In the proof of approximation or homogenisation results of free-discontinuity functionals it is of crucial importance to replace functions of bounded variation with functions whose jump set is as simple as possible, typically polyhedral, as well as to attain sufficient smoothness of the function away from its jump set. In this respect the mathematical literature provides us with a number of approximation results which are, moreover, tailor-made to deal with upper-bound inequalities. However, should the target functions satisfy some geometric constraint arising in the problem under examination, the available approximation results may fail to preserve this additional constraint. In the context of variational methods for fracture and image segmentation, in this contribution we establish a density result for special functions of bounded variation (SBV) with prescribed jump direction, describing, e.g., deformations of materials with cracks appearing only along certain directions.