  Domain discretization is an essential part of the solution procedure in
numerical simulations. Meshless methods simplify the domain discretization to
positioning of nodes in the interior and on the boundary of the domain.
However, generally speaking, the shape of the boundary is often undefined and
thus needs to be constructed before it can be discretized with a desired
internodal spacing. Domain shape construction is far from trivial and is the
main challenge of this paper. We tackle the simulation of moving boundary
problems where the lack of domain shape information can introduce difficulties.
We present a solution for 2D surface reconstruction from discretization points
using cubic splines and thus providing a surface description anywhere in the
domain. We also demonstrate the presented algorithm in a simulation of
phase-change-like problem.
