A certified conflict locator for the incremental maintenance of the Delaunay graph of semi-algebraic sets

Most of the curves and surfaces encountered in geometric modelling are defined as the set of solutions of a system of algebraic equations or inequalities (semi-algebraic sets). The Voronoi diagram of a set of sites is a decomposition of the space into proximal regions (one for each site). Voronoi diagrams have been used to answer proximity queries. The dual graph of the Voronoi diagram is called the Delaunay graph. Only approximations by conics can guarantee a proper continuity of the first order derivative at contact points, which is necessary for guaranteeing the exactness of the Delaunay graph. The central idea of this paper is that a (one time) symbolic preprocessing may accelerate the certified numerical evaluation of the Delaunay graph conflict locator. The symbolic preprocessing is the computation of the implicit equation of the generalised offset to conics. The certified computation of the Delaunay graph conflict locator relies on theorems on the uniqueness of a root in given intervals (Kantorovich, Moore-Krawczyk). For conics, the computations get much faster by considering only the implicit equations of the generalised offsets

Computer science: the hardware software and heart of IT

1st edition, 201

Voronoi diagrams of semi-algebraic sets

Most of the curves and surfaces encountered in geometric modelling are denned as the set of solutions of a system of algebraic equations and inequalities (semialgebraic sets). Many problems from different fields involve proximity queries like finding the (nearest) neighbours or quantifying the neighbourliness of two objects. The Voronoi diagram of a set of sites is a decomposition of space into proximal regions. The proximal region of a site is the locus of points closer to that site than to any other one. Voronoi diagrams allow one to answer proximity queries after locating a query point in the Voronoi zone it belongs to. The dual graph of the Voronoi diagram is called the Delaunay graph. Only approximations by conies can guarantee a proper order of continuity at contact points, which is necessary for guaranteeing the exactness of the Delaunay graph. The theoretical purpose of this thesis is to elucidate the basic algebraic and geometric properties of the offset to an algebraic curve and to reduce the semialgebraic computation of the Delaunay graph to eigenvalues computations. The practical objective of this thesis is the certified computation of the Delaunay graph for low degree semi-algebraic sets embedded in the Euclidean plane. The methodology combines interval analysis and computational algebraic geometry. The central idea of this thesis is that a (one time) symbolic preprocessing may accelerate the certified numerical evaluation of the Delaunay graph conflict locator. The symbolic preprocessing is the computation of the implicit equation of the generalised offset to conies. The reduction of the Delaunay graph conflict locator for conies from a semi-algebraic problem to a linear algebra problem has been possible through the use of the generalised Voronoi vertex (a concept introduced in this thesis). The certified numerical computation of the Delaunay graph has been possible by using an interval analysis based library for solving zero-dimensional systems of equations and inequalities (ALIAS). The certified computation of the Delaunay graph relies on theorems on the uniqueness of a root in given intervals (Kantorovitch, Moore-Krawczyk). For conies, the computations get much faster by considering only the implicit equations of the generalised offsets.Science, Faculty ofComputer Science, Department ofGraduat

Optimization of Operation Sequencing in CAPP Using Hybrid Genetic Algorithm and Simulated Annealing Approach

In any CAPP system, one of the most important process planning functions is selection of the operations and corresponding machines in order to generate the optimal operation sequence. In this paper, the hybrid GA-SA algorithm is used to solve this combinatorial optimization NP (Non-deterministic Polynomial) problem. The network representation is adopted to describe operation and sequencing flexibility in process planning and the mathematical model for process planning is described with the objective of minimizing the production time. Experimental results show effectiveness of the hybrid algorithm that, in comparison with the GA and SA standalone algorithms, gives optimal operation sequence with lesser computational time and lesser number of iterations

Optimization of Operation Sequencing in CAPP Using Hybrid Genetic Algorithm and Simulated Annealing Approach

In any CAPP system, one of the most important process planning functions is selection of the operations and corresponding machines in order to generate the optimal operation sequence. In this paper, the hybrid GA-SA algorithm is used to solve this combinatorial optimization NP (Non-deterministic Polynomial) problem. The network representation is adopted to describe operation and sequencing flexibility in process planning and the mathematical model for process planning is described with the objective of minimizing the production time. Experimental results show effectiveness of the hybrid algorithm that, in comparison with the GA and SA standalone algorithms, gives optimal operation sequence with lesser computational time and lesser number of iterations

Autonomous Navigation of Automated Guided Vehicle Using Monocular Camera

This paper presents a hybrid control algorithm for Automated Guided Vehicle (AGV) consisting of two independent control loops: Position Based Control (PBC) for global navigation within manufacturing environment and Image Based Visual Servoing (IBVS) for fine motions needed for accurate steering towards loading/unloading point. The proposed hybrid control separates the initial transportation task into global navigation towards the goal point, and fine motion from the goal point to the loading/unloading point. In this manner, the need for artificial landmarks or accurate map of the environment is bypassed. Initial experimental results show the usefulness of the proposed approach.COBISS.SR-ID 27383808

Autonomous Navigation of Automated Guided Vehicle Using Monocular Camera

This paper presents a hybrid control algorithm for Automated Guided Vehicle (AGV) consisting of two independent control loops: Position Based Control (PBC) for global navigation within manufacturing environment and Image Based Visual Servoing (IBVS) for fine motions needed for accurate steering towards loading/unloading point. The proposed hybrid control separates the initial transportation task into global navigation towards the goal point, and fine motion from the goal point to the loading/unloading point. In this manner, the need for artificial landmarks or accurate map of the environment is bypassed. Initial experimental results show the usefulness of the proposed approach.COBISS.SR-ID 27383808