Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 11

Search results for: Centroidal Voronoi Tessellations

11 Multi-Agent Coverage Control with Bounded Gain Forgetting Composite Adaptive Controller

Authors: Mert Turanli, Hakan Temeltas

Abstract:

In this paper, we present an adaptive controller for decentralized coordination problem of multiple non-holonomic agents. The performance of the presented Multi-Agent Bounded Gain Forgetting (BGF) Composite Adaptive controller is compared against the tracking error criterion with a Feedback Linearization controller. By using the method, the sensor nodes move and reconfigure themselves in a coordinated way in response to a sensed environment. The multi-agent coordination is achieved through Centroidal Voronoi Tessellations and Coverage Control. Also, a consensus protocol is used for synchronization of the parameter vectors. The two controllers are given with their Lyapunov stability analysis and their stability is verified with simulation results. The simulations are carried out in MATLAB and ROS environments. Better performance is obtained with BGF Adaptive Controller.

Keywords: Adaptive control, Centroidal Voronoi Tessellations, composite adaptation, coordination.

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10 3D Mesh Coarsening via Uniform Clustering

Authors: Shuhua Lai, Kairui Chen

Abstract:

In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: Coarsening, mesh clustering, shape approximation, mesh simplification.

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9 Spatial Structure of First-Order Voronoi for the Future of Roundabout Cairo since 1867

Authors: Ali Essam El Shazly

Abstract:

The Haussmannization plan of Cairo in 1867 formed a regular network of roundabout spaces, though deteriorated at present. The method of identifying the spatial structure of roundabout Cairo for conservation matches the voronoi diagram with the space syntax through their geometrical property of spatial convexity. In this initiative, the primary convex hull of first-order voronoi adopts the integral and control measurements of space syntax on Cairo’s roundabout generators. The functional essence of royal palaces optimizes the roundabout structure in terms of spatial measurements and the symbolic voronoi projection of 'Tahrir Roundabout' over the Giza Nile and Pyramids. Some roundabouts of major public and commercial landmarks surround the pole of 'Ezbekia Garden' with a higher control than integral measurements, which filter the new spatial structure from the adjacent traditional town. Nevertheless, the least integral and control measures correspond to the voronoi contents of pollutant workshops and the plateau of old Cairo Citadel with the visual compensation of new royal landmarks on top. Meanwhile, the extended suburbs of infinite voronoi polygons arrange high control generators of chateaux housing in 'garden city' environs. The point pattern of roundabouts determines the geometrical characteristics of voronoi polygons. The measured lengths of voronoi edges alternate between the zoned short range at the new poles of Cairo and the distributed structure of longer range. Nevertheless, the shortest range of generator-vertex geometry concentrates at 'Ezbekia Garden' where the crossways of vast Cairo intersect, which maximizes the variety of choice at different spatial resolutions. However, the symbolic 'Hippodrome' which is the largest public landmark forms exclusive geometrical measurements, while structuring a most integrative roundabout to parallel the royal syntax. Overview of the symbolic convex hull of voronoi with space syntax interconnects Parisian Cairo with the spatial chronology of scattered monuments to conceive one universal Cairo structure. Accordingly, the approached methodology of 'voronoi-syntax' prospects the future conservation of roundabout Cairo at the inferred city-level concept.

Keywords: Roundabout Cairo, first-order Voronoi, space syntax, spatial structure.

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8 A 3D Virtual Navigation System Integrating User Positioning and Pre-Download Mechanism

Authors: Ching-Sheng Wang, Yu-Hung Su, Ching-Yang Hong

Abstract:

This paper takes the actual scene of Aletheia University campus – the Class 2 national monument, the first educational institute in northern Taiwan as an example, to present a 3D virtual navigation system which supports user positioning and pre-download mechanism. The proposed system was designed based on the principle of Voronoi Diagra) to divide the virtual scenes and its multimedia information, which combining outdoor GPS positioning and the indoor RFID location detecting function. When users carry mobile equipments such as notebook computer, UMPC, EeePC...etc., walking around the actual scenes of indoor and outdoor areas of campus, this system can automatically detect the moving path of users and pre-download the needed data so that users will have a smooth and seamless navigation without waiting.

Keywords: GPS, Positioning, RFID, Virtual Navigation, Voronoi Diagram.

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7 Geometric Data Structures and Their Selected Applications

Authors: Miloš Šeda

Abstract:

Finding the shortest path between two positions is a fundamental problem in transportation, routing, and communications applications. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of visibility graphs in point-to-point motion planning in the Euclidean plane and an alternative approach using Voronoi diagrams that decreases the probability of collisions with obstacles. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the plane using either only straight connections between pairs of points (minimum spanning tree) or allowing the addition of auxiliary points to the set to obtain shorter spanning networks (minimum Steiner tree).

Keywords: motion planning, spanning tree, Steiner tree, Delaunay triangulation, Voronoi diagram.

