On the structure of multiple translational tilings by

Dynamic circle separability between convex

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A polygonal cover of a finite collection of pairwise disjoint convex compact sets in the plane is a finite collection of non-overlapping bounded convex polygons such that each polygon covers exactly one convex set. We show that computing a polygonal cover with worst case minimal number of sides

This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3-D defined by a set of polygons

A polygonal cover of a finite collection of pairwise disjoint convex compact sets in the plane is a finite collection of non-overlapping convex polygons such that each polygon covers exactly one convex set. We show that computing a polygonal cover with worst case minimal number of sides reduces

graphs. These algorithms adopt a variety of representations (e.g., straight-line, polyline, visibility), and update the drawing in a smooth way.

The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in two-dimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.

This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensor-based planning, visibility, decision-theoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.

Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple change-point analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.