Primitives for the manipulation of general subdivisions and the computation of Voronoi

Guibas, Leonidas J.; Stolfi, Jorge

doi:10.1145/282918.282923

Cited by 1,009 publications

(143 citation statements)

References 4 publications

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“…Algorithms for computing the Delaunay triangulation of a point set include flipping, plane sweep, divide-and-conquer [10,11] in 2D space, in addition to, incremental and gift-wrapping [12] in 2D plus 3D space. For more details, readers are referred to citation [9].…”

Section: Explicit Methodsmentioning

confidence: 99%

Survey on 3D Surface Reconstruction

2016

J Inf Process Syst

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The recent advent of increasingly affordable and powerful 3D scanning devices capable of capturing high resolution range data about real-world objects and environments has fueled research into effective 3D surface reconstruction techniques for rendering the raw point cloud data produced by many of these devices into a form that would make it usable in a variety of application domains. This paper, therefore, provides an overview of the existing literature on surface reconstruction from 3D point clouds. It explains some of the basic surface reconstruction concepts, describes the various factors used to evaluate surface reconstruction methods, highlights some commonly encountered issues in dealing with the raw 3D point cloud data and delineates the tradeoffs between data resolution/accuracy and processing speed. It also categorizes the various techniques for this task and briefly analyzes their empirical evaluation results demarcating their advantages and disadvantages. The paper concludes with a cross-comparison of methods which have been evaluated on the same benchmark data sets along with a discussion of the overall trends reported in the literature. The objective is to provide an overview of the state of the art on surface reconstruction from point cloud data in order to facilitate and inspire further research in this area.

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Section: Explicit Methodsmentioning

confidence: 99%

Survey on 3D Surface Reconstruction

2016

J Inf Process Syst

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“…In general, algorithms exist for meshing two-and three-dimensional domains in O(n log n) time with O(n) space for an n element mesh. In two dimensions, these algorithms are the Delauney triangulation via plane sweep and divide-andconquer (Fortune, 1987;Guibas and Stolfi, 1985). For three-dimensional domains, octree, advancing front, and Delauney techniques are available (Shephard and Georges, 1991;Löhner and Parikh, 1988;Watson, 1981).…”

Section: Profilingmentioning

confidence: 99%

Addressing the computational cost of large EIT solutions

2012

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Abstract. Electrical Impedance Tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a FEM mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations.An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations, and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources.This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two-and threedimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

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“…Concerning its complexity, Delaunay triangulation can be computed in O(|V |log(|V |)) time [6,12,20]. The scanline algorithm can be implemented to find all the overlaps in O(l|V |(log|V | + l)) time [3], where l is the number of overlaps.…”

Section: A Proximity Stress Model For Node Overlap Removalmentioning

confidence: 99%

Efficient Node Overlap Removal Using a Proximity Stress Model

Gansner

2009

Graph Drawing

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Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a post-processing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using little additional area. This paper presents a new node overlap removal algorithm that does well by these measures.

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Primitives for the manipulation of general subdivisions and the computation of Voronoi

Cited by 1,009 publications

References 4 publications

Survey on 3D Surface Reconstruction

Survey on 3D Surface Reconstruction

Addressing the computational cost of large EIT solutions

Efficient Node Overlap Removal Using a Proximity Stress Model

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