The 'pseudo-harmonic' extension is an approximation to the common harmonic extension for extending a function over a domain based on its trace along the boundary of the domain. On a circle the two extension methods produce identical results. We present explicit formulas for the computation of distance functions and intersection points needed in the 'pseudo-harmonic' extension on a circle, a square, and a pentagon. While the harmonic extension needs the solution of a Laplace problem for each new boundary function, the 'pseudo-harmonic' extension can reuse the distance functions and intersection points for any piecewise continuous function defined on the boundary of the domain.