3D Spline Interpolation Matlab

Question

I have two 3D arrays:

 A=[
12751   4616    15915
15864   4622    15667
12877   4683    21050
15816   4668    21253
11374   5006    18495
16995   5466    18493
11638   4880    20023
17078   4938    20006
11576   4886    17011
];

and

 B=[
12402   2138    15743
10285   3175    15851
10237   3084    21052
12130   2129    21299
8074    3802    18505
14515   1623    18497
8415    3713    19856
14462   1120    20061
8340    3711    17145
14483   1157    16990];

and I want to do spline or 3D interpolation between them using Interp3 in Matlab.How should I define V in VI = interp3(X,Y,Z,V,XI,YI,ZI)?

Or Y in yy = spline(x,Y,xx).

Answer 1

I don't quite understand your data, is B a function of A (or visa versa)? Also, those arrays appear to be 1D, not 3D. Can you clarify this?

In your function call

yy = spline(x, Y, xx)

Y is the dependent variable which you are interpolating: Y is a function of x and the result of the above function call is to return the value of Y at xx. As an example in one dimension, try

x = linspace(0., 2.*pi, 100);
Y = sin(x);

% What is the value of Y (or sin(x)) at pi/2?
xx = pi/2.;
yy = spline(x, Y, xx); % This should result in yy = 1.000

Check out the spline documentation for more information and examples of using this function.

Now this function is only for 1D fitting, and is (I presume) equivalent to yy = interp1(x, Y, xx, 'spline'). If you want to do a three dimensional lookup, you'll have to use interp3, which generalises the above example to 3D. So rather than just one independent coordinate x, we have two more, y, and z and three coordinates for the point at which we want to perform the look up: xx, yy and zz. The function you are interpolating must be a 3D function of the coordinates (x, y, z). Try, as an example:

x = linspace(-1., 1., 100); y = x; z = x;
[X, Y, Z] = meshgrid(x, y, z);
s = exp(-sqrt(X.^2 + Y.^2 + Z.^2));

sinterp = interp3(x, y, z, s, 0., 0., 0.) % Should give sinterp = 0.9827