\documentclass[journal]{vgtc}                     % final (journal style)
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% \documentclass[review,journal]{vgtc}              % review (journal style)
%\documentclass[review,journal,hideappendix]{vgtc} % review (journal style)
%\documentclass[widereview]{vgtc}                  % wide-spaced review
%\documentclass[preprint,journal]{vgtc}            % preprint (journal style)


%% Uncomment one of the lines above depending on where your paper is
%% in the conference process. ``review'' and ``widereview'' are for review
%% submission, ``preprint'' is for pre-publication in an open access repository,
%% and the final version doesn't use a specific qualifier.

%% If you are submitting a paper to a conference for review with a double
%% blind reviewing process, please use one of the ``review'' options and replace the value ``0'' below with your
%% OnlineID. Otherwise, you may safely leave it at ``0''.
% \onlineid{1780}

%% In preprint mode you may define your own headline. If not, the default IEEE copyright message will appear in preprint mode.
%\preprinttext{To appear in IEEE Transactions on Visualization and Computer Graphics.}

%% In preprint mode, this adds a link to the version of the paper on IEEEXplore
%% Uncomment this line when you produce a preprint version of the article 
%% after the article receives a DOI for the paper from IEEE
%\ieeedoi{xx.xxxx/TVCG.201x.xxxxxxx}

%% declare the category of your paper, only shown in review mode
\vgtccategory{Research}

%% please declare the paper type of your paper to help reviewers, only shown in review mode
%% choices:
%% * algorithm/technique
%% * application/design study
%% * evaluation
%% * system
%% * theory/model
\vgtcpapertype{algorithm/technique}

%% Paper title.
\title{Simplicial Approximation of Deforming 3D Spaces\\for Visualizing Fusion Plasma Simulation Data}
% \title{Fast and Invertible Approximation of Deforming 3D Space\\in Fusion Simulations for Visualization and Analysis}
% \title{Framework for Visualization and Analysis of Deforming 3D Space in Fusion Simulations}
% \title{Meshing Deforming 3D Space for\\Visualization and Analysis}

%% Author ORCID IDs should be specified using \authororcid like below inside
%% of the \author command. ORCID IDs can be registered at https://orcid.org/.
%% Include only the 16-digit dashed ID.
\author{%
  \authororcid{Congrong~Ren}{0009-0006-6285-7271}
  and 
  \authororcid{Hanqi~Guo}{0000-0001-7776-1834}
}

\authorfooter{
  %% insert punctuation at end of each item
  \item Congrong~Ren and Hanqi~Guo are with The Ohio State University. E-mail: \{ren.452\,$|$\,guo.2154\}@osu.edu\,.
}

%% Abstract section.
\abstract{%
  We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations, scientific variables (e.g., density and temperature) are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in 3D space poses challenges for visualization tasks such as volume rendering and isosurfacing. To address these challenges, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deforming 3D space. Our algorithm introduces no new nodes and operates with reduced time complexity, generating a mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. In the algorithm, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then we independently search for a feasible tetrahedralization of each partition taking nonconvexity into consideration. We demonstrate use cases of our method for visualizing XGC simulation data on ITER and W7-X.
  % A free copy of this paper and all supplemental materials are available at \url{https://OSF.IO/2NBSG}.
}

%% Keywords that describe your work. Will show as 'Index Terms' in journal
%% please capitalize first letter and insert punctuation after last keyword
\keywords{Simplicial meshing, triangulation, spatially-varying mesh, isosurfacing, volume rendering.}

% A teaser figure can be included as follows
\teaser{
  \centering
  \includegraphics[width=0.98\linewidth]{figs/teaser.pdf}
  \caption{
   Illustrations and isosurfacing results of XGC fusion plasma simulation data for tokamaks (top) and stellarators (bottom) in the cylindrical coordinate system $(R,Z,\phi)^\intercal$, where $R$, $Z$, and $\phi$ represent radial, axial, and toroidal coordinates, respectively. (a) Simulation domain and magnetic field lines in two devices, the International Thermonuclear Experimental Reactor (ITER)~\cite{aymar2002iter,mukhovatov2003overview} and Wendelstein 7-X (W7-X)~\cite{erckmann2007electron,geiger2014physics}, based on the concepts of tokamaks and stellarators, respectively. ITER exhibits a uniform shape along the toroidal axis, while W7-X features a twisting geometry. (b) XGC output data, consisting of (1) 2D triangular meshes on discrete poloidal planes and (2) connectivities between mesh nodes in every pair of adjacent planes approximating the magnetic lines (only shown in the ITER case). (c) Isosurfacing results derived from XGC data by our tetrahedralization algorithm. The upper shows isosurfaces of a scalar function, \textit{normalized electrostatic potential perturbation} ($\delta n_e/n_{e0}$) in ITER. The lower is a isosurface of \textit{poloidal magnetic flux} ($\Psi$) (a.k.a., \textit{flux surface}) in W7-X, colored by \textit{perturbed electrostatic potential} ($\delta\Phi$).
   % (c) Illustration of a tokamak. Two 2D poloidal planes with $\Delta\phi=\pi$ are shown, but actually we use XGC data discretized into 16 poloidal planes. The gray lines show trajectories of arbitrarily chosen particles. Each poloidal plane is meshed into an identical unstructured triangular grid. Part of the triangular mesh in the circled region is shown on the right. The whole mesh has 56,980 nodes and 112,655 cells.
  }
  \label{fig:teaser}
}

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\begin{document}

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%%%%%%%%%%%%%%%%%%%%%% START OF THE PAPER %%%%%%%%%%%%%%%%%%%%%%
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%% The ``\maketitle'' command must be the first command after the
%% ``\begin{document}'' command. It prepares and prints the title block.
%% the only exception to this rule is the \firstsection command
\input{1.intro}
\input{2.related}
\input{3.preliminaries}
\input{4.method}
\input{5.case-studies}
\input{6.discussion}
\input{7.conclusion}

%% if specified like this the section will be omitted in review mode
\acknowledgments{%
he authors thank
Drs. Choong-Seock Chang, Michael Churchill, Robert Hager, Seung-Hoe Ku, Zeyu Guo, and Rephael Wenger for insightful discussions. This research is supported by DOE DE-SC0022753.  It is also supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357.
}

% \section*{Supplemental Materials}
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% \appendix % You can use the `hideappendix` class option to skip everything after \appendix

% \section{About Appendices}

\end{document}

