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UVC Applications

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\nAuthor: Edward Vigmond edward.vigmond@ihu-liryc.fr\n\ <h2 id=\"UVCs-applied\">Applying UVCs\n

This tutorial demonstrates how to\ \ apply UVCs.

\n<h2 id=\"introduction\">Introduction\n

UVCs allow one\ \ to easily define structures on a mesh or transfwer data between two meshes. We\ \ can view UVC space as the reference frame and as such, transferring from Cartesian\ \ to UVC space is a pull operation, and going the other way is a push.

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If\ \ transferring scalar data between meshes, it suffices to have the UVCs of where\ \ the data is on the source mesh, and interpolate based on UVC positions on the\ \ destination mesh.

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For transferring gradients and directions, the quantities\ \ are vectors which are first pulled to UVC and pushed to Cartesian\ \ making use of the deformation gradient. In these cases, the deformation gradient\ \ is calculated by taking the gradient of the UVCs with respect to the Cartesian\ \ coordiantes. Care must be taken performing the calculation for the <span class=\"\ math inline\">\(\phi\) coordinate because of the branch cut at <span class=\"\ math inline\">\(\pi\). Even though the value <span class=\"math inline\"\

\(\phi\) decreases when going clockwise, crossing from <span class=\"\ math inline\">\(\pi\) to <span class=\"math inline\">\(-\pi\),\ \ the gradient is still positive because we need to ignore the branch cut and continue\ \ to increase <span class=\"math inline\">\(\phi\) above <span class=\"\ math inline\">\(\pi\).

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The program closest_hc_wf.py is\ \ capable of these mappings. To see how to use the program, detailed help is available:

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closest_hc_wf.py -h

05_igbutils