Going with the Flow

Given a sequence of poses of a body we study the motion resulting when the body is immersed in a (possibly) moving, incompressible medium. With the poses given, say, by an animator, the governing second-order ordinary differential equations are those of a rigid body with time-dependent inertia acted upon by various forces. Some of these forces, like lift and drag, depend on the motion of the body in the surrounding medium. Additionally, the inertia must encode the effect of the medium through its added mass. We derive the corresponding dynamics equations which generalize the standard rigid body dynamics equations. All forces are based on local computations using only physical parameters such as mass density. Notably, we approximate the effect of the medium on the body through local computations avoiding any global simulation of the medium. Consequently, the system of equations we must integrate in time is only 6 dimensional (rotation and translation). Our proposed algorithm displays linear complexity and captures intricate natural phenomena that depend on body-fluid interactions.

The bunny and armadillo mesh are courtesy of the Stanford Computer Graphics Laboratory. The eel and the turtle mesh are courtesy of DigitalLife3D at the University of Massachusetts, Amherst. We are grateful to crowinhand, Zacxophone, bulut- and FFishAsia for the models of the leaves. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109 “Discretization in Geometry and Dynamics,” the Caltech Center for Information Science & Technology, and the Einstein Foundation Berlin. Additional support was provided by SideFX software.