  We investigate the morphology of a toroidal fluid membrane vesicle confined
inside a spherical container. The equilibrium shapes are assembled in a
geometrical phase diagram as a function of scaled area and reduced volume of
the membrane. For small area the vesicle can adopt its free form. When
increasing the area, the membrane cannot avoid contact and touches the
confining sphere along a circular contact line, which extends to a zone of
contact for higher area. The elastic energies of the equilibrium shapes are
compared to those of their confined counterparts of spherical topology to
predict under which conditions a topology change is favored energetically.
