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<div>Yup. This is a known issue with how pretty much every implementation of OpenGL renders quadrilaterals.</div>
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<div>For the most part, ParaView will interpolate the fields on your hexahedra and quadrilaterals correctly. For example, in either data set, if you add a plot over line filter and plot along the Y axis, you will see that the plot over line filter is symmetrically
interpolating the cells (see the attached screenshot).</div>
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<div>The issue is that both data sets are rendered by sending quadrilaterals to the OpenGL rendering engine. Every implementation of OpenGL I have run into in at least the last 15 years internally breaks the quadrilaterals into triangles (because it makes the
rasterization faster). It turns out, the linear interpolation of the two triangles is subtly different than the bi-linear interpolation on a quadrilateral. And, most importantly for your specific question, the interpolation is subtly different depending on
which which diagonal is used to split the quadrilateral. In your case, the rendering system is picking different diagonals for the rotationally isomorphic quadrilaterals (ooh, that sounds mathy) and is causing the asymmetric interpolation.</div>
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<div>We've had multiple discussions about fixing this. In the end we decided to leave it as it is. The issue is that the fix is to break polygons like quadrilaterals into several triangles that are closer to the bilinear interpolation. The issue is that it
would add a large computation and memory overhead for an issue that is almost never noticeable.</div>
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<div>-Ken</div>
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<span style="font-weight:bold">From: </span>Marco Goetz <<a href="mailto:marco.goetz@tu-dresden.de">marco.goetz@tu-dresden.de</a>><br>
<span style="font-weight:bold">Date: </span>Wednesday, March 18, 2015 at 4:20 AM<br>
<span style="font-weight:bold">To: </span>"<a href="mailto:paraview@paraview.org">paraview@paraview.org</a>" <<a href="mailto:paraview@paraview.org">paraview@paraview.org</a>><br>
<span style="font-weight:bold">Subject: </span>[EXTERNAL] [Paraview] Bug in interpolation of point data<br>
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<p class="MsoNormal">Hello,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">I tried to interpolate nodal values using ParaView.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">But for symmetric problems there are asymmetric results, as can be seen in the figures appended.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I tested it with hexahedron and quad type elements, but both give the same results.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">You can find my simplified input file also appended.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Hopefully you can help me to create symmetric interpolation results for symmetric problems.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thank you in advance, best regard<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal">Marco Götz<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">----------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">Technische Universität Dresden<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:DE">Faculty of Civil Engineering<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:DE">Institute for Structural Analysis<o:p></o:p></span></p>
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