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.

Cartoon image vectorization based on shape subdivision

Abstract: This paper presents a non-pixel-based skeletonization method for vectorizing cartoon images. The constrained Delaunay triangulation technique is applied to subdivide a shape into a set of non-overlapping triangles. Then, certain triangles in the triangulation are merged to remove artifacts. The skeleton of a shape is obtained from the skeletons of its constituent parts. Experimental results show that the proposed method is more accurate and efficient than a typical thinning method.

Direct isosurface extraction from scattered volume data

Abstract: Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction over a structured grid. We propose a method based on spatial domain partitioning using a kd-tree and an indexing scheme for efficient neighbor search. Our approach consists of a geometry extraction and a rendering step. The geometry extraction step computes points on the isosurface by linearly interpolating between neighboring pairs of samples. The neighbor information is retrieved by partitioning the 3D domain into cells using a kd-tree. The cells are merely described by their index and bitwise index operations allow for a fast determination of potential neighbors. We use an angle criterion to select appropriate neighbors from the small set of candidates. The output of the geometry step is a point cloud representation of the isosurface. The final rendering step uses point-based rendering techniques to visualize the point cloud. Our direct isosurface extraction algorithm for scattered volume data produces results of quality close to the results from standard isosurface extraction algorithms for gridded volume data (like marching cubes). In comparison to 3D mesh generation algorithms (like Delaunay tetrahedrization), our algorithm is about one order of magnitude faster for the examples used in this paper.

A centroid-based sampling strategy for kriging global modeling and optimization

Abstract: A new sampling strategy is presented for kriging-based global modeling. The strategy is used within a kriging/response surface (RSM) algorithm for solving NLP containing black-box models. Black-box models describe systems lacking the closed-form equations necessary for conventional gradient-based optimization. System optima can be alternatively found by building iteratively updated kriging models, and then refining local solutions using RSM. The application of the new sampling strategy results in accurate global model generation at lower sampling expense relative to a strategy using randomized and heuristic-based sampling for initial and subsequent model construction, respectively. The new strategy relies on construction of an initial kriging model built using sampling data obtained at the feasible region's convex polytope vertices and centroid. Updated models are constructed using additional sampling information obtained at Delaunay triangulation centroids. The new sampling algorithm is applied within the kriging-RSM framework to several numerical examples and case studies to demonstrate proof of concept. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Optimization for first order Delaunay triangulations

Abstract: This paper discusses optimization of quality measures over first order Delaunay triangulations. Unlike most previous work, our measures relate to edge-adjacent or vertex-adjacent triangles instead of only to single triangles. We give efficient algorithms to optimize certain measures, including measures related to the area ratio of adjacent triangles, angle between outward normals of adjacent triangles (for polyhedral terrains), and number of convex vertices. Some other measures are shown to be NP-hard. These include maximum vertex degree, number of convex edges, and number of mixed vertices. For the latter two measures we provide, for any constant @e>0, factor ([email protected]) approximation algorithms that run in 2^O^(^1^/^@e^)@?n and 2^O^(^1^/^@e^^^2^)@?n time (when the Delaunay triangulation is given). For minimizing the maximum vertex degree, the NP-hardness proof provides an inapproximability result. Our results are presented for the class of first order Delaunay triangulations, but also apply to triangulations where for every triangle at least two edges are fixed. The approximation result on maximizing the number of convex edges is also extended to k-th order Delaunay triangulations.

EDTD-SC: An IoT Sensor Deployment Strategy for Smart Cities

Abstract: A smart city is a geographical area that uses modern technologies to facilitate the lives of its residents. Wireless sensor networks (WSNs) are important components of smart cities. Deploying IoT sensors in WSNs is a challenging aspect of network design. Sensor deployment is performed to achieve objectives like increasing coverage, strengthening connectivity, improving robustness, or increasing the lifetime of a given WSN. Therefore, a sensor deployment method must be carefully designed to achieve such objective functions without exceeding the available budget. This study introduces a novel deployment algorithm, called the Evaluated Delaunay Triangulation-based Deployment for Smart Cities (EDTD-SC), which targets not only sensor distribution, but also sink placement. Our algorithm utilizes Delaunay triangulation and k-means clustering to find optimal locations to improve coverage while maintaining connectivity and robustness with obstacles existence in sensing area. The EDTD-SC has been applied to real-world areas and cities, such as Midtown Manhattan in New York in the United States of America. The results show that the EDTD-SC outperforms random and regular deployments in terms of area coverage and end-to-end-delay by 29.6% and 29.7%, respectively. Further, it exhibits significant performance in terms of resilience to attacks.