How to implement bilinear interpolation?

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I'm trying to implement bilinear interpolation to an image after affine transformation (using numpy only), and I don't understand how to implement ?

I know how to use nearest neighbor interpolation (easy):

X = np.round(coords[0,:])
Y = np.round(coords[1,:])

but I don't know how to use bilinear interpolation instead.

I could use some help, thanks :)

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