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T-spline simplification and local refinement

Thomas W. Sederberg, David L. Cardon, G. Thomas Finnigan, Nicholas S. North, Jianmin Zheng, Tom Lyche
2004 ACM Transactions on Graphics  
The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.  ...  This concept is used in the local refinement algorithm in Section 4.3 and in the T-spline simplification algorithm in Section 5.  ...  This new local refinement algorithm plays a key role in the T-spline simplification algorithm presented in this paper. The paper is organized as follows.  ... 
doi:10.1145/1015706.1015715 fatcat:2dscj7wex5awnl7e2wederqfvy

T-spline simplification and local refinement

Thomas W. Sederberg, David L. Cardon, G. Thomas Finnigan, Nicholas S. North, Jianmin Zheng, Tom Lyche
2004 ACM SIGGRAPH 2004 Papers on - SIGGRAPH '04  
The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.  ...  This concept is used in the local refinement algorithm in Section 4.3 and in the T-spline simplification algorithm in Section 5.  ...  This new local refinement algorithm plays a key role in the T-spline simplification algorithm presented in this paper. The paper is organized as follows.  ... 
doi:10.1145/1186562.1015715 fatcat:ad3wlqrl5veyxprglchzq6wslm

Localized Topological Simplification of Scalar Data [article]

Jonas Lukasczyk, Christoph Garth, Ross Maciejewski, Julien Tierny
2020 arXiv   pre-print
This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA).  ...  Given a scalar field f and a selection of extrema to preserve, the proposed localized topological simplification (LTS) derives a function g that is close to f and only exhibits the selected set of extrema  ...  This localized simplification problem can be solved by adapting the iterative simplification algorithm of Tierny and Pasucci [56] to this special setting.  ... 
arXiv:2009.00083v1 fatcat:bkeqcv6u7naztoydmqn32lg554

Local, algebraic simplifications of Gaussian random fields

Theodor Bjorkmo, M.C. David Marsh
2018 Journal of Cosmology and Astroparticle Physics  
This application is particularly useful when one is concerned with the field locally around special points (e.g.  ...  In this work, we show how that problem can be completely circumvented for the local Taylor coefficients of a Gaussian random field with a Gaussian (or 'square exponential') covariance function.  ...  Nevertheless, we expect our method to offer useful simplifications to a wide variety of practical applications of Gaussian random fields and Gaussian processes.  ... 
doi:10.1088/1475-7516/2018/12/022 fatcat:v5gos6pvqfazpd3m5ml53idoza

Why Local Search Excels in Expression Simplification [article]

Ben Ruijl, Aske Plaat, Jos Vermaseren, Jaap van den Herik
2014 arXiv   pre-print
In this work, we investigate the state space properties of Horner schemes and find that the domain is relatively flat and contains only a few local minima.  ...  Finding suitable Horner schemes is assumed to be hard, due to the lack of local heuristics. Recently, MCTS was reported to be able to find near optimal schemes.  ...  Section 2 gives an informative background on simplification methods, section 3 provides an overview of related algorithms, and section 4 gives the experimental setup.  ... 
arXiv:1409.5223v1 fatcat:shogso2jjzbgdlcflyoiy7dodu

Local, Smooth, and Consistent Jacobi Set Simplification [article]

Harsh Bhatia and Bei Wang and Gregory Norgard and Valerio Pascucci and Peer-Timo Bremer
2013 arXiv   pre-print
We prove that the algorithm is correct and terminates only once no more local, smooth and consistent simplifications are possible.  ...  We focus on simplifications that can be realized by smooth approximations of the corresponding functions and show how this implies simultaneously simplifying contiguous subsets of the Jacobi set.  ...  By construction f * is local, smooth, and consistent, and thus forms a valid simplification.  ... 
arXiv:1307.7752v1 fatcat:ux4vjcy7cnb6zjhhefr5zr7w6y

Local, smooth, and consistent Jacobi set simplification

Harsh Bhatia, Bei Wang, Gregory Norgard, Valerio Pascucci, Peer-Timo Bremer
2015 Computational geometry  
We prove that the algorithm is correct and terminates only once no more local, smooth and consistent simplifications are possible.  ...  Contributions To overcome the current limitations in Jacobi set simplification, we introduce a new direct simplification framework for Jacobi sets of two Morse functions defined on a common smooth, compact  ...  By construction f * is local, smooth, and consistent, and thus forms a valid simplification.  ... 
doi:10.1016/j.comgeo.2014.10.009 fatcat:ejqtnrks45f4tg53e57xipqhju

Higher spins at the quintic order: Localization effect and simplifications

Dimitri Polyakov
2016 Physical Review D  
the related 5-point interaction vertex in the low energy limit of string theory and find that: the structure of the quintic s_1-s_2-s_3-s_4-s_5 higher spin interaction gets drastically simplified and localized  ...  The simplification is that for u = 4, all the ψ-fields of 4 operators have to couple to the ψ-fields of the operator with the highest spin value, given by s max = Σs − 2.  ...  The manifest expressions for the vertex operators V s−1|t for the frame-like fields with s > 3 become far more complicated, however, a significant simplification occurs for the case t = s − 3.  ... 
doi:10.1103/physrevd.93.045001 fatcat:25cnerdkkvam3lvf5boxa4znrq

