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702
Incremental search methods for reachability analysis of continuous and hybrid systems
 In Hybrid Systems: Computation and Control
, 2004
"... 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 conseq ..."
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Cited by 60 (6 self)
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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
Collision Detection: Algorithms and Applications
, 1996
"... this paper, we address the first two elements by presenting general a purpose collision detection and contact area determination algorithm for simulations. The collision response is application dependent. The algorithm reports the contact area and thus enables the application to compute an appropria ..."
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Cited by 58 (1 self)
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this paper, we address the first two elements by presenting general a purpose collision detection and contact area determination algorithm for simulations. The collision response is application dependent. The algorithm reports the contact area and thus enables the application to compute an appropriate response. Our algorithm not only addresses interaction between a pair of general polygonal objects, but also large environments consisting of hundreds of moving parts, such as those encountered in the manufacturing plants. Furthermore, we do not assume the motions of the objects to be expressed as a closed form function of time. Our collision detection scheme is efficient and accurate (to the resolution of the models). Given the geometric models, the algorithm precomputes the convex hull and a hierarchical representation of each model in terms of oriented bounding boxes. At runtime, it uses tight fitting axisaligned bounding boxes to pair down the number of object pair interactions to only those pairs within close proximity [12]. For each pair of objects whose bounding boxes overlap, the algorithm checks whether their convex hulls are intersecting based on the closest feature pairs [22]. Finally for each object pair whose convex hulls overlap, it makes use of oriented bounding box hierarchy (OBBTree) to check for actual contact [18]. Organization: The rest of the paper is organized as follows: Section 2 reviews some of the previous work in collision detection. Section 3 outlines the algorithm for pruning the number of object pairs. We briefly describe the closest feature and contact determination algorithms in Section 4. Finally, we describe the imple leftmark
Mesh Generation
 Handbook of Computational Geometry. Elsevier Science
, 2000
"... this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary. ..."
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Cited by 57 (8 self)
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this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.
A Fast and Robust GJK Implementation for Collision Detection of Convex Objects
, 1999
"... This paper presents an implementation of the GilbertJohnsonKeerthi 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 ..."
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Cited by 56 (2 self)
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This paper presents an implementation of the GilbertJohnsonKeerthi 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.
An experimental analysis of selfadjusting computation
 In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI
, 2006
"... Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a r ..."
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Cited by 51 (25 self)
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Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize selfadjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.
Classroom examples of robustness problems in geometric computations
 In Proc. 12th European Symposium on Algorithms, volume 3221 of Lecture Notes Comput. Sci
, 2004
"... ..."
The Delaunay hierarchy
 Internat. J. Found. Comput. Sci
"... 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, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into s ..."
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Cited by 50 (7 self)
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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, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the level below. Point location is done by walking in a triangulation to determine the nearest neighbor of the query at that level, then the walk restarts from that neighbor at the level below. Using a small subset (3%) to sample a level allows a small memory occupation; the walk and the use of the nearest neighbor to change levels quickly locate the query.
Examples of 3D grasp quality computations
 Proc. IEEE Intl. Conf. on Robotics and Automation
, 1999
"... Prewious grasp quality research i s main ly theoretical, and has assumed that contact types and positions are given, in order t o preserve the generality of the proposed quality measures. T h e example results provided by these works either ignore hand geometry and kinematics entirely o r involve ..."
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Cited by 49 (10 self)
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Prewious grasp quality research i s main ly theoretical, and has assumed that contact types and positions are given, in order t o preserve the generality of the proposed quality measures. T h e example results provided by these works either ignore hand geometry and kinematics entirely o r involve only the simplest of grippers. W e present a unique grasp analysis sys tem that, when given a 3 0 object, hand, and pose f o r the hand, can accurately determine the types of contacts that wall occur between the links of the hand and the object, and compute two measures of quality f o r the grasp. Using models of two articulated robotic hands, we analyze several grasps of a polyhedral model of a telephone handset, and we use a novel technique t o wisualize the 6D space used in these computations. In addition, we demonstrate the possibility of using this sys tem f o r synthesizing high quality grasps by performing a search over a subset of possible hand configurations. 1
Interactive Cutaway Illustrations
 Computer Graphics Forum
, 2003
"... 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 ..."
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Cited by 49 (0 self)
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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 computerbased 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 wellknown artistic or technical illustration techniques. All methods of this paper make use of modern graphics hardware functionality to achieve interactive frame rates.
Delaunay Tessellation of Proteins: Four Body Nearest Neighbor Propensities of Amino Acid Residues
 J. Comput. Biol
, 1996
"... Delaunay tessellation is applied for the first time in the analysis of protein structure. By representing the location of amino acid residues in protein chains by C a atoms, the protein structure is described as a set of points in threedimensional space. Delaunay tessellation of a protein structure ..."
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Cited by 48 (5 self)
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Delaunay tessellation is applied for the first time in the analysis of protein structure. By representing the location of amino acid residues in protein chains by C a atoms, the protein structure is described as a set of points in threedimensional space. Delaunay tessellation of a protein structure generates an aggregate of spacefilling irregular tetrahedra, or Delaunay simplices. The vertices of each simplex define objectively four nearest neighbor C a atoms, i.e. four nearest neighbor residues. A simplex classification scheme is introduced in which simplices are divided into five classes based on the relative positions of vertex residues in the protein primary sequence. Statistical analysis of the residue composition of Delaunay simplices reveals nonrandom preferences for certain quadruplets of amino acids to be clustered together. This nonrandom preference may be used to develop a fourbody potential that can be used in evaluating sequencestructure compatibility for the purpose o...