34702291
Polyhedral Assembly Partitioning Using Maximally Covered Cells in Arrangements of Convex Polytopes
We study the following problem: Given a collection A of polyhedral parts in 3D, determine whether there exists a subset S of the parts that can be moved as a rigid body by infinitesimal translation and rotation, without colliding with the rest of the parts, A\S. A negative result implies that the object whose constituent parts are the collection A cannot be taken apart with two hands. A positive result, together with the list of movable parts in S and a direction of motion for S, can be used by an assembly sequence planner (it does not, however, give the complete specification of an assembly operation). This problem can be transformed into that of traversing an arrangement of convex polytopes in the space of directions of rigid motions. We identify a special type of cells in that arrangement, which we call the maximally covered cells, and we show that it suffices for the problem at hand to consider a representative point in each of these special cells rather than to compute the entire arrangement. Using this observation, we devise an algorithm which is complete (in the sense that it is guaranteed to find a solution if one exists), simple, and improves significantly over the best previously known solutions. We describe an implementation of our algorithm and report experimental results obtained with this implementation.
36092896
Fractionally cascaded information in a sensor network
11907465
Deformable Free-Space Tilings for Kinetic Collision Detection†
We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously. Unlike classical collision detection methods that rely on bounding volume hierarchies, our method is based on deformable tilings of the free space surrounding the polygons. The basic shape of our tiles is that of a pseudo-triangle, a shape sufficiently flexible to allow extensive deformation, yet structured enough to make detection of self-collisions easy. We show different schemes for maintaining pseudo-triangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that the pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. In addition, by refining the pseudo-triangulation, we show triangulations of points that only change about O(n 7 / 3 ) times for linear motion. We then describe an algorithm for maintaining a pseudo-triangulation of a set of convex polygons. Finally, we extend our algorithm to the general case of maintaining a pseudo-triangulation of a set of moving or deforming simple polygons.
10626633
Cylindrical static and kinetic binary space partitions
We describe the first known algorithm for efficiently maintaining a Binary Space Partition (BSP) for n continuously moving segments in the plane, whose interiors remain disjoint throughout the motion. Under reasonable assumptions on the motion, we show that the total number of times this BSP changes is O.n 2 / ,a nd that we can update the BSP in O.logn/ expected time per change. Throughout the motion, the expected size of the BSP is O.n logn/. We also consider the problem of constructing a BSP for n static triangles with pairwise-disjoint interiors in R 3 . We present a randomized algorithm that constructs a BSP of size O.n 2 / in O.n 2 log 2 n/ expected time. We also describe a deterministic algorithm that constructs a BSP of size O..nCk/log 2 n/ and height O.logn/ in O..nCk/log 3 n/ time, where k is the number of intersection points between the edges of the projections of the triangles onto the xy-plane. This is the first known algorithm that constructs a BSP of O.logn/ height for disjoint triangles inR 3 . © 2000 Elsevier Science B.V. All rights reserved.
2060671
Landmark Selection and Greedy Landmark-Descent Routing for Sensor Networks
We study the problem of landmark selection for landmark-based routing in a network of fixed wireless communication nodes. We present a distributed landmark selection algorithm that does not rely on global clock synchronization, and a companion local greedy landmark-based routing scheme. We assume no node location information, and that each node can communicate with some of its geographic neighbors. Each node is named by its hop count distances to a small number of nearby landmarks. Greedy routing at a node is performed to equalize its vector of landmark distances to that of the destination. This is done by following the shortest path to the landmark that maximizes the ratio of its distances to the source and the destination. In addition, we propose a method to alleviate the difficulty in routing to destinations near the boundaries by virtually expanding the network boundaries. The greedy routing, when combined with our landmark selection scheme, has a provable bounded path stretch relative to the best path possible, and guarantees packet delivery in the continuous domain. In the discrete domain, our simulations show that the landmark selection scheme is effective, and the companion routing scheme performs well under realistic settings. Both the landmark selection and greedy routing assumes no specific communication model and works with asymmetric links. Although some of the analysis are non-trivial, the algorithms are simple, flexible and cost-effective enough to warrant a real-world deployment.
