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Adapt lf::io to support higher order polynomials #114

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craffael opened this issue Mar 3, 2019 · 3 comments
Open

Adapt lf::io to support higher order polynomials #114

craffael opened this issue Mar 3, 2019 · 3 comments
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@craffael
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craffael commented Mar 3, 2019

At the moment the function write_tikz outputs nodes of the mesh and connects them with straight line segments (codim=1 entities). I propose to add another option to WriteTikz named TikzOutputControl::SecondOrder which will connect the nodes using parabolas.

This functionality is mainly interesting for Geometry Elements that use second order (or higher) geometry approximation in which case the trias/quads can be represented exactly. But Implementing this functionality is not trivial because the Geometry interface doesn't provide us with the parametrization of the parabola directly. I propose to solve this problem as follows:

For every edge connecting two nodes we evaluate the edge geometry element at three points: at the two endpoints and at the point in the middle (average of the endpoints). We then construct a parabola that goes through these three points and give this parametrization to tikz.

@craffael craffael added the Enhancement New feature or request label Mar 3, 2019
@anianruoss anianruoss self-assigned this Mar 3, 2019
@anianruoss
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I will implement the same functionality for lf::io::writeMatplotlib. As I am not very well versed in MATLAB, I think it would be easier if you extend lf::io::writeMatlab @hiptmair. What do you think?

@anianruoss anianruoss changed the title Adapt write_tikz to support higher order polynomials Adapt lf::io to support higher order polynomials Mar 3, 2019
@hiptmair
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hiptmair commented Mar 3, 2019

I will take care of the MATLAB visualization tool, but only in the near future, because it will be an afternoon's work to implement and test everything.

@craffael
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craffael commented Mar 7, 2019

I have seen that Paraview supports up to order 10 lagrangian elements since about a year. I will update the VTKWriter accordingly.

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