Interpolate x,y coordinates and timesteps

Heallo,

I have an array M with x, y, coordinates points in the 1st and 2nd column [x= M(2:end,1); y= M(2:end,2)]. The following columns are the values (for example temperatures) for different timesteps [timesteps = M(1,3:end].

How can I interpolate the x,y coordinates and the timesteps?

clc
clear

M(5,7)=0;
M(1,2:7)=0:10:50;
M(2:5,1)=1:4;
M(2:5,2)=1:0.5:2.5;
M(2,3:7)=100:3:112;
M(3,3:7)=110:3:122;
M(4,3:7)=120:3:132;
M(5,3:7)=120:3:132;

[Mathieu NOE]

seems to me (if I understand correctly) that x and y are not independant variables.

we can do a 2D interpolation beetween x and time (or y and time , as x and y are linked) , but we cannot make any 3D interpolation as if x,y and time are independant data.

[Patrick Frey]

Yes, you are right. x and y are linked, because for example M(2,1) is the x-value and M(2,2) is the corresponding y-value.x and y are coordinates of a specific point.

So, like this...or is there a better solution?

clc
clear

MM(5,7)=0;
MM(1,2:7)=0:10:50;
MM(2:5,1)=1:4;
MM(2:5,2)=1:0.5:2.5;
MM(2,3:7)=100:3:112;
MM(3,3:7)=110:3:122;
MM(4,3:7)=120:3:132;
MM(5,3:7)=120:3:132;

X= MM(2:5,1);
time= MM(1,3:7);
V = MM(2:5,3:7)';

[XX,TIME] = meshgrid(X,time);

x_query = [1.5];
time_query = [25];

query_values_M = interp2(XX,TIME,V,x_query,time_query)

[Mathieu NOE]

exact !!

[Patrick Frey]

thank you for your help

[Mathieu NOE]

my pleasure !!

Answer 1

[Florian Bidaud]

In your example, you only have a 2D M array, but I guess what you want is a 3D interpolation, so with another dimension in M ?

M = [[103,113,123,123]',[106,116,126,126]',[109,119,129,126]',[112,122,132,132]'];
% Building an example of a 3 dimensional array
values(:,1,:) = M;
values(:,2,:) = M*1.05; 
values(:,3,:) = M*1.1;
values(:,4,:) = M*1.15; 

timesteps = (20:10:50)';
x = (1:4)';
y = (1:0.5:2.5)';

% query values
x_query = [1.1 3.2];
y_query = [1.3 2.2];
time_query = [21 45];

query_values = interp3(x,y,timesteps,values,x_query,y_query,time_query)

query_values = 1×2

109.8465 144.1890

[Patrick Frey]

Sorry my question was not clear. x and y-values are not independant variables. But thanks for your help