How to find the values of a function at any desired point given its value at some arbitrary points??

If my function u(x,y,z) values is given at say 5 points (x,y,z).....now I want to find the value of the function at the meshgrid points [x,y,z]=meshgrid (0:.1:1,0:.1:1,0:.1:1) ,x=[1 2 3 4 5],y=[1 2 3 4 5],z=[1 2 3 4 5] u=[1 8 27 64 125]

Answer 1

[Bjorn Gustavsson]

Five points worth of information is not a lot for interpolation in 3-D - plot the points and all their connections and see how utterly little it is.

You can try scatteredInterpolant and hope that your points are inside the convex hull of your 5 points and that your function is "very nice".

HTH

[Apashanka Das]

Okay what happens if the value is defined for say 3000 points ?? Clearly speaking my x,y,z is (3000×1) matrix and my u(x,y,z) is also (3000×1) matrix....now using these data I want to calculate u at the corner points of a 3-d grid where grid properties is defined my me.....can anyone please help how to do it in matlab

[Bjorn Gustavsson]

That's much better! For a 3-D grid 3000 points would be approximately 14.5^3 points - i.e. you could have a regular grid with 14.5 points per dimension. If your function is not too meanspirited over your domain you might get a rather good interpolation. The curse of dimensionality are "lurking at the horizon" - if you had an additional dimension or two the number of points-per dimension in a regular grid would go down to 7.4 then ~5.

It would still be scatteredInterpolant.

HTH

[Apashanka Das]

Thanks a lot