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On a construction of a hierarchy of best linear spline approximations using a finite element approach

D.F. Wiley, B. Hamann, M. Bertram
2004 IEEE Transactions on Visualization and Computer Graphics  
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doi:10.1109/tvcg.2004.29 pmid:15794137 fatcat:jcdndufpizbr7mihjfunwgbl34

Best Quadratic Spline Approximation for Hierarchical Visualization [article]

D. F. Wiley, H. R. Childs, B. Hamann, K. I. Joy, N. L. Max
2002 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
We use quadratic basis functions and compute best quadratic simplicial spline approximations that are C0-continuous everywhere.  ...  We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation.  ...  Acknowledgements This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.  ... 
doi:10.2312/vissym/vissym02/133-140 fatcat:am5czuz3mzbstbagqh33eucnne

Hierarchical Spline Approximations [chapter]

David F. Wiley, Martin Bertram, Benjamin W. Jordan, Bernd Hamann, Kenneth I. Joy, Nelson L. Max, Gerik Scheuermann
2003 Mathematics and Visualization  
We first describe a best linear spline approximation scheme, understood in a least squares sense, and refine on initial mesh using repeated bisection of simplices (intervals, triangles, or tetrahedra)  ...  The enhancements we discuss are: (i) using a finite element approach that only considers original data sites during subdivision, (ii) including first-derivative information in the error functional and  ...  Acknowledgements This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.  ... 
doi:10.1007/978-3-642-55787-3_5 fatcat:z5qitzxwgjgtzmqg2looyvpzqq

Using quadratic simplicial elements for hierarchical approximation and visualization

David F. Wiley, Henry R. Childs, Bernd Hamann, Kenneth I. Joy, Nelson Max, Robert F. Erbacher, Philip C. Chen, Matti Groehn, Jonathan C. Roberts, Craig M. Wittenbrink
2002 Visualization and Data Analysis 2002  
Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.  ...  Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided.  ...  Our overall goal is the construction of a hierarchical data representation over 2D or 3D domains, using a bestapproximation approach based on curved quadratic finite elements and quadratic polynomials  ... 
doi:10.1117/12.458802 dblp:conf/vda/WileyCHJM02 fatcat:z2nm5zlbpbg7zhysnfmermyj7m

Elliptic grid generation techniques in the framework of isogeometric analysis applications

J. Hinz, M. Möller, C. Vuik
2018 Computer Aided Geometric Design  
One can use the same approach to find an approximation of the given contours to any desired accuracy, the only difference being that one should perform the projection over a set of elements on which both  ...  This approach makes sense whenever a structured representation of the geometry with linear elements is desired as in most finite-difference (FD) and structured finite-volume (FV) settings.  ... 
doi:10.1016/j.cagd.2018.03.023 fatcat:swj4bhwuwvbybptvq3ddfjegdu

Natural hierarchical refinement for finite element methods

Petr Krysl, Eitan Grinspun, Peter Schröder
2003 International Journal for Numerical Methods in Engineering  
key words: Finite element, mesh refinement, hierarchical, adaptive approximation, subdivision surface, subdivision element method SUMMARY Current formulations of adaptive finite element mesh refinement  ...  refinement concepts are not of much help, for instance on subdivision surfaces.  ...  Let us delimit, by a set of assumptions, the types of finite element approximations that we wish to consider.  ... 
doi:10.1002/nme.601 fatcat:4say4kjvxjemfelnihw5hljvgm

Metric-aware processing of spherical imagery

Michael Kazhdan, Hugues Hoppe
2010 ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10  
Our solution is to construct an adapted hierarchy of finite elements, adjusted at the poles to maintain derivative continuity, and selectively coarsened to bound element anisotropy.  ...  Our approach builds on the commonly used equirectangular parameterization, which provides differentiability, axial symmetry, and grid sampling.  ...  We also thank Jeremy Goldhaber-Fiebert for assistance with image capture and Greg Turk for publishing his implementation of reaction diffusion.  ... 
doi:10.1145/1866158.1866175 fatcat:zavsdmvd7ngfhbvkbvrkv4wl6e

