Lagrange interpolation in 2D?

Hi all,

I'd like to find the interpolating polynomials on a 2d domain.

Imagine we have sample points (x1, y1), ... ,(xn, yn), and values at these points (z1, ..., zn), what is the interpolation polynomials for this 2-dimensional case? Is there a library in MATLAB to do this?

Further more, if the values at these points are matrices (m1, ... , mn), can we interpolate these matrices?

Many thanks!

Answer 1

[John D'Errico]

That you can't find it is a good thing.

Lagrange interpolation is a nice thing for ONE purpose only: to teach students some basic ideas. What those teachers fail to followup with is that it is a bad thing to use when you really need to do interpolation. So then those students go into the world, and try to use it. Worse, then they want to do stuff like use it for 2-d interpolation. Don't do it. The idea has "bad" written all over it.

There are many schemes around for 2-d interpolation/modeling. Use one of them. Start with scatteredInterpolant, or you might use radial basis function interpolation (I recall it being on the FEX), or approximation tools like my gridfit (on the FEX), or neural nets. Or there is Kriging, or use splines.

[Xh Du]

Hi John,

I agree that Lagrange interpolation is not the best choice, but I need the solution to my problem for now cause I have a deadline coming and no sufficient time for studying/implementing/testing another interpolation scheme.

I did try to follow the same idea as 1d interpolating polynomials, but when it comes to 2d, in order to derive Lagrange basis polynomials, in the denominator, xj - xi may equal to 0. How can I solve this problem then?

I followed this Wiki page: https://en.wikipedia.org/wiki/Lagrange_polynomial

[Torsten]

https://de.mathworks.com/matlabcentral/fileexchange/25962-lagrange-interpolation-in-2d

Best wishes

Torsten.

[Xh Du]

Hi Torsen,

This one works, I should interpolate x first then y dimension, many thanks!

[image-pro]

Hi Xh Du

Can you tell me how to interpolate image using lagrange method