Efficiently Navigating a Random Delaunay Triangulation

International audiencePlanar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. Whilst many algorithms have been proposed, very little theoretical analysis is available for the properties of the paths generated or the computational resources required to generate them. In this work, we propose and analyse a new planar navigation algorithm for the Delaunay triangulation. We then demonstrate a number of strong theoretical guarantees for the algorithm when it is applied to a random set of points in a convex region

TetGen, towards a quality tetrahedral mesh generator

TetGen is a C++ program for generating quality tetrahedral meshes aimed to support numerical methods and scientific computing. It is also a research project for studying the underlying mathematical problems and evaluating algorithms. This paper presents the essential meshing components developed in TetGen for robust and efficient software implementation. And it highlights the state-of-the-art algorithms and technologies currently implemented and developed in TetGen for automatic quality tetrahedral mesh generation

Movement around real and virtual cluttered environments

Two experiments investigated participants’ ability to search for targets in a cluttered small-scale space. The first experiment was conducted in the real world with two field of view conditions (full vs. restricted), and participants found the task trivial to perform in both. The second experiment used the same search task but was conducted in a desktop virtual environment (VE), and investigated two movement interfaces and two visual scene conditions. Participants restricted to forward only movement performed the search task quicker and more efficiently (visiting fewer targets) than those who used an interface that allowed more flexible movement (forward, backward, left, right, and diagonal). Also, participants using a high fidelity visual scene performed the task significantly quicker and more efficiently than those who used a low fidelity scene. The performance differences between all the conditions decreased with practice, but the performance of the best VE group approached that of the real-world participants. These results indicate the importance of using high fidelity scenes in VEs, and suggest that the use of a simple control system is sufficient for maintaining ones spatial orientation during searching

Movement around real and virtual cluttered environments

Two experiments investigated participants’ ability to search for targets in a cluttered small-scale space. The first experiment was conducted in the real world with two field of view conditions (full vs. restricted), and participants found the task trivial to perform in both. The second experiment used the same search task but was conducted in a desktop virtual environment (VE), and investigated two movement interfaces and two visual scene conditions. Participants restricted to forward only movement performed the search task quicker and more efficiently (visiting fewer targets) than those who used an interface that allowed more flexible movement (forward, backward, left, right, and diagonal). Also, participants using a high fidelity visual scene performed the task significantly quicker and more efficiently than those who used a low fidelity scene. The performance differences between all the conditions decreased with practice, but the performance of the best VE group approached that of the real-world participants. These results indicate the importance of using high fidelity scenes in VEs, and suggest that the use of a simple control system is sufficient for maintaining ones spatial orientation during searching

Timely Near-Optimal Path Generation for an Unmanned Aerial System in a Highly Constrained Environment

A current challenge in path planning is the ability to efficiently calculate a near-optimum path solution through a highly-constrained environment in near-real time. In addition, computing performance on a small unmanned aerial vehicle is typically limited due to size and weight restrictions. The proposed method determines a solution quickly by first mapping a highly constrained three-dimensional environment to a two-dimensional weighted node surface in which the weighting accounts for both the terrain gradient and the vehicle\u27s performance. The 2D surface is then discretized into triangles which are sized based upon the vehicle maneuverability and terrain gradient. The shortest feasible path between the nodes of the two-dimensional triangulated surface is determined using an A* algorithm. An optimal path is then chosen through the unconstrained corridor to yield a quick near-optimal path solution in three-dimensional space. This technique requires prior knowledge of the terrain map and vehicle performance. The cost to traverse each segment of the map is independent of the starting position on the map and can be pre-calculated once the goal position is known. The proposed method allows for a rapid path solution from any start position to a goal position while satisfying all constraints. It was shown that employing the methodology herein resulted in near-optimal solutions in less than a couple seconds for the scenarios tested. The future work section proposes methods for improving the algorithms efficiency even further