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    Leo,<br>
    <br>
    Here is the *.tex file.<br>
    <br>
    Sorry for the trouble with the *.pdf file. For whatever reason, my
    "tool chain" here (WinXP-64;&nbsp;<span class="moz-smiley-s1"><span> :-)
      </span></span> =&gt; emacs-21.2 =&gt; *.tex =&gt; latex =&gt;
    *.dvi =&gt; dvips =&gt; *.ps =&gt; GSview+ImageMagick-6.3.3-Q16
    =&gt; *.pdf =&gt; Adobe Reader-10.1.3) works OK.<br>
    <br>
    Sam<br>
    <br>
    On 6/10/2012 8:45 PM, Yuanxin Liu wrote:
    <blockquote
cite="mid:CAH+HHJ-AZYPkZPo-9NL8X8d-D-zYPYYDFNTJgd3U8OJMY_nnRw@mail.gmail.com"
      type="cite">Hi, Sam,&nbsp;
      <div>&nbsp; I am still having trouble with the file. I tried to open it
        with several programs on windows &nbsp; and linux platforms and could
        not open it. &nbsp;If you have a .tex file, maybe you can try to post
        that instead.</div>
      <div>thanks,</div>
      <div>Leo</div>
      <div><br>
        <div class="gmail_quote">On Sun, Jun 10, 2012 at 8:49 PM, Samuel
          Key <span dir="ltr">&lt;<a moz-do-not-send="true"
              href="mailto:samuelkey@bresnan.net" target="_blank">samuelkey@bresnan.net</a>&gt;</span>
          wrote:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div bgcolor="#FFFFFF" text="#000000"> Leo,<br>
              <br>
              Here is the *.pdf file again.<br>
              <br>
              Sam
              <div>
                <div class="h5"><br>
                  <br>
                  On 6/10/2012 6:36 PM, Yuanxin Liu wrote: </div>
              </div>
              <blockquote type="cite">
                <div>
                  <div class="h5">Hi, Sam,&nbsp;
                    <div>&nbsp; Would you mind reposting this? &nbsp;The pdf file
                      seems corrupt.</div>
                    <div>thanks,</div>
                  </div>
                </div>
                <div>Leo<br>
                  <br>
                  <div class="gmail_quote">
                    <div>
                      <div class="h5">On Sun, Jun 10, 2012 at 7:38 PM,
                        Samuel Key <span dir="ltr">&lt;<a
                            moz-do-not-send="true"
                            href="mailto:samuelkey@bresnan.net"
                            target="_blank">samuelkey@bresnan.net</a>&gt;</span>
                        wrote:<br>
                      </div>
                    </div>
                    <blockquote class="gmail_quote" style="margin:0 0 0
                      .8ex;border-left:1px #ccc solid;padding-left:1ex">
                      <div bgcolor="#FFFFFF" text="#000000">
                        <div>
                          <div class="h5"> Hi Leo,<br>
                            <br>
                            Though likely more arithmetically intense
                            than you would like, I have attached a
                            3-page write-up on how to do an exact
                            integration over the surface of a bi-linear
                            isoparametric coordinate based quadrilateral
                            in three-space. It is easily adapted to a
                            flux integration as well.<br>
                            <br>
                            If it helps, please free to incorporate it
                            into ParaView.<br>
                            <br>
                            Sam Key. </div>
                        </div>
                        <div>
                          <div>
                            <div>
                              <div class="h5"><br>
                                <br>
                                <br>
                                <br>
                                On 6/10/2012 12:55 PM, Yuanxin Liu
                                wrote: </div>
                            </div>
                            <blockquote type="cite">
                              <div>
                                <div class="h5">Hi,&nbsp;<br>
                                  &nbsp; &nbsp;This is not really a bug, but just
                                  what the linear precision integration
                                  does. &nbsp;As you can see
                                  in&nbsp;vtkIntegrateAttributes.cxx:215, the
                                  quad cell is basically cut into two
                                  triangles along a diagonal,
                                  integration is done for each triangle
                                  and the results are added up. &nbsp; So,
                                  depending where your "1" falls on a
                                  diagonal vertex, you will get
                                  different results.
