PhongPD: Gradient-continuous penetration metric for polygonal models using Phong projection

We present a novel algorithm to compute a gradient-continuous penetration depth (PhongPD) between two interpenetrated polygonal models. Our penetration depth (PD) formulation ensures separating the intersected models by translation, and the amount of such translation is close to an optimal motion to resolve interpenetration in most cases. In order to achieve the gradient-continuity in our algorithm, we interpolate tangent planes continuously over the contact space and then perform a projection along a normal direction defined by the interpolated tangent planes; this projection scheme is known as Phong projection. We have implemented our PhongPD algorithm and certifies its continuity using three benchmarks consisting of diverse combinatorial complexities, and show that our algorithm shows smoother PD results than a conventional Euclidean-projection-based PD method.