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Given a compact set $K$ in the plane, which does not contain any triple ofpoints forming a vertical and a horizontal segment, and a map $f\in C(K)$, wegive a construction of functions $g,h\in C(\mathbb R)$ such that$f(x,y)=g(x)+h(y)$ for all $(x,y)\in K$. This provides a constructive proof ofa part of Sternfeld's theorem on basic embeddings in the plane. In our proofthe set $K$ is approximated by a finite set of points.

Constructive decomposition of a function of two variables as a sum of functions of one variable