Metric-aware processing of spherical imagery

Michael Kazhdan, Hugues Hoppe
2010 ACM SIGGRAPH Asia 2010 papers on - SIGGRAPH ASIA '10  
Our solution is to construct an adapted hierarchy of finite elements, adjusted at the poles to maintain derivative continuity, and selectively coarsened to bound element anisotropy.  ...  Our approach builds on the commonly used equirectangular parameterization, which provides differentiability, axial symmetry, and grid sampling.  ...  We also thank Jeremy Goldhaber-Fiebert for assistance with image capture and Greg Turk for publishing his implementation of reaction diffusion.  ... 
doi:10.1145/1882262.1866175 fatcat:ysuofp2rgnhxrewu4kqq4jrriy

Metric-aware processing of spherical imagery

Michael Kazhdan, Hugues Hoppe
2010 ACM Transactions on Graphics  
Our solution is to construct an adapted hierarchy of finite elements, adjusted at the poles to maintain derivative continuity, and selectively coarsened to bound element anisotropy.  ...  Our approach builds on the commonly used equirectangular parameterization, which provides differentiability, axial symmetry, and grid sampling.  ...  We also thank Jeremy Goldhaber-Fiebert for assistance with image capture and Greg Turk for publishing his implementation of reaction diffusion.  ... 
doi:10.1145/1882261.1866175 fatcat:or6qbyngojh75pcow4huskatum

Estimating the Laplace-Beltrami Operator by Restricting 3D Functions

Ming Chuang, Linjie Luo, Benedict J. Brown, Szymon Rusinkiewicz, Michael Kazhdan
2009 Computer graphics forum (Print)  
We present a novel approach for computing and solving the Poisson equation over the surface of a mesh.  ...  As in previous approaches, we define the Laplace-Beltrami operator by considering the derivatives of functions defined on the mesh.  ...  Differentiating a Normal Field One approach for computing the curvature is to solve for an approximate normal field by finding the linear combination of elements that best fits the sampled normals.  ... 
doi:10.1111/j.1467-8659.2009.01524.x fatcat:yndsyrw67rhirlhocahlbgoipm

CHARMS: a simple framework for adaptive simulation

Eitan Grinspun, Petr Krysl, Peter Schröder
2002 ACM Transactions on Graphics  
Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations.  ...  Indeed, building adaptive solvers can be a daunting task especially for 3D finite elements.  ...  Figure 2 : 2 Illustration of the finite-element (left) and basis-function (right) points of view using linear B-splines.  ... 
doi:10.1145/566654.566578 fatcat:xh2dy5yagjhkzpfli2s3ykhxtm

Parametric finite elements with bijective mappings

Patrick Zulian, Teseo Schneider, Kai Hormann, Rolf Krause
2017 BIT Numerical Mathematics  
We present an alternative approach which combines parametric finite elements with smooth bijective mappings leaving the choice of approximation spaces free.  ...  The discretization of the computational domain plays a central role in the finite element method.  ...  We thank the anonymous reviewers for their useful comments which helped improving both content and presentation of this paper.  ... 
doi:10.1007/s10543-017-0669-6 fatcat:u644s7v52rhirncctz366r43cm

Page 3268 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
20044:65021 show that web-splines form a stable basis for splines on arbitrary domains in R”, which provides optimal approximation power.  ...  To illustrate the performance of the method, it is applied to a scattered data fitting problem and a finite element approximation of an elliptic boundary value problem.” 2004d:65021 65D10 62502 65C20 92D25  ... 

Scattered data interpolation with multilevel B-splines

S. Lee, G. Wolberg, S.Y. Shin
1997 IEEE Transactions on Visualization and Computer Graphics  
The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function.  ...  Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function.  ...  Seungyong Lee performed work on this paper while he was a visiting scholar in the Department of Computer Science at the City College of New York. This work was supported in part by U.S.  ... 
doi:10.1109/2945.620490 fatcat:vkg6py5le5cxnfcgetzt46lb6e

Page 4520 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
Summary: “A uniform approach for constructing absorbing artifi- cial boundary conditions for second-order linear hyperbolic equa- tions is proposed.  ...  A. (2-AOS-M); Pavlov, V. I. (2-AOS-M) Numerical solution of elliptic problems of order 2 by the method of least squares using spline approximation on rectangular grids. (Russian.  ... 
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