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0dbcca5093
- add math to sphinx to generate the formulas - change the icon to deformed hexahedrons - add a test on deformed hexahedrons - update the example use case on the doc to deformed hexahedrons
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2.0 KiB
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50 lines
2.0 KiB
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.. _scaled_jacobian_page:
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***************
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Scaled Jacobian
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***************
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The **Scaled Jacobian** mesh quality criteria is a scalar measure of the deviation from the perfect element in the geometrical sense. This measure normalizes the range of reported values between [0,1] for a normal element, the value of 1 is considered a perfect element and 0 a element with a collapsed side. Negative values are also accepted for invalid elements.
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The **Scaled Jacobian** is implemented for all volumetric elements (except for polyhedrons, returning 0).
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For tetrahedrons and hexahedrons, the formulas are
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defined in `The Verdict Library Reference Manual [1] <https://gitlab.kitware.com/third-party/verdict/-/blob/master/SAND2007-2853p.pdf>`_.
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For pyramid, the minimum scaled jacobian of the four tetrahedrons formed
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in the four vertices of the pyramid base is reported.
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For pentahedron, a decomposition into tetrahedron is also done.
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For hexahedron prisms, the minimum scaled jacobian between two pentahedrons and one hexahedron is reported.
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* Geometrically the Scaled Jacobian of a **tetrahedron** can be understood by the follow figure:
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.. image:: ../images/scaled_jacobian_tetra.png
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:align: center
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The reported Scaled Jacobian will be 1 if :math:`\alpha=45^{\circ}`
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* For **hexadrons** this measure return 1 for the perfect non rotated elements:
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.. image:: ../images/scaled_jacobian_hexa.png
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:align: center
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The reported Scaled Jacobian will be 1 if :math:`\alpha=0^{\circ}` for all the vertices
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*To visualize the Scaled Jacobian quality criterion in your mesh:*
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.. |img| image:: ../images/scaled_jacobian.png
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#. Display your mesh in the viewer.
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#. Choose **Controls > Volume Controls > Scaled Jacobian** or click *"Scaled Jacobian"* button |img| of the toolbar.
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Your mesh will be displayed in the viewer with its elements colored according to the applied mesh quality control criterion:
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.. image:: ../images/scaled_jacobian_mesh_hexa.png
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:align: center
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**See Also** a sample TUI Script of a :ref:`tui_scaled_jacobian` filter.
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