  Local contact line pinning prevents droplets from rearranging to minimal
global energy, and models for droplets without pinning cannot predict their
shape. We show that experiments are much better described by a theory,
developed herein, that does account for the constrained contact line motion,
using as example droplets on tilted plates. We map out their shapes in suitable
phase spaces. For 2D droplets, the critical point of maximum tilt depends on
the hysteresis range and Bond number. In 3D, it also depends on the initial
width, highlighting the importance of the deposition history.