LOCALIS: Locally-adaptive Line Simplification for GPU-based Geographic Vector Data Visualization [article]

Alireza Amiraghdam Department of Informatics University of Zurich)
2019 arXiv   pre-print
In our work, we present a GPU-based algorithm for real-time simplification and rendering of large line vector datasets directly on the GPU.  ...  Simplification Results Our locally-adaptive line simplification technique, LOCALIS, demonstrates that real-time line simplification can be applied to interactive vector map visualization applications.  ...  CONCLUSION In this paper we have presented LOCALIS, our locally-adaptive line simplification algorithm based on the Douglas-Peucker line simplification algorithm.  ... 
arXiv:1909.05511v1 fatcat:m6p7bwgwd5evxm2bnhac2tfumq

A proposed simplification of the adaptive local deconvolution method

S. Hickel, N. A. Adams, Stéphanie Salmon, Eric Sonnendrücker, Michael Dumbser, Claus-Dieter Munz
2007 ESAIM: Proceedings and Surveys  
The adaptive local deconvolution method (ALDM) [9] provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows.  ...  Computational results for isotropic turbulence and plane channel flow show that the simplified adaptive local deconvolution (SALD) method performs similarly to the original method ALDM and at least as  ...  A simplification of the algorithm is proposed leading to the simplified adaptive local deconvolution (SALD) method.  ... 
doi:10.1051/proc:2007008 fatcat:ouw24hunfbdgrghourrb2pqlvi

Influence Of Human Body Geometry Simplification On Local Heat Transfer

Jingxian Xu, Agnes Psikuta, Jun Li, Simon Annaheim, René Rossi
2018 Zenodo  
This study aims at determining the influence of geometric simplification on heat transfer by comparing local and global htc at various body regions.  ...  Inaccurate htc due to geometric simplification may result in predictive errors in human thermal response and compromise the model validation.  ... 
doi:10.5281/zenodo.1404522 fatcat:ukjittrgkvbwbmx5fdifs3fiam

Simplification des cartes géographiques par minimisation de la déformation locale

Pascal J. Frey, Houman Borouchaki
2002 Comptes rendus. Mathematique  
In this Note, we propose a new simplification method based on a measure of the local deformation of the surface.  ...  Dans cette Note, on propose une nouvelle méthode de simplification basée sur une mesure de déformation locale de la surface.  ...  Schéma général de simplification Pour pouvoir résoudre ce problème de simplification de complexité NP-complet, on considère une approche incrémentale où à chaque itération l'écart local entre la triangulation  ... 
doi:10.1016/s1631-073x(02)02250-1 fatcat:yz2bqta5ojbspmgwrylzjqedje

A local proof of the Breuil–Mézard conjecture in the scalar semi-simplification case

Fabian Sander
2016 Journal of the London Mathematical Society  
We give a new local proof of the Breuil-Mézard conjecture in the case of a reducible representation of the absolute Galois group of Q_p, p>2, that has scalar semi-simplification, via a formalism of Paškūnas  ...  In this thesis we want to give a purely local proof of the conjecture in the socalled scalar semi-simplification case.  ...  We define σ(w, τ ) := σ(τ ) ⊗ Sym b−a−1 L 2 ⊗ det a and let σ(w, τ ) be the semi-simplification of the reduction of a K-invariant O-lattice modulo .  ... 
doi:10.1112/jlms/jdw038 fatcat:cdv3l5z465conlt6d76uifu5qa

The Effect of Head Model Simplification on Beamformer Source Localization

Frank Neugebauer, Gabriel Möddel, Stefan Rampp, Martin Burger, Carsten H. Wolters
2017 Frontiers in Neuroscience  
Variance localization seems more robust against modeling errors than kurtosis.  ...  Depending on the source position, both effects can each be in the magnitude of centimeters, rendering their modeling necessary for successful localization.  ...  For the solution of the forward problem, the geometrical and electromagnetic features of the head need to be modeled, and every modeling also necessitates an appropriate simplification due to the high  ... 
doi:10.3389/fnins.2017.00625 pmid:29209157 pmcid:PMC5701642 fatcat:euqgw5zcanc2xowfzrrsx6zkz4

Interactive Procedure for Localized Monitoring and Control of Polyline Simplification

Barry Kronenfeld, Lawrence Stanislawski, Barbara P. Buttenfield, Ethan Shavers
2022 Abstracts of the International Cartographic Association  
Available operations include dynamic parameterization of automated algorithms, spot tools for manual local feature modification, and real-time feedback on assessment metrics.  ...  This research develops and tests procedures for interactive simplification of polyline features with near real-time assessment capabilities.  ...  Smoothing was performed until the resulting polyline contained no noticeably sharp angles when displayed at 2x the target scale, and typically (but not always) resulted in a reduction in local displacement  ... 
doi:10.5194/ica-abs-4-2-2022 fatcat:mosyzckz4nd7xaqp2ebz6hfrhu
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