PhongPD

Continuous Penetration Depth Computation for Rigid Models using Dynamic Minkowski Sums

Youngeun Lee¹, Evan Behar², Jyh-Ming Lien² and Young J. Kim¹

¹Department of Computer Science & Engineering

Ewha Womans University, Seoul, Korea

youngeunlee@ewhain.net, kimy@ewha.ac.kr

²Department of Computer Science

George Mason University, VA, USA

behare@gmail.com, jmlien@cs.gmu.edu

Computer-Aided Design [Paper]

(Presented at the Symposium on Solid and Physical Modeling 2016)

Abstract

We present a novel, real-time algorithm for computing the continuous penetration depth (CPD) between two interpen-etrating 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 nd 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.

Benchmarking Scenarios

1. Cone & Axes

The red cone moves along the blue arrow while penetrating into the yellow axes.