Figure 4.

(a) Asymptotic solution for the membrane's shape inside the transition region (solid line), the extrapolation of its quadratic behaviour in the far field (dashed line) to where the slope is zero, thereby estimating the position of the contact point (circled), and the membrane's shape in the contact-potential limit that δ_A=0 (dotted). Also shown is the vertical displacement of the asymptotic solution from the limiting case of a contact potential. (b,c) Schematic of the boundary conditions (4.8) and (4.9) for (b) bound vesicles, for which x_D=L_D=0, and (c) dimpled vesicles.