                                  <div> <br>
                                  </div>
                                  <div>Leo</div>
                                  <div><br>
                                  </div>
                                  <br>
                                </div>
                              </div>
                              <div class="gmail_quote">
                                <div>
                                  <div class="h5">On Sat, Jun 9, 2012 at
                                    8:57 AM, Magician <span dir="ltr">&lt;<a
                                        moz-do-not-send="true"
                                        href="mailto:f_magician@mac.com"
                                        target="_blank">f_magician@mac.com</a>&gt;</span>
                                    wrote:<br>
                                  </div>
                                </div>
                                <blockquote class="gmail_quote"
                                  style="margin:0 0 0
                                  .8ex;border-left:1px #ccc
                                  solid;padding-left:1ex">
                                  <div>
                                    <div class="h5">Hi all,<br>
                                      <br>
                                      <br>
                                      Now I found a bug of the filter.<br>
                                      <br>
                                      My ParaView's version is 3.14.1.<br>
                                      I define node names as below:<br>
                                      &gt; c--d<br>
                                      &gt; | &nbsp;|<br>
                                      &gt; a--b<br>
                                      <br>
                                      Case 1: a=1.0, b=0.0, c=0.0, d=0.0<br>
                                      Integration Value = 0.33333<br>
                                      <br>
                                      Case 2: a=0.0, b=1.0, c=0.0, d=0.0<br>
                                      Integration Value = 0.16666<br>
                                      <br>
                                    </div>
                                  </div>
                                  ( Case 3: a=0.0, b=0.0, c=1.0, d=0.0
                                  <div class="im"><br>
                                    Integration Value = 0.16666<br>
                                    <br>
                                    Case 4: a=0.0, b=0.0, c=0.0, d=1.0<br>
                                    Integration Value = 0.33333<br>
                                    <br>
                                    So Integration Values are calculated
                                    as (2*a+b+c+2*d)/6.<br>
                                    I think it's not a good result.<br>
                                  </div>
                                  <span><font color="#888888">,br&gt; <br>
                                      Magician<br>
                                    </font></span>
                                  <div>
                                    <div>
                                      <div class="im"><br>
                                        <br>
                                        On(2012/06/08, at 12:54,
                                        Magician wrote:<br>
                                        <br>
                                        &gt; Hi all,<br>
                                        &gt;<br>
                                        &gt;<br>
                                      </div>
                                      &gt; I'm now comparing integjation
                                      results of each postprocessors.
                                      <div class="im"><br>
                                        &gt; I made a simple Quadratic
                                        VTK model as below:<br>
                                        &gt;&gt; # vtk DataFile Version
                                        2.0<br>
                                      </div>
                                      ( &gt;
                                      <div>
                                        <div class="h5"><br>
                                          &gt;&gt; QuadCell<br>
                                          &gt;&gt; ASCII<br>
                                          &gt;&gt; DATASET
                                          UNSTRUCTURED_GRID<br>
                                          &gt;&gt; POINTS 4 FLOAT<br>
                                          &gt;&gt; 0 0 0<br>
                                          &gt;&gt; 1 0 0<br>
                                          &gt;&gt; 0 1 0<br>
                                          &gt;&gt; 1 1 0<br>
                                          &gt;&gt; CELLS 1 5<br>
                                          &gt;&gt; 4 0 1 3 2<br>
                                          &gt;&gt; CELL_TYPES 1<br>
                                          &gt;&gt; 9<br>
                                          &gt;&gt; POINT_DATA 4<br>
                                          &gt;&gt; SCALARS scalar FLOAT
                                          1<br>
                                          &gt;&gt; LOOKUP_TABLE DEFAULT<br>
                                          &gt;&gt; 0.0<br>
                                          &gt;&gt; 1.0<br>
                                          &gt;&gt; 2.0<br>
                                          &gt;&gt; 4.0<br>
                                          &gt;<br>
                                          &gt; When I apply Point Data
                                          to Cell Data filter,<br>
                                          &gt; scalar values are
                                          interpolated as 1.75.<br>
                                          &gt; It may be calculated as
                                          (0.0+1.0+2.0+4.0)/4.0.<br>
                                          &gt;<br>
                                          &gt; But when I apply
                                          Integrate Variables filter,<br>
                                          &gt; scalar value is
                                          integrated as 1.833....<br>
                                          &gt; The area value of
                                          quadratic cell is 1.0, so I
                                          thought<br>
                                          &gt; integrated values should
                                          be equal to cell data.<br>
                                          &gt;<br>
                                          &gt; How the integrated value
                                          is calculated?<br>
                                          &gt;<br>
                                          &gt;<br>
                                          &gt; Magician<br>
                                          <br>
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                                <div class="h5"> <br>
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