We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target o...

Skeleton extraction algorithm can transform two-dimensional map into a skeleton diagram, which provide more convenience to global path planning of the complex map. This article first extracts skeleton extraction of the global map using the skeleton extraction algorithm and finds all paths of flat map. Based on this we can use search algorithms to search, and find a feasible path connecting star...

We present an algorithm for generating G 1-continuous spiral-like tool paths for machining pockets without islands. The pocket may be an arbitrary simply-connected 2D shape bounded by straight-line segments and circular arcs. Based on the Voronoi diagram of the pocket we generate a sequence of nested Jordan curves (“wave fronts”) inside the pocket that are linked to form a spiral-like tool path...

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new app...

CASPA is a stochastic process algebra tool for performance and dependability modelling, analysis and verification. It is based entirely on the symbolic data structure MTBDD (Multi-Terminal Binary Decision Diagram) which enables the tool to handle models with very large state space. This paper describes an extension of CASPA’s solving engine for path-based approximation of MTTFF (Mean Time To Fi...

We present a new approach for motion planning and maintainability studies in complex 3D CAD environments. It automatically computes a collision-free path for moving objects among stationary and completely known obstacles. Our framework uses a combination of analytic, criticalitybased and probabilistic techniques to compute the path. It starts with an global strategy, which uses an approximate V...

It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given...

This paper analyzes the patterns of the Monte Carlo data for a large number of variables and minterms, in order to characterize the circuit path length behavior. We propose models that are determined by training process of shortest path length derived from a wide range of binary decision diagram (BDD) simulations. The creation of the model was done use of feed forward neural network (NN) modeli...

A large variety of problems in digital system design, combinational optimization and verification can be formulated in terms of operations performed on Boolean functions. The time complexity of Binary Decision Diagram (BDD) representing a Boolean function is directly related to the path length of that BDD. In this paper we present a method to generate a BDD with minimum path length. The Average...