Consider a sphere sitting on an $xy$-plane, and take 2D slices parallel to the $xy$-plane at various heights of z. Suppose we take 10 slices, evenly spaced along the $z$-axis, and now have 10 images of circles each with a corresponding $z$.
My goal would be a function that could learn from these 10 slices, such that if I were to input a new value of z, it would draw a circle (that is ideally close to the correct circle at that height).
Would there be a way to train something like a neural network to take the height z as the input, and output circles corresponding to the slice of a sphere at a particular height?
Such a method should scale to multiple dimensions. For example, if I had some multidimensional object I wished to reconstruct using slices of that object. Note that the parameter corresponding to slices may now be a vector.
EDIT: The goal is to interpolate between 2D shapes that do not have simple analytic solutions. For example, one image is a circle and another is a rectangle.
The problems I am facing are where there are no simple analytic solutions for new shapes as a function of z. Imagine that there exists a very rugged non-linear 3D object (like the cross section of a person) - but we can only determine a few slices of this object as it is computationally expensive for some reason. We wish to interpolate between these few slices and generate a 3D object. Such a solution should also work for strange multidimensional shapes beyond 3D.