PolyDepth: Real-time Penetration Depth Computation using Iterative Contact-Space Projection

TL;DR

PolyDepth introduces a real-time algorithm for computing penetration depth between polygonal models using iterative contact-space projection and local optimization, enabling efficient collision analysis for complex models.

Contribution

It presents a novel iterative contact-space projection method with LCP formulation for real-time penetration depth computation on complex models.

Findings

Handles models with tens of thousands of triangles.

Operates at interactive rates.

Provides accurate local penetration depth estimates.

Abstract

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.