Intermediate links of plane curves

For a smooth complex curve C, we consider the link L(r) intersection of C with the boundary of B(r), where B(r) denotes an Euclidean ball of radius r>0. We prove that the diagram D(r) obtained from L(r) by a complex stereographic projection satisfies that the Euler characteristic of the part of C in B(r) equals the rotation number of D(r) minus the writhe of D(r). As a consequence we show that if D(r) has no negative Seifert circles and L(r) is strongly quasipositive and fibred, then the Yamada-Vogel algorithm applied to D(r) yields a quasipositive braid.