Interactive generalized penetration depth computation for rigid and articulated models using object norm

We present a novel, real-time algorithm to accurately approximate the generalized penetration depth (PDg) between two overlapping rigid or articulated models. Given the high complexity of computing PDg, our algorithm approximates PDg based on iterative, constrained optimization on the contact space, defined by the overlapping objects. The main ingredient of our algorithm is a novel and general formulation of distance metric, the object norm, in a configuration space for articulated models, and a compact closed-form solution for it. Then, we perform constrained optimization, by linearizing the contact constraint, and minimizing the object norm under such a constraint. In practice, our algorithm can compute locally optimal PDg for rigid or articulated models consisting of tens of thousands of triangles in tens of milliseconds. We also suggest three applications using PDg computation: retraction-based motion planning, physically-based animation, and data-driven grasping.