Principal Geodesic Dynamics

Maxime Tournier  Lionel Reveret 

Paper [PDF 2.2Mb] | Movie [MP4 26.8Mb]


This paper presents a new integration of a data-driven approach using dimension reduction and a physically-based simulation for real-time character animation. We exploit Lie group statistical analysis techniques (Principal Geodesic Analysis, PGA) to approximate the pose manifold of a motion capture sequence by a reduced set of pose geodesics. We integrate this kinematic parametrization into a physically-based animation approach of virtual characters, by using the PGA-reduced parametrization directly as generalized coordinates of a Lagrangian formulation of mechanics. In order to achieve real-time without sacrificing stability, we derive an explicit time integrator by approximating existing variational integrators. Finally, we test our approach in task-space motion control. By formulating both physical simulation and inverse kinematics time stepping schemes as two quadratic programs, we propose a features-based control algorithm that interpolates between the two metrics. This allows for an intuitive trade-off between realistic physical simulation and controllable kinematic manipulation.

Tournier, M., Reveret, L., "Principal Geodesic Dynamics", ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA'12,, Lausanne, Switzerland, 29-31 jul, 2012.

Paper [PDF, 2.2Mb]
Video [MP4 26.8Mb]

AUTHOR = {Tournier, Maxime and Reveret, Lionel},
TITLE = {{Principal Geodesic Dynamics}},
BOOKTITLE = {{EG/SIGGRAPH Symposium on Computer Animation, SCA}},
YEAR = {2012},
MONTH = Jul,
EDITOR = {Paul Kry and Jehee Lee},
PUBLISHER = {Eurographics Association},
ADDRESS = {Lausanne, Switzerland},
DOI = {10.2312/SCA/SCA12/235-244},