ Average Length hypothesis</a> operation. </p>\r
+\r
+<p> </p>\r
\r
-<p class="whs4">In this dialog box you can set:</p>\r
+<p class="whs9"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs10"></p>\r
\r
-<p class="whs4"> </p>\r
+<h3>Number of segments hypothesis </h3>\r
\r
-<ul type="disc" class="whs5">\r
- \r
- <li class=kadov-p><p class="whs4"><span style="font-weight: bold;"><B>Name \r
- </B></span>of your Arithmetic 1D hypothesis;</p></li>\r
- \r
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Start</B></span> \r
- and <span style="font-weight: bold;"><B>End length</B></span> values</p></li>\r
-</ul>\r
+<p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis \r
+ can be applied for meshing of edges composing your geometrical object. \r
+ Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span> \r
+ of segments, which will split these edges. In other words your edges will \r
+ be split into a definite number of segments with approximately the same \r
+ length. The points on the edges generated by these segments will represent \r
+ nodes of your mesh. Later these nodes will be used for meshing of the \r
+ faces abutting to these edges.</p>\r
+\r
+<p> </p>\r
+\r
+<p class="whs3">You can set the type of distribution for this \r
+ hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span> \r
+ dialog bog : </p>\r
+\r
+<p class="whs3"> </p>\r
+\r
+<p class="whs3"><span style="font-weight: bold;"><B>Equidistant \r
+ Distribution</B></span> - all segments will have the same length</p>\r
+\r
+<p><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs11"></p>\r
+\r
+<p> </p>\r
+\r
+<p class="whs6">Scale Distribution - <span style="font-weight: normal;">each \r
+ next segment differs from the previous according to the formula:</span> \r
+ A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i \r
+ </span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is</span> \r
+ Scale Factor </p>\r
+\r
+<p class="whs6"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs12">\</p>\r
+\r
+<p class="whs6"> </p>\r
+\r
+<p class="whs6">Distribution with Table Density - <span style="font-weight: normal;">you \r
+ input a number of pairs</span> t - F(t) <span style="font-weight: normal;">and \r
+ the program computes the formula, which will rule the change of length \r
+ of segments.</span></p>\r
+\r
+<p class="whs6"> </p>\r
+\r
+<p class="whs6"><img src="../pics/a-nbsegments3.png" x-maintain-ratio="TRUE" width="333px" height="386px" border="0" class="img_whs13"></p>\r
+\r
+<p class="whs6"> </p>\r
+\r
+<p class="whs6">Distribution with Analytic Density - <span \r
+ style="font-weight: normal;">you input the formula, which will rule the \r
+ change of length of segments</span></p>\r
+\r
+<h3><img src="../pics/a-nbsegments4.png" x-maintain-ratio="TRUE" width="333px" height="285px" border="0" class="img_whs14"></h3>\r
+\r
+<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> \r
+ a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining \r
+ Number of Segments hypothesis</a> operation. </p>\r
+\r
+<h3> </h3>\r
+\r
+<h3>Start and End Length hypothesis.</h3>\r
+\r
+<p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis \r
+ allows to divide a geometrical edge into segments so that the first and \r
+ the last segments have a specified length. The length of each but the \r
+ first segment differs from length of the previous one by a constant factor. \r
+ Then mesh nodes are constructed at segment ends location and 1D mesh elements \r
+ are constructed on them.</p>\r
+\r
+<p> </p>\r
+\r
+<p><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs15"></p>\r
+\r
+<p class="whs3"> </p>\r
+\r
+<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> \r
+ a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining \r
+ Start and End Length hypothesis</a> \r
+ operation. </p>\r
+\r
+<p> </p>\r
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