This communication is concerned with a geometric constraint, the so-called accessibility constraint, for shape and topology optimization of structures built by additive manufacturing. It is common practice in metallic additive manufacturing to use sacrificial supports to maintain the built structure, submitted to intense thermal residual stresses, so that it does not deform too much during its construction. Once the building stage is over, the supports are no longer useful and they have to be removed. It turns out that such a removal can be very difficult or even impossible if the supports are hidden deep inside the complex geometry of the structure. We propose the following criterion for evaluating the ease of support removal: the contact zone between the structure and its supports must be accessed from the exterior by a straight line which does not cross any other part of the structure. It is a proxy for the possibility to cut the head of the supports attached to the structure with some cutting tool. Our work gives a new mathematical way to evaluate such an accessibility constraint, which is based on distance functions, solutions of eikonal equations. The main advantage is the possibility of computing shape derivatives of such a criterion with respect to both the structure and the support. We shall present several numerical examples in 2D and 3D, in the context of the level-set method for topology optimization. Our approach is able to optimize simultaneously the mechanical performance of a structure and the accessibility of its building supports, guaranteeing its manufacturability.