دانلود رایگان مقاله محاسبه عمق نفوذ برای مدل سفت با مبالغ مینکوفسکی پویا

Abstract

We present a novel, real-time algorithm for computing the continuous penetration depth (CPD) between two interpenetrating rigid models bounded by triangle meshes. Our algorithm guarantees gradient continuity for the penetration depth (PD) results, unlike conventional penetration depth (PD) algorithms that may have directional discontinuity due to the Euclidean projection operator involved with PD computation. Moreover, unlike prior CPD algorithms, our algorithm is able to handle an orientation change in the underlying model and deal with a topologically-complicated model with holes. Given two intersecting models, we interpolate tangent planes continuously on the boundary of the Minkowski sums between the models and find the closest point on the boundary using Phong projection. Given the high complexity of computing the Minkowski sums for polygonal models in 3D, our algorithm estimates a solution subspace for CPD and dynamically constructs and updates the Minkowski sums only locally in the subspace. We implemented our algorithm on a standard PC platform and tested its performance in terms of speed and continuity using various benchmarks of complicated rigid models, and demonstrated that our algorithm can compute CPD for general polygonal models consisting of tens of thousands of triangles with a hole in a few milli-seconds while guaranteeing the continuity of PD gradient. Moreover, our algorithm can compute more optimal PD values than a state-of-the-art PD algorithm due to the dynamic Minkowski sum computation.

8. Conclusion

In this paper, we have presented a new algorithm to compute continuous PD at interactive rates. We estimate a solution subspace for CPD, and rapidly build local Minkowski sums in the subspace. Then, we interpolate tangent planes continuously over the boundary on the Minkowski sums and perform Phong projection onto it. Our algorithm is applicable to an arbitrary polygonal model with holes. For future work, we would like to further explore a CPD method that can handle both deep and shallow penetrations. We are also interested in finding a less conservative continuity condition than Theorem 3. Extending our algorithm to generalized PD is an interesting research direction and quite possible. Finally, we would like to apply our algorithm to applications such as penalty-based contact dynamics or haptic rendering to stabilize the simulation results.