x = 0:0.1:1;
y = -1:0.1:1;
[X,Y] = meshgrid(x,y);
Z = X.^2+Y.^2+0.1*(-1+2*rand(size(X)));
[Xout,Yout,Zout] = prepareSurfaceData(X,Y,Z);
S = fit([Xout,Yout],Zout,"poly22")
Linear model Poly22:
S(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
Coefficients (with 95% confidence bounds):
p00 = 0.01879 (-0.001415, 0.039)
p10 = -0.02596 (-0.1119, 0.05996)
p01 = -0.007346 (-0.02993, 0.01523)
p20 = 1.018 (0.9357, 1.101)
p11 = 0.009983 (-0.02819, 0.04815)
p02 = 0.9853 (0.963, 1.008)
xq = 0:0.01:0.5;
yq = -1:0.01:0;
[Xq,Yq] = meshgrid(xq,yq);
S(Xq,Yq)
ans = 101×51
1.0115 1.0112 1.0112 1.0113 1.0117 1.0122 1.0130 1.0140 1.0151 1.0165 1.0181 1.0199 1.0218 1.0240 1.0264 1.0290 1.0318 1.0348 1.0380 1.0414 1.0450 1.0489 1.0529 1.0571 1.0615 1.0662 1.0710 1.0760 1.0813 1.0867
0.9918 0.9915 0.9915 0.9916 0.9920 0.9926 0.9933 0.9943 0.9955 0.9968 0.9984 1.0002 1.0022 1.0044 1.0067 1.0093 1.0121 1.0151 1.0184 1.0218 1.0254 1.0292 1.0332 1.0374 1.0419 1.0465 1.0513 1.0564 1.0616 1.0671
0.9723 0.9721 0.9720 0.9722 0.9725 0.9731 0.9738 0.9748 0.9760 0.9774 0.9789 0.9807 0.9827 0.9849 0.9873 0.9899 0.9927 0.9957 0.9989 1.0023 1.0059 1.0097 1.0138 1.0180 1.0224 1.0270 1.0319 1.0369 1.0422 1.0476
0.9530 0.9528 0.9527 0.9529 0.9532 0.9538 0.9546 0.9555 0.9567 0.9581 0.9597 0.9614 0.9634 0.9656 0.9680 0.9706 0.9734 0.9764 0.9796 0.9830 0.9866 0.9905 0.9945 0.9987 1.0031 1.0078 1.0126 1.0177 1.0229 1.0283
0.9339 0.9337 0.9336 0.9338 0.9341 0.9347 0.9355 0.9364 0.9376 0.9390 0.9406 0.9424 0.9443 0.9465 0.9489 0.9515 0.9543 0.9573 0.9605 0.9640 0.9676 0.9714 0.9754 0.9796 0.9841 0.9887 0.9935 0.9986 1.0038 1.0093
0.9150 0.9148 0.9147 0.9149 0.9153 0.9158 0.9166 0.9176 0.9187 0.9201 0.9217 0.9235 0.9255 0.9277 0.9300 0.9326 0.9355 0.9385 0.9417 0.9451 0.9487 0.9525 0.9565 0.9608 0.9652 0.9698 0.9747 0.9797 0.9850 0.9904
0.8964 0.8961 0.8961 0.8962 0.8966 0.8971 0.8979 0.8989 0.9000 0.9014 0.9030 0.9048 0.9068 0.9090 0.9114 0.9140 0.9168 0.9198 0.9230 0.9264 0.9300 0.9338 0.9379 0.9421 0.9465 0.9512 0.9560 0.9611 0.9663 0.9718
0.8779 0.8776 0.8776 0.8777 0.8781 0.8786 0.8794 0.8804 0.8816 0.8829 0.8845 0.8863 0.8883 0.8905 0.8929 0.8955 0.8983 0.9013 0.9045 0.9079 0.9115 0.9154 0.9194 0.9236 0.9281 0.9327 0.9375 0.9426 0.9478 0.9533
0.8595 0.8593 0.8593 0.8594 0.8598 0.8603 0.8611 0.8621 0.8633 0.8646 0.8662 0.8680 0.8700 0.8722 0.8746 0.8772 0.8800 0.8830 0.8862 0.8896 0.8933 0.8971 0.9011 0.9053 0.9098 0.9144 0.9193 0.9243 0.9296 0.9350
0.8414 0.8412 0.8412 0.8413 0.8417 0.8422 0.8430 0.8440 0.8452 0.8465 0.8481 0.8499 0.8519 0.8541 0.8565 0.8591 0.8619 0.8649 0.8681 0.8716 0.8752 0.8790 0.8830 0.8873 0.8917 0.8963 0.9012 0.9062 0.9115 0.9169
surf(Xq,Yq,S(Xq,Yq))
