Motion from Shape Change
ACM Transactions on Graphics · Volume 42 (4) · SIGGRAPH 2023
We consider motion effected by shape change. Such motions are ubiquitous in nature and
the human made environment, ranging from
single cells to platform divers and jellyfish. The shapes may be immersed in various
media ranging from the very viscous to air
and nearly inviscid fluids. In the absence of external forces these settings are
characterized by constant momentum. We exploit
this in an algorithm which takes a sequence of changing shapes, say, as modeled by an
animator, as input and produces corresponding
motion in world coordinates. Our method is based on the geometry of shape change and an
appropriate variational principle. The
corresponding Euler-Lagrange equations are first order ODEs in the unknown rotations and
translations and the resulting time stepping
algorithm applies to all these settings without modification as we demonstrate with a
broad set of examples.