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In this paper, we propose a novel penetration metric, called deformablepenetration depth PDd, to define a measure of inter-penetration between twolinearly deforming tetrahedra using the object norm. First of all, we show thata distance metric for a tetrahedron deforming between two configurations can befound in closed form based on object norm. Then, we show that the PDd betweenan intersecting pair of static and deforming tetrahedra can be found by solvinga quadratic programming (QP) problem in terms of the distance metric withnon-penetration constraints. We also show that the PDd between two,intersected, deforming tetrahedra can be found by solving a similar QP problemunder some assumption on penetrating directions, and it can be also acceleratedby an order of magnitude using pre-calculated penetration direction. We haveimplemented our algorithm on a standard PC platform using an off-the-shelf QPoptimizer, and experimentally show that both the static/deformable anddeformable/deformable tetrahedra cases can be solvable in from a few to tens ofmilliseconds. Finally, we demonstrate that our penetration metric isthree-times smaller (or tighter) than the classical, rigid penetration depthmetric in our experiments.

A Penetration Metric for Deforming Tetrahedra using Object Norm