  Sleeve functions are generalizations of the well-established ridge functions
that play a major role in the theory of partial differential equation, medical
imaging, statistics, and neural networks. Where ridge functions are non-linear,
univariate functions of the distance to hyperplanes, sleeve functions are based
on the squared distance to lower-dimensional manifolds. The present work is a
first step to study general sleeve functions by starting with sleeve functions
based on finite-length curves. To capture these curve-based sleeve functions,
we propose and study a two-step method, where first the outer univariate
function - the profile - is recovered, and second the underlying curve is
represented by a polygonal chain. Introducing a concept of well-separation, we
ensure that the proposed method always terminates and approximate the true
sleeve function with a certain quality. Investigating the local geometry, we
study an inexact version of our method and show its success under certain
conditions.
