2D circular interpolation (theta, phi) angles

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Albert
Albert 2021-8-3
评论： Bjorn Gustavsson 2021-8-3
Hi, I have a 2D matrix Z that is function of theta and phi coordinates Z(theta,phi). I have a regular grid of theta and phi coordinates along with the value of Z. Then, I have some scattered points theta_i and phi_i for which I want to interpolate the value of Z. This I can do it easily by doing:
Z_i = interp2(theta,phi,Z);
However, the sampling of matrix Z is limited. For example, if the theta and phi step is 1 degree (then theta from 0:1:179 and phi 0:1:359), it may happen that a valid scattered point falls at one edge of the sampling. For instance a point (theta_i,phi_i) = (0,359.5) will raise a NaN during interp2 because it does not know how to interpolate. Due to the circular symmetry of (theta, phi) angles in fact Z(0,360) = Z(0,0) so that all information needed for interpolation is there, however how can I make interp2 make aware of this angular symmetry? I realized using 'spline' actually provides a valid number, however I would prefer not to use it. Thanks!

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Bjorn Gustavsson
Bjorn Gustavsson 2021-8-3
Simply concatenate the Z-values for columns and rows corresponding to theta and phi equal 0 and 1 at the end of Z and extend the range of theta and phi to 0:181 and 0:361. (You might also consider extending to negative angles):
Znew = Z([end-1:end,1:end,1:2],[end-1:end,1:end,1:2]);
theta_new = -2:181;
phi_new = -2:361;
The reason to extend beyond 0-360 is that this ensure periodicity even for the different spline-interpolation methods (I think this is a sufficient number of points added even for 'cubic' interpolation).
HTH

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