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function [coeffs]=netcdf_ecco_GenericgridCoeffs(x0,y0,x_all,y_all); |
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%This script is a two point interpolation scheme, which yields more continuous |
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%results than a one point "closest neighbor" interpolation scheme for example. |
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% |
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%Within a quadrilateral, the interpolated value is the projection of the |
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%observed point on the closest side. |
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% |
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%As with the closest point scheme, there is no discontinuity through edges |
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%separating two neighboring quadrilaterals. |
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% |
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x=ones([length(x_all) size(x0)]); for icur=1:length(x_all); x(icur,:,:)=x0; end; |
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y=ones([length(x_all) size(x0)]); for icur=1:length(x_all); y(icur,:,:)=y0; end; |
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|
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alpha=zeros(size(x)); beta=zeros(size(x)); gamma=zeros(size(x)); coeffs=zeros(size(x)); |
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x_all2=zeros([length(x_all) size(x0,1) 1]); for icur=1:length(x_all); x_all2(icur,:,:)=x_all(icur); end; |
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y_all2=zeros([length(y_all) size(x0,1) 1]); for icur=1:length(y_all); y_all2(icur,:,:)=y_all(icur); end; |
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for icur=1:4; |
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|
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x=circshift(x,[0 0 1]); y=circshift(y,[0 0 1]); |
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alpha=circshift(alpha,[0 0 1]); beta=circshift(beta,[0 0 1]); gamma=circshift(gamma,[0 0 1]); |
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v1x=x_all2(:,:)-x(:,:,1); v1y=y_all2(:,:,1)-y(:,:,1); v2x=x(:,:,2)-x(:,:,1); v2y=y(:,:,2)-y(:,:,1); |
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alpha(:,:,1)=(v1x.*v2x+v1y.*v2y)./(v2x.*v2x+v2y.*v2y); |
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x_tmp=x(:,:,1)+alpha(:,:,1).*v2x; y_tmp=y(:,:,1)+alpha(:,:,1).*v2y; |
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beta(:,:,1)=(x_all2(:,:,1)-x_tmp).^2+(y_all2(:,:,1)-y_tmp).^2; |
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|
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gamma(:,:,1)=(v1x.*v1x+v1y.*v1y); |
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|
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end |
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beta=reshape(beta,[size(beta,1)*size(beta,2) size(beta,3)]); |
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betamin=min(beta,[],2); |
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for icur=1:4; |
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beta=circshift(beta,[0 1]); |
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tmp1=find(beta(:,1)==betamin); |
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beta(tmp1,1)=1; beta(tmp1,2:4)=0; |
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end |
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beta=reshape(beta,[size(alpha,1) size(alpha,2) size(alpha,3)]); |
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|
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|
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for icur=1:4; |
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alpha=circshift(alpha,[0 0 1]); beta=circshift(beta,[0 0 1]); coeffs=circshift(coeffs,[0 0 1]); |
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coeffs(:,:,1)=coeffs(:,:,1)+(1-alpha(:,:,1)).*beta(:,:,1); |
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coeffs(:,:,2)=coeffs(:,:,2)+alpha(:,:,1).*beta(:,:,1); |
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end |
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|
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%revert to closest neighbor if very close, to avoid computer precision issue: |
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gamma=reshape(gamma,[size(gamma,1)*size(gamma,2) size(gamma,3)]); gamma=gamma./(max(gamma,[],2)*ones(1,4)); |
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coeffs=reshape(coeffs,[size(coeffs,1)*size(coeffs,2) size(coeffs,3)]); |
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for icur=1:4; |
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coeffs=circshift(coeffs,[0 0 1]); gamma=circshift(gamma,[0 0 1]); |
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tmp1=find(squeeze(gamma(:,1))>0.99); |
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coeffs(tmp1,1)=1; coeffs(tmp1,2:4)=0; |
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end |
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coeffs=reshape(coeffs,[size(alpha,1) size(alpha,2) size(alpha,3)]); |
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