Interpolate to 3D functions

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Hy, In math classes, I've learned that given some points in 2D space: a(1,2), b(7,3), c(8,5),...

You can find an equation that goes through these points (using interpolation).

Now I was wondering if the same is possible for 3D points? Could a(x,y,z), b(x',y',z'), c(x",y",z"),... result me in a 3D surface, like for example x²+y²+z² = 1 (a sphere)?

Thanks for the help