# Interpolating at vertices of a mesh

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Sanwar Ahmad on 5 Aug 2020
Edited: Bruno Luong on 6 Aug 2020
I have created a mesh using the initmesh in 2D, which gives the nodes (p), boundary (e) and triangular elements (t). I have a function/vector calculated at each triangular elements, I need to interpolate the function at the vertices of the mesh. How do I do it?
Bruno Luong on 6 Aug 2020
In theory you cannot.
A function that is piecewise constant on elements is discontinuos at the vertices and you cannot speak about value at the vertices. So there is no interpolation that can provide you this value.

Robert U on 6 Aug 2020
for interpolation between meshes you can have a look at the built-in function scatteredinterpolant().
More information on interpolating scattered data can be found in the Matlab documentation: https://de.mathworks.com/help/matlab/math/interpolating-scattered-data.html
Kind regards,
Robert

Bruno Luong on 6 Aug 2020
Edited: Bruno Luong on 6 Aug 2020
In theory you cannot.
A function that is piecewise constant on elements is discontinuos at the vertices and you cannot speak about value at the vertices. So there is no interpolation that can provide you this value.
Now you might be able to make a fake discrete weighted mean at the vertices v for all elements Ti that share this vertice. There is two common strategies is take the weight as
f(v) = sum (wi*f(Ti)) / sum(wi)
• wi = surface of the elements
• wi = angle at the vertice
This link might be helpful, in their pseudo code just replace "facte normal" by "facet value"