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6 Visual Analytics of Higher Order Information for Trajectory Datasets

Authors: Ye Wang, Ickjai Lee

Abstract:

Due to the widespread of mobile sensing, there is a strong need to handle trails of moving objects, and trajectories. This paper proposes three visual analytics approaches for higher order information of trajectory datasets based on the higher order Voronoi diagram data structure. Proposed approaches reveal geometrical, topological, and directional information. Experimental resultsdemonstrate the applicability and usefulness of proposed three approaches.

Keywords: Visual Analytics, Higher Order Information, Trajectory Datasets, Spatio-temporal data.

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5 Optimal Algorithm for Constructing the Delaunay Triangulation in Ed

Authors: V. Tereshchenko, D. Taran

Abstract:

In this paper we propose a new approach to constructing the Delaunay Triangulation and the optimum algorithm for the case of multidimensional spaces (d ≥ 2). Analysing the modern state, it is possible to draw a conclusion, that the ideas for the existing effective algorithms developed for the case of d ≥ 2 are not simple to generalize on a multidimensional case, without the loss of efficiency. We offer for the solving this problem an effective algorithm that satisfies all the given requirements. But theoretical complexity of the problem it is impossible to improve as the Worst - Case Optimality for algorithms of solving such a problem is proved.

Keywords: Delaunay triangulation, multidimensional space, Voronoi Diagram, optimal algorithm.

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4 Coverage Strategies for Wireless Sensor Networks

Authors: Nor Azlina Ab. Aziz, Kamarulzaman Ab. Aziz, Wan Zakiah Wan Ismail

Abstract:

Coverage is one of the main research interests in wireless sensor networks (WSN), it is used to determine the quality of service (QoS) of the networks. Therefore this paper aims to review the common strategies use in solving coverage problem in WSN. The strategies studied are used during deployment phase where the coverage is calculated based on the placement of the sensors on the region of interest (ROI). The strategies reviewed are categorized into three groups based on the approaches used, namely; force based, grid based or computational geometry based approach.

Keywords: Computational geometry, coverage, Delaunay triangulation, force, grid, Voronoi diagram, wireless sensor networks.

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3 Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes

Authors: Antonio Breda d’Azevedo

Abstract:

Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no “planification” for n-dimensional polytopes. However we show that it is possible to make a “surfacification” of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).

Keywords: Maps, representation, polytopes.

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2 The Influence of Fiber Volume Fraction on Thermal Conductivity of Pultruded Profile

Authors: V. Lukášová, P. Peukert, V. Votrubec

Abstract:

Thermal conductivity in the x, y and z-directions was measured on a pultruded profile that was manufactured by the technology of pulling from glass fibers and a polyester matrix. The results of measurements of thermal conductivity showed considerable variability in different directions. The caused variability in thermal conductivity was expected due fraction variations. The cross-section of the pultruded profile was scanned. An image analysis illustrated an uneven distribution of the fibers and the matrix in the cross-section. The distribution of these inequalities was processed into a Voronoi diagram in the observed area of the pultruded profile cross-section. In order to verify whether the variation of the fiber volume fraction in the pultruded profile can affect its thermal conductivity, the numerical simulations in the ANSYS Fluent were performed. The simulation was based on the geometry reconstructed from image analysis. The aim is to quantify thermal conductivity numerically. Above all, images with different volume fractions were chosen. The results of the measured thermal conductivity were compared with the calculated thermal conductivity. The evaluated data proved a strong correlation between volume fraction and thermal conductivity of the pultruded profile. Based on presented results, a modification of production technology may be proposed.

Keywords: Numerical simulation, pultruded profile, volume fraction, thermal conductivity.

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1 3D Star Skeleton for Fast Human Posture Representation

Authors: Sungkuk Chun, Kwangjin Hong, Keechul Jung

Abstract:

In this paper, we propose an improved 3D star skeleton technique, which is a suitable skeletonization for human posture representation and reflects the 3D information of human posture. Moreover, the proposed technique is simple and then can be performed in real-time. The existing skeleton construction techniques, such as distance transformation, Voronoi diagram, and thinning, focus on the precision of skeleton information. Therefore, those techniques are not applicable to real-time posture recognition since they are computationally expensive and highly susceptible to noise of boundary. Although a 2D star skeleton was proposed to complement these problems, it also has some limitations to describe the 3D information of the posture. To represent human posture effectively, the constructed skeleton should consider the 3D information of posture. The proposed 3D star skeleton contains 3D data of human, and focuses on human action and posture recognition. Our 3D star skeleton uses the 8 projection maps which have 2D silhouette information and depth data of human surface. And the extremal points can be extracted as the features of 3D star skeleton, without searching whole boundary of object. Therefore, on execution time, our 3D star skeleton is faster than the “greedy" 3D star skeleton using the whole boundary points on the surface. Moreover, our method can offer more accurate skeleton of posture than the existing star skeleton since the 3D data for the object is concerned. Additionally, we make a codebook, a collection of representative 3D star skeletons about 7 postures, to recognize what posture of constructed skeleton is.

Keywords: computer vision, gesture recognition, skeletonization, human posture representation.

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