径向基函数插值（3）二维数据的插值

二维数据的插值过程跟一维数据的过程一样，

只不过在显示二维的数据插值的过程中，需要meshgrid函数产生数据，进行显示插入数据的输出值。

产生二维数据：

clear all; figure;
%**************************************************************************
% 2D Interpolation
%**************************************************************************
%Matlab standard interpolation using griddata 
rand('seed',0)
x = rand(50,1)*4-2; y = rand(50,1)*4-2;
z = x.*exp(-x.^2-y.^2);

ti = -2:.05:2; 
[XI,YI] = meshgrid(ti,ti);
ZI = griddata(x,y,z,XI,YI,'cubic');

subplot(2,2,1); mesh(XI,YI,ZI), hold, axis([-2 2 -2 2 -0.5 0.5]); 
plot3(x,y,z,'.r'), hold off; title('Interpolation using Matlab function griddata(method=cubic)');

subplot(2,2,3); pcolor(abs(ZI - XI.*exp(-XI.^2-YI.^2))); colorbar; title('griddata(method=cubic) interpolation error');

过程跟一维的数据一样

% 2D Interpolation
%**************************************************************************
%Matlab standard interpolation using griddata 
rand('seed',0)
x = rand(50,1)*4-2; y = rand(50,1)*4-2;
z = x.*exp(-x.^2-y.^2);

ti = -2:.05:2; 
[XI,YI] = meshgrid(ti,ti);
ZI = griddata(x,y,z,XI,YI,'cubic');

subplot(2,2,1); mesh(XI,YI,ZI), hold, axis([-2 2 -2 2 -0.5 0.5]); 
plot3(x,y,z,'.r'), hold off; title('Interpolation using Matlab function griddata(method=cubic)');

subplot(2,2,3); pcolor(abs(ZI - XI.*exp(-XI.^2-YI.^2))); colorbar; title('griddata(method=cubic) interpolation error');
%%
%RBF interpolation
%op=rbfcreate([X(:)'; Y(:)'], Z(:)','RBFFunction', 'thinplate'); rbfcheck(op);
%op=rbfcreate([X(:)'; Y(:)'], Z(:)','RBFFunction', 'linear'); rbfcheck(op);
%op=rbfcreate([X(:)'; Y(:)'], Z(:)','RBFFunction', 'cubic'); rbfcheck(op);
%op=rbfcreate([X(:)'; Y(:)'], Z(:)','RBFFunction', 'gaussian'); rbfcheck(op);
op=rbfcreate([x'; y'], z','RBFFunction', 'multiquadric', 'RBFConstant', 2);
rbfcheck(op);
%op=rbfcreate(x, y,'RBFFunction', 'gaussian');
%op=rbfcreate(x, y);
ZI = rbfinterp([XI(:)'; YI(:)'], op);

ZI = reshape(ZI, size(XI));
subplot(2,2,2); mesh(XI,YI,ZI), hold
plot3(x,y,z,'.r'), hold off; title('RBF interpolation'); axis([-2 2 -2 2 -0.5 0.5]);
subplot(2,2,4); pcolor(abs(ZI - XI.*exp(-XI.^2-YI.^2))); colorbar; title('RBF interpolation error');

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