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I need an explanation about Bilinear Interpolation. I use KNN and find $4$ points which I need to use bilinear interpolation to find unknown position.
I was unable to understand explanations in other sites. I need to write equations for $x$ and $y$ using bilinear interpolation. How can i do this ?

Please fully describe.

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Bilinear interpolation is just the extension of linear interpolation for interpolating functions of two variables.

A bilinear function write $$z=A+B x+C y +D x y$$ You can easily check that, if $x$ is fixed, $z$ is linear with respect to $y$ and vice-versa.

So, if you have four data points $(x_i,y_i,z_i)$, you have to solve four linear equations for four unknowns $A,B,C,D$; when you have them, just apply the formula for the point you want to interpolate at.

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  • $\begingroup$ is this z a point on z axis ? if so how to use for 2d plane ? if i apply for above formula can i get the coordinates of the unknown x and y $\endgroup$
    – Harry1234
    Jun 29, 2015 at 12:38

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