Correlate two sets of data defined on different meshings of the same surface

Hello,

I am trying to correlated two data sets defined on a surface embedded in 3d. The problem is that the two data sets are defined on two separate meshes, which are moreover slighty displaced with respect to each other, i.e. the underlying x,y,z coordinates are different. Moreover, the mesh densities are also very different (see image below, there are roughly 3 blue x's for every 1 orange o).

Note: The reason for this is that one set of data is defined at the centre of mass of a 3d tetrahedral mesh, while the second set of data is defined on a separate 2d triangular mesh. Both meshes are representations of the same physical surface-like object though.

Question: How do I find which 3 x's correspond to a single orange o? If I could find that, I could average the data over these 3 neighbouring x's and have a 1:1 mapping between the blue points and the orange points.

Or does anyone have another way of doing this?

I am attaching a mat file with the x,y,z coordinates of the two sets, the orange ones are in 'surface_vertices', and the blue ones in 'cm_vertices'.

Please help!

Answer 1

[KSSV]

You can get the respective mesh Z values to a required grid, using interpolation menthods.

Read about griddata, scatteredinterpolation.

[Anshuman Pal]

Can I do this even if the function is multi-valued, i.e. the surface curves back on itself?

[KSSV]

No that case might fail...

[Anshuman Pal]

Thought so. I will leave this question open to see if anyone else has a different idea. I will ask around for interpolation of multi-valued functions in the meantime.