We propose a fast algorithm for rendering general irregular grids. Our method uses a sweep-plane approach to accelerate ray casting, and can handle disconnected and nonconvex (even with holes) unstructured irregular grids with a rendering cost that decreases as the “disconnectedness” decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. In this paper, we establish the practicality of our method through experimental results based on our implementation, and we also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids.

Research in robotic grasping has flourished in the last 25 years. A recent survey by Bicchi [1] covered over 140 papers, and many more than that have been published. Stemming from our desire to implement some of the work in grasp analysis for particular hand designs, we created an interactive grasping simulator that can import a wide variety of hand and object models and can evaluate the grasps formed by these hands. This system, dubbed “GraspIt!,” has since expanded in scope to the point where we feel it could serve as a useful tool for other researchers in the field. To that end, we are making the system publicly available (GraspIt! is available for download for a variety of platforms from

This paper presents an implementation of the Gilbert-Johnson-Keerthi algorithm for computing the distance between convex objects, that has improved performance, robustness, and versatility over earlier implementations. The algorithm presented here is especially fit for use in collision detection of objects modeled using various types of geometric primitives, such as boxes, cones, and spheres, and their images under affine transformation, for instance, as described in VRML.

We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation.

In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and consequently on the generation of safety certificates; however, inability to prove safety with these tools does not necessarily result in a proof of unsafety. In this paper, we propose an alternative approach, which aims at the fast falsification of safety properties; this approach provides the designer with a complementary set of tools to the ones based on conservative analysis, providing additional insight into the characteristics of the system under analysis. Our algorithms are based on algorithms originally proposed for robotic motion planning; the key idea is to incrementally grow a set of feasible trajectories by exploring the state space in an efficient way. The ability of the proposed algorithms to analyze the reachability and safety properties of general continuous and hybrid systems is demonstrated on examples from the literature. 1

In this paper we discuss different approaches to generate cutaway illustrations. The purpose of such a drawing is to allow the viewer to have a look into an otherwise solid opaque object. Traditional methods to draw these kinds of illustrations are evaluated to extract a small and effective set of rules for a computer-based rendering of cutaway illustrations. We show that our approaches are not limited to a specific rendering style but can be successfully combined with a great variety of well-known artistic or technical illustration techniques. All methods of this paper make use of modern graphics hardware functionality to achieve interactive frame rates.

We present a novel and fast algorithm to compute penetration depth (PD) between two polyhedral models for physically-based animation. Given two overlapping polyhedra, it computes the minimal translation distance to separate them using a combination of object-space and image-space techniques. The algorithm computes pairwise Minkowski sums of decomposed convex pieces and performs a closest point query using rasterization hardware. It uses bounding volume hierarchies, object-space and image-space culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner. We demonstrate its application to contact response computation and a time-stepping method for dynamic simulation.

Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. The success of this approach crucially depends on the choice of the predicates used for abstraction. In this paper, we focus on identifying these predicates automatically by analyzing spurious counter-examples generated by the search in the abstract state-space. We present the basic techniques for discovering new predicates that will rule out closely related spurious counter-examples, optimizations of these techniques, implementation of these in the verification tool, and case studies demonstrating the promise of the approach.

Abstract. Computing reachable sets is an essential step in most analysis and synthesis techniques for hybrid systems. The representation of these sets has a deciding impact on the computational complexity and thus the applicability of these techniques. This paper presents a new approach for approximating reachable sets using oriented rectangular hulls (ORHs), the orientations of which are determined by singular value decompositions of sample covariance matrices for sets of reachable states. The orientations keep the over-approximation of the reachable sets small in most cases with a complexity of low polynomial order with respect to the dimension of the continuous state space. We show how the use of ORHs can improve the efficiency of reachable set computation significantly for hybrid systems with nonlinear continuous dynamics.