Strong approximation of special functions of bounded variation functions with prescribed jump direction

In this note, we show that special functions of bounded variation (SBV)$\mathrm{SBV)}$ functions with jump normal lying in a prescribed set of directions N$\mathcal {N}$ can be approximated by sequences of SBV$\mathrm{SBV}$ functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to N$\mathcal {N}$, moreover the functions are smooth away from their jump set.