  Acoustic levitation has recently demonstrated the ability to create
volumetric content by trapping and quickly moving particles along reference
paths to reveal shapes in mid-air. However, the problem of specifying
physically feasible trap trajectories to display desired shapes remains
unsolved. Even if only the final shape is of interest to the content creator,
the trap trajectories need to determine where and when the traps need to be,
for the particle to reveal the intended shape. We propose OptiTrap, the first
structured numerical approach to compute trap trajectories for acoustic
levitation displays. Our approach generates trap trajectories that are
physically feasible and nearly time-optimal, and reveal generic mid-air shapes,
given only a reference path (i.e., a shape with no time information). We
provide a multi-dimensional model of the acoustic forces around a trap to model
the trap-particle system dynamics and compute optimal trap trajectories by
formulating and solving a non-linear path following problem. We formulate our
approach and evaluate it, demonstrating how OptiTrap consistently produces
feasible and nearly optimal paths, with increases in size, frequency, and
accuracy of the shapes rendered, allowing us to demonstrate larger and more
complex shapes than ever shown to date.
