Continuous penetration depth computation for rigid models using dynamic Minkowski sums

Youngeun Lee, Evan Behar, Jyh Ming Lien, Young J. Kim

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)14-25
Number of pages12
JournalCAD Computer Aided Design
StatePublished - 1 Sep 2016

Bibliographical note

Funding Information:
This work was supported in part by NRF in Korea ( 2014K1A3A1A17073365 , 2015R1A2A1A15055470 ). E. Behar and J.-M. Lien were supported by the Korean Federation of Science and Technology Societies (KOFST) grant funded by the Korean government, and by US NSF IIS-096053 , CNS-1205260 , EFRI-1240459 , AFOSR FA9550-12-1-0238 .

Publisher Copyright:
© 2016 Elsevier Ltd


  • Collision detection
  • Convolution
  • Minkowski sum
  • Penetration depth


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