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Conference Papers Year : 2012

Principal Geodesic Dynamics

Maxime Tournier
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Lionel Reveret


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.
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Dates and versions

hal-00727384 , version 1 (06-09-2012)



Maxime Tournier, Lionel Reveret. Principal Geodesic Dynamics. SCA 2012 - EG/SIGGRAPH Symposium on Computer Animation, Jul 2012, Lausanne, Switzerland. pp.235-244, ⟨10.2312/SCA/SCA12/235-244⟩. ⟨hal-00727384⟩
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