The objective of this work is to fill graphics of surfaces with hole-meeting shape conditions, i.e., we want to determine values of a surface inside a hole – where it is not defined – by means of its values outside the hole – where it is properly defined – in such a way that the final reconstructed surface be fair and smooth enough. The procedure considered to get this aim is based on a one-dimensional hole-filling problem, leading to a kind of “wireframe” surface. We develop the theoretical aspects of the problem and we show some graphical examples to illustrate the proposed method.