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Discrete Sibson interpolation

S.W. Park, L. Linsen, O. Kreylos, J.D. Owens, B. Hamann
2006 IEEE Transactions on Visualization and Computer Graphics  
platform to scholars worldwide. a Voronoi diagram of all data points.  ...  Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional  ...  s method of generating discrete Voronoi diagrams.  ... 
doi:10.1109/tvcg.2006.27 pmid:16509383 fatcat:axbd4w2crvckrn6gasjswxb3di

Star-shaped metrics for mechanical metamaterial design

Jonàs Martínez, Mélina Skouras, Christian Schumacher, Samuel Hornus, Sylvain Lefebvre, Bernhard Thomaszewski
2019 ACM Transactions on Graphics  
We present a method for designing mechanical metamaterials based on the novel concept of Voronoi diagrams induced by star-shaped metrics.  ...  Our method generates a smoothly-graded pattern (a) when interpolating between three star-shaped distance functions (b) on a regular honeycomb lattice.  ...  Metric interpolation is performed by linearly blending between the parameter values of the two metrics. of Voronoi diagrams over triangular lattices are the same as those of Voronoi diagrams over honeycomb  ... 
doi:10.1145/3306346.3322989 fatcat:tuyzpoupz5bjdllj7vzkfmt4ym

An Interpolant Based on Line Segment Voronoi Diagrams [chapter]

Hisamoto Hiyoshi, Kokichi Sugihara
2000 Lecture Notes in Computer Science  
This paper considers the interpolation for multi-dimensional data using  ...  Acknowledgement This work is supported by the Grant-in-Aid for Scienti c Research of the Japanese Ministry of Education, Science, Sports and Culture.  ...  Recently, the authors studied another interpolant using Voronoi diagrams when G consists of n points in R 2 3,7 .  ... 
doi:10.1007/978-3-540-46515-7_10 fatcat:lj3hb3uhl5bk3n4hzluwooryum

Vector Interpolation on Natural Element Method

Diego Pereira Botelho, Yves Marechal, Brahim Ramdane
2016 IEEE transactions on magnetics  
However, in the meshless methods context, the construction of vector shape functions is not direct and very little work has been published on vector interpolation.  ...  This work is a first proposal of a NEM-based vector interpolation for polygonal cells. Fundamental results of the developed approach are demonstrated.  ...  NATURAL ELEMENT METHOD The natural element method makes use of the Voronoï diagram for the construction of its shape functions.  ... 
doi:10.1109/tmag.2015.2496422 fatcat:wutfkxe76rdqpmndzpqedg4cqm

Potential of Voronoi Diagram for the Conserved Remapping of Precipitation

Ki-Hwan Kim, Eun-Hee Lee, Song-You Hong
2018 Monthly Weather Review  
This study considers a remapping algorithm between irregularly distributed observations and grid points based on Voronoi diagrams and examines its potential for verification of precipitation forecasts.  ...  It is also shown that different interpolation methods have an impact on verification results of precipitation forecast from a numerical weather prediction model against station observations.  ...  This work has been carried out through the R&D project on the development of global numerical weather prediction systems of the Korea Institute of Atmospheric Prediction Systems (KIAPS), funded by the  ... 
doi:10.1175/mwr-d-17-0350.1 fatcat:rpwtl2b7cfgn5lhdj5uj5wnjjq

Constructing natural neighbor interpolation based grid DEM using CUDA

Simin You, Jianting Zhang
2012 Proceedings of the 3rd International Conference on Computing for Geospatial Research and Applications - COM.Geo '12  
In this study, we present a set of General Purpose computing Graphics Processing Unit(GPGPU) based algorithms that can significant speed up the process.  ...  Natural Neighbor Interpolation (NNI) is a popular approach to DEM construction from point datasets but is computationally intensive.  ...  Compared to Ter-raNNI, our approach is nearly an order faster in generating Voronoi diagrams and nearly two orders better in constructing grid DEMs.  ... 
doi:10.1145/2345316.2345349 dblp:conf/comgeo/YouZ12 fatcat:s33ibpzdy5cizpj4swopp6wlpy

Surface modelling with guaranteed consistency — An object-based approach [chapter]

Christopher M. Gold, Thomas Roos
1994 Lecture Notes in Computer Science  
We describe here an object-otiented approach, in the sense that the data objects themselves form the spatial structure used for interpolation.  ...  The methods described here use the Voronoi diagram to generate surfaces which pass precisely through all data objects (points and line segments) and have no inadvertent surface or slope discontinuities  ...  Acknowledgements This research was made possible by the foundation of an Industrial Research Chair in Geomatics at Lava1 University, jointly funded by the Natural Sciences and Engineering Research Council  ... 
doi:10.1007/3-540-58795-0_36 fatcat:oj6jtpa6hbez3kmeo3zwwomucq

Adaptive Refinement based Integral Method for Load Transfer in Fluid/Structure Interaction Problems

Pan Cheng, Zekai Ding, Wu Zhang
2019 IOP Conference Series: Materials Science and Engineering  
Generally speaking, two classes of methods have been developed and applied in engineering: point wise interpolation and mapping method.  ...  In fluid-structure interaction simulations using a partitioned approach, especially aeroelastic analysis, each physics component solves on its own mesh, and the interface between these meshes are in general  ...  The newly created surface mesh is an approximation of Voronoi diagram.  ... 
doi:10.1088/1757-899x/685/1/012011 fatcat:edej2bftpjdyvcuktlekpwjeeq

