We present a novel, real-time algorithm to accurately approximate the generalized penetration depth ( PD g ) between two overlapping rigid or articulated models. Given the high complexity of computing PD g , our algorithm approximates PD g based on iterative, constrained optimization on the contact space, defined by the overlapping objects. The main ingredient of our algorithm is a novel and general formulation of distance metric, the object norm , in a configuration space for articulated models, and a compact closed-form solution for it. Then, we perform constrained optimization, by linearizing the contact constraint, and minimizing the object norm under such a constraint. In practice, our algorithm can compute locally optimal PD g for rigid or articulated models consisting of tens of thousands of triangles in tens of milliseconds. We also suggest three applications using PD g computation: retraction-based motion planning, physically-based animation, and data-driven grasping.

We present fast CCD algorithm for general rigid and articulated models based on conservative advancement. We have implemented the CCD algorithm with two different acceleration techniques which can handle rigid models, and have extended one of them to articulated models. The resulting algorithms take a few milliseconds for rigid models with tens of thousands of triangles, and a few milliseconds for articulated models with tens of links. We show that the performance of our algorithms is much faster than existing CCD algorithms for polygon-soup models and it is also comparable to competing CCD algorithms that are limited to manifold models.

We present six-degree-of-freedom (6DoF) haptic rendering algorithms using translational (PDt) and generalized penetration depth (PDg). Our rendering algorithm can handle any type of object/object haptic interaction using penalty-based response and makes no assumption about the underlying geometry and topology. Moreover, our rendering algorithm can effectively deal with multiple contacts. Our penetration depth algorithms for PDtand PDgare based on a contact-space projection technique combined with iterative, local optimization on the contact-space. We circumvent the local minima problem, imposed by the local optimization, using motion coherence present in the haptic simulation. Our experimental results show that our methods can produce high-fidelity force feedback for general polygonal models consisting of tens of thousands of triangles at near-haptic rates, and are successfully integrated into an off-the-shelf 6DoF haptic device. We also discuss the benefits of using different formulations of penetration depth in the context of 6DoF haptics.

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.

We present a novel algorithm to perform continuous collision detection(CCD) between non-rigid, deformable models using local advancement. Given the initial and final configurations of a deformable model, our algorithm computes linear deformation by interpolating the vertices from the initial to the final configurations with a straight line path and checks for collision along that path. Our approach is applicable to polygon-soup models with arbitrary topology, handles self-collisions and makes no assumption about the underlying non-rigid motion. We accelerate the algorithm by computing motion bounds on the primitives and their bounding volumes. These bounds are combined with hierarchical culling techniques and used for fast collision checking. In practice, we have observed up to four times improvement in running time because of local advancement.

We present a simple and fast algorithm to perform continuous collision detection between polygonal models undergoing rigid motion for interactive applications. Our approach can handle all triangulated models and makes no assumption about the underlying geometry and topology. The algorithm uses the notion of conservative advancement (CA), originally developed for convex polytopes. We extend this formulation to general models using swept sphere volume hierarchy and present a compact formulation to compute the motion bounds along with a novel controlling scheme. We have implemented the algorithm and highlight its performance on various benchmarks. In practice, our algorithm can perform continuous collision queries in few milli-seconds on models composed of tens of thousands of triangles.

We present a simple algorithm to compute the Hausdorff distance between complicated, polygonal models at interactive rates. The algorithm requires no assumptions about the underlying topology and geometry. To avoid the high computational and implementation complexity of exact Hausdorff distance calculation, we approximate the Hausdorff distance within a user-specified error bound. The main ingredient of our approximation algorithm is a novel polygon subdivision scheme, calledVoronoi subdivision, combined with culling between the models based on bounding volume hierarchy (BVH). Thiscross-cullingmethod relies on tight yet simple computation of bounds on the Hausdorff distance, and it discards unnecessary polygon pairs from each of the input models alternatively based on the distance bounds. This algorithm can approximate the Hausdorff distance between polygonal models consisting of tens of thousands triangles with a small error bound in real-time, and outperforms the existing algorithm by more than an order of magnitude. We apply our Hausdorff distance algorithm to the measurement of shape similarity, and the computation of penetration depth for physically-based animation. In particular, the penetration depth computation using Hausdorff distance runs at highly interactive rates for complicated dynamics scene.