Delaunay triangulation

About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.

Efficient triangulation-based pathfinding

Abstract: In this paper we present a method for abstracting an environment represented using constrained Delaunay triangulations in a way that significantly reduces pathfinding search effort, as well as better representing the basic structure of the environment. The techniques shown here are ideal for objects of varying sizes and environments that are not axis-aligned or that contain many dead-ends, long corridors, or jagged walls that complicate other search techniques. In fact, the abstraction simplifies pathfinding to deciding to which side of each obstacle to go. This technique is suited to real-time computation both because of its speed and because it lends itself to an anytime algorithm, allowing it to work when varying amounts of resources are assigned to pathfinding. We test search algorithms running on both the base triangulation (Triangulation A* - TA*) and our abstraction (Triangulation Reduction A* - TRA*) against A* and PRA* on grid-based maps from the commercial games Baldur's Gate and WarCraft III. We find that in these cases almost all paths are found much faster using TA*, and more so using TRA*.

On optimal interpolation triangle incidences

Abstract: The problem of determining optimal incidences for triangulating a given set of vertices for the model problem of interpolating a convex quadratic surface by piecewise linear functions is studied An exact expression for the maximum error is derived, and the optimality criterion is minimization of the maximum error The optimal incidences are shown to be derivable from an associated Delaunay triangulation and hence are computable in $O(N\log N)$ time for N vertices

Coverage Optimization and Spatial Load Balancing by Robotic Sensor Networks

Abstract: This technical note studies robotic sensor networks performing static coverage optimization with area constraints. Given a density function describing the probability of events happening and a performance function measuring the cost to service a location, the objective is to position sensors in the environment so as to minimize the expected servicing cost. Moreover, because of load balancing considerations, the area of the region assigned to each robot is constrained to be a pre-specified amount. We characterize the optimal configurations as center generalized Voronoi configurations. The generalized Voronoi partition depends on a set of weights, one per robot, assigned to the network. We design a Jacobi iterative algorithm to find the weight assignment whose corresponding generalized Voronoi partition satisfies the area constraints. This algorithm is distributed over the generalized Delaunay graph. We also design the ?move-to-center-and-compute-weight? strategy to steer the robotic network towards the set of center generalized Voronoi configurations while monotonically optimizing coverage.