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Interpolation of given data in 2d domain

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ravi shukla
ravi shukla 2023-4-5
编辑： Davide Masiello 2023-4-6
x=0,4,6,9,11,17,20
y=0,2,3,7,10,15
x is (7,1) vector & y is (6,1)
z will have (known data) 7*6=42 values in this domain.
how to interpolate z to some new x & y. let say now x(5,1)=0,5,10,15,20 & y(6,1)= 0,3,6,9,12,15.
I am using "griddata" bit getting very lil error. please help!

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回答（1 个）

Davide Masiello
Davide Masiello 2023-4-5
Ran in:
Example
xdata = linspace(1,10,10)
xdata = 1×10
1 2 3 4 5 6 7 8 9 10
ydata = linspace(0,1,11)
ydata = 1×11
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
zdata = rand(length(ydata),length(xdata))
zdata = 11×10
0.8112 0.0708 0.5041 0.6023 0.0818 0.1820 0.7003 0.4842 0.3335 0.6683 0.6788 0.8340 0.0349 0.5122 0.0715 0.9324 0.2119 0.2980 0.4767 0.1168 0.5219 0.1053 0.9267 0.0636 0.9447 0.8776 0.3619 0.3600 0.0824 0.3414 0.6298 0.9852 0.5891 0.6079 0.6031 0.0961 0.9830 0.2188 0.9467 0.5634 0.6200 0.2704 0.6060 0.2413 0.8322 0.6864 0.3460 0.5554 0.4096 0.2714 0.4857 0.1183 0.4792 0.5002 0.2580 0.4702 0.4455 0.6356 0.7466 0.3907 0.9321 0.8234 0.5167 0.7972 0.9827 0.5531 0.2857 0.6909 0.0056 0.7744 0.5190 0.9112 0.0090 0.8131 0.5675 0.9623 0.0170 0.9269 0.9812 0.2971 0.4493 0.6002 0.2361 0.8474 0.6592 0.4733 0.6316 0.8359 0.8067 0.9577 0.6325 0.8260 0.2111 0.7607 0.2610 0.6142 0.3501 0.8030 0.6859 0.8245
x0 = [2.5 3.5 4.5 5.5];
y0 = [0.25 0.35 0.45 0.55];
z0 = interp2(xdata,ydata,zdata,x0,y0)
z0 = 1×4
0.6516 0.5111 0.4579 0.5660
  2 个评论
ravi shukla
ravi shukla 2023-4-5
how will i get z0(4,4)? similarly as old zdata.
which means z0 with x0(1) and y0(1), y0(2), y0(3) , y0(4) and similar combinations of x0(2).. x0(3)... x0(4) with all y0s
Davide Masiello
Davide Masiello 2023-4-6
编辑：Davide Masiello 2023-4-6
Ran in:
xdata = linspace(1,10,20);
ydata = linspace(0,20,30);
[xgrid,ygrid] = meshgrid(xdata,ydata);
zdata = sin(xgrid)+cos(ygrid);
figure(1)
surf(xgrid,ygrid,zdata)
Now, if you want data at a certain fixed x0 and variable y, you can do
x0 = 6.5;
z0 = interp2(xdata,ydata,zdata,x0,ydata);
You can visualise this
figure(2)
subplot(2,1,1)
surf(xgrid,ygrid,zdata),hold on
plot3(x0*ones(size(ydata)),ydata,z0,'r','LineWidth',4)
subplot(2,1,2)
plot(ydata,z0)
xlabel('y')
ylabel('z')
legend('x0 = 6.5')
Same thing for fixed y0
y0 = 5.66;
z0 = interp2(xdata,ydata,zdata,xdata,y0);
figure(3)
subplot(2,1,1)
surf(xgrid,ygrid,zdata),hold on
plot3(xdata,y0*ones(size(xdata)),z0,'r','LineWidth',4)
subplot(2,1,2)
plot(xdata,z0)
xlabel('y')
ylabel('z')
legend('y0 = 5.66')
In general, you can extrapolate any path on the surface of z for a given function y(x).
x0 = xdata;
y0 = -2*x0+18;
z0 = interp2(xdata,ydata,zdata,x0,y0);
figure(4)
subplot(2,1,1)
surf(xgrid,ygrid,zdata),hold on
plot3(x0,y0,z0,'r','LineWidth',4)
subplot(2,1,2)
plot3(x0,y0,z0,'k','LineWidth',2)
xlabel('x')
ylabel('y')
zlabel('z')
legend('y = -2x+18')

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