Interpolating a set of points into a function

Sorry if I’m not wording this post right, I’m still new to FEniCS.
I am trying to interpolate a set of points into a function. I see that the interpolate functions dolfin.fem.interpolation.interpolate(v, V) and dolfin.cpp.function.Function.interpolate() are both a way to interpolate an expression into a finite element space, but I’m starting out with a discrete set of points. Is there a way to go from a discrete set of points to a function or finite element space in FEniCS?

You need to think about the mathematical implications of such an interpolation. Does the points align with the degrees of freedom? If not, how should such an interpolation operation work?

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