  When we move on snow, sand, or mud, the ground deforms under our feet,
immediately affecting our gait. We propose a physically based model for
computing such interactions in real time, from only the kinematic motion of a
virtual character. The force applied by each foot on the ground during contact
is estimated from the weight of the character, its current balance, the foot
speed at the time of contact, and the nature of the ground. We rely on a
standard stress-strain relationship to compute the dynamic deformation of the
soil under this force, where the amount of compression and lateral displacement
of material are, respectively, parameterized by the soil's Young modulus and
Poisson ratio. The resulting footprint is efficiently applied to the terrain
through procedural deformations of refined terrain patches, while the addition
of a simple controller on top of a kinematic character enables capturing the
effect of ground deformation on the character's gait. As our results show, the
resulting footprints greatly improve visual realism, while ground compression
results in consistent changes in the character's motion. Readily applicable to
any locomotion gait and soft soil material, our real-time model is ideal for
enhancing the visual realism of outdoor scenes in video games and virtual
reality applications.
