Projective Minkowski set

The Minkowski set or the central symmetry set (CSS) of a smooth curve Γ on the affine plane is the envelope of chords connecting pairs of points such that the tangents to Γ at them are parallel. Singularities of CSS are of interest, in particular, for applications (for example, in computer graphics). A generalization of the Minkowski set is considered in the paper, namely, the projective Minkowski set with respect to a line on the plane; in the case of general position, we describe its singularities and the bifurcation set of lines corresponding to lines defining the projective Minkowski set having singularities being more degenerate than those of the Minkowski set for a generic line.