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.

Energy Efficient Coverage with Variable Sensing Radii in Wireless Sensor Networks

Abstract: Wireless sensor networks (WSN) consist of spatially distributed autonomous devices using sensors to cooperatively monitor physical or environmental conditions. Generally, sensor nodes are resource-constraint in terms of size, power and bandwidth, therefore energy-efficient design becomes one of the fundamental goals in WSN. To provide reliable service in surveillance as well as energy efficiency, significant attention has recently been devoted to dynamic coverage algorithms based on sensors which are capable of adjusting its transmission and sensing range. In this paper, we propose two local sensing radii optimization schemes based on one-hop approximation of Delaunay Triangulation to minimize the energy consumption and extend the lifetime of networks. Furthermore, we prove that our approximation of Delaunay triangulation guarantees complete coverage and generates the same radii assignment as traditional Delaunay triangulation. Our ns-2 based simulation shows performance improvements in many aspects such as coverage ratio, sensing energy consumption, node failure rate, and lifetime of networks.

Delaunay Meshing of Piecewise Smooth Complexes without Expensive Predicates

Abstract: Recently a Delaunay refinement algorithm has been proposed that can mesh piecewise smooth complexes which include polyhedra, smooth and piecewise smooth surfaces, and non-manifolds. However, this algorithm employs domain dependent numerical predicates, some of which could be computationally expensive and hard to implement. In this paper we develop a refinement strategy that eliminates these complicated domain dependent predicates. As a result we obtain a meshing algorithm that is practical and implementation-friendly.

Modelling three-dimensional fields in geoscience with the Voronoi diagram and its dual

Abstract: The objects studied in geoscience are often not man-made objects, but rather the spatial distribution of three-dimensional continuous geographical phenomena such as the salinity of a body of water, the humidity of the air or the percentage of gold in the rock (phenomena that tend to change over time). These are referred to as fields, and their modelling with geographical information systems is problematic because the structures of these systems are usually twodimensional and static. Raster structures (voxels or octrees) are the most popular solutions, but, as I argue in this thesis, they have several shortcomings for geoscientific fields. As an alternative to using rasters for representing and modelling three-dimensional fields, I propose using a new spatial model based the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT). I argue that constructing the VD/DT of the samples that were collected to study the field can be beneficial for extracting meaningful information from it. Firstly, the tessellation of space obtained with the VD gives a clear and consistent definition of neighbourhood for unconnected points in three dimensions, which is useful since geoscientific datasets often have highly anisotropic distributions. Secondly, the efficient and robust reconstruction of the field can be obtained with natural neighbour interpolation, which is entirely based on the properties of the VD. Thirdly, the tessellations of the VD and the DT make possible, and even optimise, several spatial analysis and visualisation operations. A further important consideration is that the VD/DT is locally modifiable (insertion, deletion and movement of points), which permits us to model the temporal dimension, and also to interactively explore a dataset, thus gaining insight by observing on the fly the consequences of manipulations and spatial analysis operations. In this thesis, the development of this new spatial model is from an algorithmic point of view, i.e. I describe in details algorithms to construct, manipulate, analyse and visualise fields represented with the VD/DT. A strong emphasis is put on the implementation of the spatial model, and, for this reason, the many degeneracies that arise in three-dimensional geometric computing are described and handled. A new data structure, the augmented quad-edge, is also presented. It permits us to store simultaneously both the VD and the DT, and helps in the analysis of fields. Finally, the usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications in geoscience.

The impact of different gridding methods on catchment geomorphology and soil erosion over long timescales using a landscape evolution model

Abstract: Many digital elevation models are gridded from irregularly spaced data. This study examines differences in catchment geomorphology and hydrology as a result of kriging and Delaunay triangulation gridding methods. Both methods have been widely used as tools for placing irregularly spaced data onto a regular grid. In the past, numerical modelling has been performed with little assessment of model input variability and the variability produced by different gridding methods has not been fully assessed. Given the importance of the impact of digital elevation model error and potential impact on model output, little work has been done to understand the impact of this type of potential error. Examination of the different catchment realizations demonstrates that when using kriging (point or block) or Delaunay triangulation there are subtle differences in catchment area and elevation as well as networking properties. Subtle differences also exist in hillslope profile. Nevertheless, when comparing catchment descriptors such as the hypsometric curve, area–slope relationship and cumulative area distribution there is little hydrological and geomorphological difference between these catchments. Further, when these digital elevation models are used as landscape input in a long-term landscape evolution model (i.e. SIBERIA) there is little geomorphological difference or hydrological difference between the two digital elevation models after a 50 000 year modelled period. Consequently either method is appropriate for the study catchment. These findings provide confidence in the conversion of irregularly spaced data onto a regular grid using kriging or Delaunay triangulation and that either method can be used. Copyright © 2006 John Wiley & Sons, Ltd.

Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual

Abstract: Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often three-dimensional (3D), they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly anisotropic distributions of samples. In the geographical information system (GIS) community, raster structures (voxels or octrees) are the most popular solutions, but, as we show in this paper, they have shortcomings for modelling and analysing 3D geoscientific fields. As an alternative to using rasters, we propose a new spatial model based on the Voronoi diagram (VD) and its dual the Delaunay tetrahedralisation (DT), and argue that they have many advantages over other tessellations. We discuss the main properties of the 3D VD/DT, present some GIS operations that are greatly simplified when the VD/DT is used, and, to analyse two or more fields, we also present a variant of the map algebra framework where all the operations are performed directly on VDs. The usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications.