A Fast Robust Algorithm for Computing Discrete Voronoi Diagrams

Velic, Mirko; May, David A.; Moresi, Louis

doi:10.1007/s10852-008-9097-6

Cited by 16 publications

(16 citation statements)

References 14 publications

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“…The numerical implementation is the particle-in-cell finite element code Underworld in which material properties are carried by Lagrangian integration points and mapped to element properties through a local, discrete Voronoi, integration scheme (Veli c et al, 2008). Models are confined to a 3D Cartesian domain (Fig.…”

Section: Model Descriptionmentioning

confidence: 99%

Geodynamics of oceanic plateau and plume head accretion and their role in Phanerozoic orogenic systems of China

Betts

Moresi

Miller

et al. 2015

Geoscience Frontiers

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a b s t r a c tWe present three 3D numerical models of deep subduction where buoyant material from an oceanic plateau and a plume interact with the overriding plate to assess the influence on subduction dynamics, trench geometry, and mechanisms for plateau accretion and continental growth. Transient instabilities of the convergent margin are produced, resulting in: contorted trench geometry; trench migration parallel with the plate margin; folding of the subducting slab and orocline development at the convergent margin; and transfer of the plateau to the overriding plate. The presence of plume material beneath the oceanic plateau causes flat subduction above the plume, resulting in a "bowed" shaped subducting slab. In plateau-only models, plateau accretion at the edge of the overriding plate results in trench migration around the edge of the plateau before subduction is re-established directly behind the trailing edge of the plateau. The plateau shortens and some plateau material subducts. The presence of buoyant plume material beneath the oceanic plateau has a profound influence on the behaviour of the convergent margin. In the plateau þ plume model, plateau accretion causes rapid trench advance. Plate convergence is accommodated by shearing at the base of the plateau and shortening in the overriding plate. The trench migrates around the edge of the plateau and subduction is re-established well behind the trailing edge of the plateau, effectively embedding the plateau into the overriding plate. A slab window forms beneath the accreted plateau and plume material is transferred from the subducting plate to the overriding plate through the window. In all of the models, the subduction zone maintains a relatively stable configuration away from the buoyancy anomalies within the downgoing plate. The models provide a dynamic context for plateau and plume accretion in Phanerozoic accretionary orogenic systems such as the East China Orogen and the Central Asian Orogen (Altiads), which are characterised by accreted ophiolite complexes with diverse geochemical affinities, and a protracted evolution of accretion of exotic terranes including oceanic plateau and terranes with plume origins.

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Section: Model Descriptionmentioning

confidence: 99%

Geodynamics of oceanic plateau and plume head accretion and their role in Phanerozoic orogenic systems of China

Betts

Moresi

Miller

et al. 2015

Geoscience Frontiers

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“…In comparing pAVD with the algorithm of Velić et al [2008], we observe the new algorithm uses ∼6 times less memory when n p < M (“high resolution” Voronoi cell limit), and 3.6 times less when n p ∼ M (“low resolution” Voronoi cell limit). CPU times reveal pAVD is 4.3 times faster in the “high resolution limit” and ∼1.6 times faster in the “low resolution limit”.…”

Section: Examplesmentioning

confidence: 98%

“…To alleviate the practical and technical implementation challenges exact Voronoi diagrams pose, numerous algorithms to compute Approximate Voronoi Diagrams (AVDs) have been developed [ Lavender et al , 1992; Vleugels and Overmars , 1995; Vleugels et al , 1996; Teichmann and Teller , 1997; Hoff et al , 2000; Rong and Tan , 2006; Velić et al , 2008]. Examples of approximate Voronoi diagrams computed using different grid resolutions are shown in Figure 4.…”

Section: Approximate Voronoi Diagrams: From Points To Volumesmentioning

confidence: 99%

“…To access the competitiveness of the pAVD implementation, we provide CPU time and memory usage comparisons of our algorithm with several exact Voronoi diagram implementations; Voro++ [ Rycroft , 2009], Qhull [ Barber et al , 1996] and the CPU based approximate Voronoi algorithm ffbcAVD [ Velić et al , 2008]. These results are summarized in Tables 3 and 4.…”

Section: Examplesmentioning

confidence: 99%

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Volume reconstruction of point cloud data sets derived from computational geodynamic simulations

May¹

2012

Geochem Geophys Geosyst

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[1] One of the most widely used numerical modeling techniques in geodynamics to study the evolution of geomaterials is the "marker-and-cell" technique. In such methods the material lithology is represented by Lagrangian particles (markers), while the continuum equations are solved on a background mesh. Significant research has been devoted to improving the efficiency and scalability of these numerical methods to enable high-resolution simulations to be performed on modest computational resources. In contrast, little attention has been given to developing visualization techniques suitable for interrogation high-resolution 3D particle data sets. We describe an efficient algorithm for performing a volume reconstruction of the lithology field defined via particles (code available upon request from the author). The algorithm generates an Approximate Voronoi Diagram (AVD) which transforms particle data sets into a cell-based, volumetric data set. The volumetric representation enables cross sections of the material configuration to be constructed efficiently and unambiguously, thereby enabling the interior material structure of the simulation results to be analyzed. Examples from geodynamic simulations are used to demonstrate visual results possible using this visualization technique. Performance comparisons are made between existing implementations of exact and approximate Voronoi diagrams. Overall, the AVD developed herein is found to be extremely competitive as a visualizing tool for massive particle data sets as it is extremely efficient, has low memory requirements and can be trivially used in a distributed memory computing environment.

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“…In an analysis pipeline sequential processing modules obtain and pass on their input as ObjectLayer instances containing all objects and the respective features. Discrete Voronoi tessellation [24] on the object layers map is used to compute the topological relationships. These are represented in an ObjectNetwork class which contains the ObjectNeighbourhood for each object.…”

Section: Introductionmentioning

confidence: 99%

CognitionMaster: an object-based image analysis framework

Wienert

Heim²,

Kotani

et al. 2013

Diagn Pathol

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BackgroundAutomated image analysis methods are becoming more and more important to extract and quantify image features in microscopy-based biomedical studies and several commercial or open-source tools are available. However, most of the approaches rely on pixel-wise operations, a concept that has limitations when high-level object features and relationships between objects are studied and if user-interactivity on the object-level is desired.ResultsIn this paper we present an open-source software that facilitates the analysis of content features and object relationships by using objects as basic processing unit instead of individual pixels. Our approach enables also users without programming knowledge to compose “analysis pipelines“ that exploit the object-level approach. We demonstrate the design and use of example pipelines for the immunohistochemistry-based cell proliferation quantification in breast cancer and two-photon fluorescence microscopy data about bone-osteoclast interaction, which underline the advantages of the object-based concept.ConclusionsWe introduce an open source software system that offers object-based image analysis. The object-based concept allows for a straight-forward development of object-related interactive or fully automated image analysis solutions. The presented software may therefore serve as a basis for various applications in the field of digital image analysis.

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A Fast Robust Algorithm for Computing Discrete Voronoi Diagrams

Cited by 16 publications

References 14 publications

Geodynamics of oceanic plateau and plume head accretion and their role in Phanerozoic orogenic systems of China

Geodynamics of oceanic plateau and plume head accretion and their role in Phanerozoic orogenic systems of China

Volume reconstruction of point cloud data sets derived from computational geodynamic simulations

CognitionMaster: an object-based image analysis framework

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