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I have a discrete vector field, from which I want to derive the continuous one. For example, the planar vector field is defined by:

discreteVectorField = 
Table[{x, y, Normalize[{Cos[x], Tan[y]}] // N}, {x, 1, 3, 1}, {y, 1, 3, 1}];

How to interpolate the data? (When I try to draw this vector field, I noticed that ListVectorPlot by default interpolates the data given. Could I use the interpolation function?)

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dVF = Table[{{x, y}, Normalize@{Cos@x, Tan@y}}, {x, 1, 3, 1}, {y, 1,  3, 1}];
f = Interpolation@Flatten[dVF, 1];
VectorPlot[f[x, y], {x, 1, 3}, {y, 1, 3}]

Mathematica graphics

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