# Interpolating at centroid of a tetrahedral mesh

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Sanwar Ahmad am 3 Sep. 2020
Beantwortet: Ravi Kumar am 3 Sep. 2020
Hi
I have a 3D mesh with 4-noded tetrahedral elements. I defined a function/vector evaluated at the vertices of the mesh. I need to interpolate this vector at the centroid of each of the tetrahedral elements. Is there any built-in function to do that? I used pdeintrp for 2D mesh, but not sure if it works for the 3D mesh.
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### Antworten (2)

Bruno Luong am 3 Sep. 2020
The vector at the centroid of the tetrahedron is just the mean of the 4 vectors taken at 4 vertices.
So using MEAN with appropriate indexing and you are OK.
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Sanwar Ahmad am 3 Sep. 2020
Can you please clarify P1 FEM and P2 FEM?
I am using FEM and the basis functions are linear.
Bruno Luong am 3 Sep. 2020
You seem to use loosly the vocabulary. For P1 the basis functions are linear on the elements and continuoius on the entire domain. It's a triangle on 1D and "hat" like in 2D. To simplify this cumbersome description people calls it P1 elements.
The basis functions are NOT linear.

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Ravi Kumar am 3 Sep. 2020
You can use interpolateSolution if you are using equation based interfaces to setup the problem. If you are solving a structural or thermal problem, then you can use interpolateDisplacement or interpolateTemperature, respectively.
Regards,
Ravi
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