  We conduct a systematic exploration of the energy landscape of vesicle
morphologies within the framework of the Helfrich model. Vesicle shapes are
determined by minimizing the elastic energy subject to constraints of constant
area and volume. The results show that pressurized vesicles can adopt
higher-energy spindle-like configurations that require the action of point
forces at the poles. If the internal pressure is lower than the external one,
multilobed shapes are predicted. We utilize our results to rationalize the
experimentally observed spindle shapes of giant vesicles in a uniform AC field.
