  The shape assumed by a slender elastic structure is a function both of the
geometry of the space in which it exists as well as the forces it experiences.
Here, we explore by experiments, a calculation, and numerical analysis, the
morphological phase-space of a filament confined to the surface of a spherical
bubble. The morphology is controlled by varying the bending stiffness and
weight of the filament, and its length relative to the radius of the bubble. In
the regime where the dominant considerations are the geometry of confinement
and the elastic energy, we observe that the filament lies along a geodesic.
When gravitational energy becomes significant, a bifurcation occurs with a part
of the filament occupying a longitude and the rest occupying a curve that may
be approximated by a latitude. Far from the transition, when the filament is
long compared to the diameter, it coils around the selected latitude. A simple
model that describes the shape as a composite of two arcs that lie along
longitude and latitude, captures the transition. For better quantitative
agreement with the subcritical nature of the bifurcation, we study the
morphology by numerical energy minimization. Our observations and analysis of a
filament on a sphere in terms of a morphological space spanned by a purely
geometric parameter, and a parameter that compares elastic energy with body
forces, may provide guidance for packing slender structures on more complex
surfaces.