Variable Resolution Spatial Interpolation Using the Simple Recursive Point Voronoi Diagram

Robert Feick, Barry Boots
2005 Geographical Analysis  
The procedure uses the Simple Recursive Point Voronoi Diagram in which Voronoi concepts are used to tessellate space with respect to a given set of generator points.  ...  This paper introduces a procedure for progressively increasing the density of an initial point set that can be used as a basis for interpolating surfaces of variable resolution from sparse samples of data  ...  Simple Recursive Voronoi Point Diagram (SRVPD) In this paper we consider a specific form of recursive Voronoi diagram, the simple recursive point Voronoi diagram (SRPVD), in which the initial set of generators  ... 
doi:10.1111/j.1538-4632.2005.00637.x fatcat:damxcepmlrduhdtop64ycb7vrq

Resampling of data between arbitrary grids using convolution interpolation

V. Rasche, R. Proksa, R. Sinkus, P. Bornert, H. Eggers
1999 IEEE Transactions on Medical Imaging  
The volume of the Voronoi cell around each sample is used as a measure for the sampling density.  ...  In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another. The basic algorithm can be split into two steps.  ...  The Voronoi diagrams were calculated using the QHULL software package distributed by the Geometry Center, University of Minnesota. 1 QHULL generates the Voronoi diagram with an expected performance of  ... 
doi:10.1109/42.774166 pmid:10416800 fatcat:ob7fklpzmvaivmmhsqcsnbnwoa

DIGITAL ELEVATION MODEL APPROXIMATION FROM STREAM NETWORKS: A REVERSED APPROACH

M. Ghandehari
2013 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
Then, a Delaunay triangulation and Voronoi diagram are used to extract the skeleton (medial axis) of stream networks as an approximation of the catchment areas.  ...  In this article, an innovative reversed approach for the approximation of DEMs from stream networks is presented.  ...  The properties of NN interpolation method make it a good approach for irregularly distributed data; it generates a well-defined set of neighbors (by the use of a Voronoi diagram), and employs a well-behaved  ... 
doi:10.5194/isprsarchives-xl-1-w3-175-2013 fatcat:7pw2o5rqgbexvb5utci4rke4xe

A new extension of the natural element method for non-convex and discontinuous problems: the constrained natural element method(C-NEM)

J. Yvonnet, D. Ryckelynck, P. Lorong, F. Chinesta
2004 International Journal for Numerical Methods in Engineering  
The computation of these shape functions is based on a modified, constrained Voronoi diagram.  ...  Two numerical examples in elastostatics are reported to evaluate the potential of the proposed technique in highly non-convex geometries, like a crack, through which the solution becomes discontinuous.  ...  In Figure 7 (a), an example of the computation of a natural shape function making use of the standard Voronoi diagram is presented.  ... 
doi:10.1002/nme.1016 fatcat:xtsr5mmqw5hsno6dqcxoolpwvq

Voronoi diagram based optimization of dynamic reactive power sources

Weihong Huang, Kai Sun, Junjian Qi, Yan Xu
2015 2015 IEEE Power & Energy Society General Meeting  
This paper proposes a new approach to optimization of the sizes of dynamic var sources at candidate locations by a Voronoi diagram based algorithm.  ...  It first disperses sample points of potential solutions in a searching space, evaluates a cost function at each point by barycentric interpolation for the subspaces around the point, and then constructs  ...  Voronoi diagram [6] is one of the most useful data structures in computational geometry and an effective technique for generating contour map.  ... 
doi:10.1109/pesgm.2015.7286263 fatcat:4tjj2wgq4bgm7hbiqwynywidra

Interpolation-Based Reconstruction Methods for Tomographic Imaging in 3D Positron Emission Tomography

Yingbo Li, Anton Kummert, Fritz Boschen, Hans Herzog
2008 International Journal of Applied Mathematics and Computer Science  
In this respect, the geometrical structure named the Voronoi diagram and its computational construction are considered. At the end, results of performed simulation studies are presented and discussed.  ...  In the present paper, two distinct approaches to the realization of the interpolating procedure are proposed and analyzed.  ...  Fig. 6 . 6 Illustration of the interpolating procedure in all transverse planes. Fig. 8 . 8 Schematic illustration of an exemplary Voronoi diagram.  ... 
doi:10.2478/v10006-008-0006-y fatcat:ls2trjz3j5ayvog7apcagz65ie

Interactive Position-dependent Customization of Transfer Function Classification Parameters in Volume Rendering [article]

Tobias Brix, Aaron Scherzinger, Andreas Völker, Klaus Hinrichs
2015 Eurographics Workshop on Visual Computing for Biomedicine  
In direct volume rendering (DVR) and related techniques a basic operation is the classification of data values by mapping (mostly scalar) intensities to color values using a transfer function.  ...  In this paper we propose a novel approach for an interactive position-dependent customization of arbitrary parameters of the transfer function classification.  ...  Acknowledgments We would like to thank the research group of Friedemann Kiefer at the Max-Planck-Institut in Münster for providing us the biological data sets and Christoph Schülke at the Department of  ... 
doi:10.2312/vcbm.20151211 dblp:conf/vcbm/BrixSVH15 fatcat:hoercxnxwzarbh24x7sdtodxee
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