2650108
Lightweight sensing and communication protocols for target enumeration and aggregation
The development of lightweight sensing andcommunication protocols is a key requirement for designing resource constrained sensor networks. This paper introduces a set of efficient protocols and algorithms, DAM, EBAM, and EMLAM, for constructing and maintaining sensor aggregates that collectively monitor target activity in the environment. A sensor aggregate comprises those nodes in a network that satisfy a grouping predicate for a collaborative processing task. The parameters of the predicate depend on the task and its resource requirements. Since the foremost purpose of a sensor network is to selectively gather information about the environment, the formation of appropriate sensor aggregates is crucial for optimally allocating resources to sensing and communication tasks.This paper makes minimal assumptions about node onboard processing and communication capabilities so as to allow possible implementations on resource-constrained hardware. Factors affecting protocol performance are discussed. The paper presents simulation results showing how the protocol performance varies as key network and task parameters are varied. It also provides probabilistic analyses of network behavior consistent with the simulation results. The protocols have been experimentally validated on a sensor network testbed comprising 25 Berkeley MICA sensor motes.
9160404
Shape segmentation using local slippage analysis
We propose a method for segmentation of 3D scanned shapes into simple geometric parts. Given an input point cloud, our method computes a set of components which possess one or more slippable motions: rigid motions which, when applied to a shape, slide the transformed version against the stationary version without forming any gaps. Slippable shapes include rotationally and translationally symmetrical shapes such as planes, spheres, and cylinders, which are often found as components of scanned mechanical parts. We show how to determine the slippable motions of a given shape by computing eigenvalues of a certain symmetric matrix derived from the points and normals of the shape. Our algorithm then discovers slippable components in the input data by computing local slippage signatures at a set of points of the input and iteratively aggregating regions with matching slippable motions. We demonstrate the performance of our algorithm for reverse engineering surfaces of mechanical parts.
13195342
Geometric filtering of pairwise atomic interactions applied to the design of efficient statistical potentials
Distance-dependent, pairwise, statistical potentials are based on the concept that the packing observed in known protein structures can be used as a reference for comparing different 3D models for a protein. Here, packing refers to the set of all pairs of atoms in the molecule. Among all methods developed to assess three-dimensional models, statistical potentials are subject both to praise for their power of discrimination, and to criticism for the weaknesses of their theoretical foundations. Classical derivations of pairwise potentials assume statistical independence of all pairs of atoms. This assumption, however, is not valid in general. We show that we can filter the list of all interactions in a protein to generate a much smaller subset of pairs that retains most of the structural information contained in proteins. The filter is based on a geometric method called alpha shapes that captures the packing in a conformation. Statistical scoring functions derived from such subsets perform as well as scoring functions derived from the set of all pairwise interactions.
34799453
Estimating surface normals in noisy point cloud data
In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2 or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.
207156516
Registration of point cloud data from a geometric optimization perspective
We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximants of the squared distance function are used to develop a linear system whose solution gives the best aligning rigid transform for the given pair of point clouds. The rigid transform is applied and the linear system corresponding to the new orientation is build. This process is iterated until it converges. The point-to-point and the point-to-plane Iterated Closest Point (ICP) algorithms can be treated as special cases in this framework. Our algorithm can align PCDs even when they are placed far apart, and is experimentally found to be more stable than point-to-plane ICP. We analyze the convergence behavior of our algorithm and of point-to-point and point-to-plane ICP under our proposed framework, and derive bounds on their rate of convergence. We compare the stability and convergence properties of our algorithm with other registration algorithms on a variety of scanned data.
8013433
Data structures for mobile data
Computer systems commonly cache the values of variables to gain efficiency. In applications where the goal is to track attributes of a continuously moving or deforming physical system over time, caching relations between variables works better than caching individual values. The reason is that, as the system evolves, such relationships are more stable than the values of individual variables.
Kinetic data structures (KDSs) are a novel formal framework for designing and analyzing sets of assertions to cache about the environment, so that these assertion sets are at once relatively stable and tailored to facilitate or trivialize the computation of the attribute of interest. Formally, a KDS is a mathematical proof animated through time, proving the validity of a certain computation for the attribute of interest. KDSs have rigorous associated measures of performance and their design shares many qualities with that of classical data structures.
The KDS framework has led to many new and promising algorithms in applications where the efficient modeling of motion is essential. Among these are collision detection for moving rigid and deformable bodies, connectivity maintenace in ad-hoc networks, local environment tracking for mobile agents, and visibility/occlusion maintenance. This talk will survey the general ideas behind KDSs and illustrate their application to simple geometric problems that arise in virtual and physical environments.