Interpolation of given data in 2d domain

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!

Answer 1

[Davide Masiello]

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

[ravi shukla]

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]

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')