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Contract No. DE-AC36-08GO28308

Simulation Exploration through 

Immersive Parallel Planes

Preprint

Nicholas Brunhart-Lupo, Brian W. Bush, 

and Kenny Gruchalla

National Renewable Energy Laboratory

Steve Smith

Los Alamos Visualization Associates

To be presented at the IEEE Workshop on Immersive Analytics (IA)

Greenville, South Carolina

March 19–23, 2016

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Simulation Exploration through Immersive Parallel Planes

Nicholas Brunhart-Lupo∗ Brian W. Bush† Kenny Gruchalla‡ 

National Renewable Energy Laboratory National Renewable Energy Laboratory National Renewable Energy Laboratory 

Steve Smith§
 

Los Alamos Visualization Associates
 

ABSTRACT

We present a visualization-driven simulation system that tightly 

couples systems dynamics simulations with an immersive virtual 

environment to allow analysts to rapidly develop and test hypotheses in a high-dimensional parameter space. To accomplish this, 

we generalize the two-dimensional parallel-coordinates statistical 

graphic as an immersive “parallel-planes” visualization for multivariate time series emitted by simulations running in parallel with 

the visualization. In contrast to traditional parallel coordinate’s 

mapping the multivariate dimensions onto coordinate axes represented by a series of parallel lines, we map pairs of the multivariate 

dimensions onto a series of parallel rectangles. As in the case of 

parallel coordinates, each individual observation in the dataset is 

mapped to a polyline whose vertices coincide with its coordinate 

values. Regions of the rectangles can be “brushed” to highlight and 

select observations of interest: a “slider” control allows the user to 

filter the observations by their time coordinate. In an immersive 

virtual environment, users interact with the parallel planes using a 

joystick that can select regions on the planes, manipulate selection, 

and filter time. The brushing and selection actions are used to both 

explore existing data as well as to launch additional simulations corresponding to the visually selected portions of the input parameter 

space. As soon as the new simulations complete, their resulting observations are displayed in the virtual environment. This tight feedback loop between simulation and immersive analytics accelerates 

users’ realization of insights about the simulation and its output. 

Index Terms: I.3.7 [Computer Graphics]: Three-Dimensional 

Graphics and Realism—Virtual reality 

1 INTRODUCTION

Parallel-coordinates statistical graphics [12] have proven value 

in the interactive exploration of moderately large multivariate 

datasets [13]. However, for sufficiently large datasets they can suffer from over-plotting of the polylines representing individual observations, which obscures the underlying correlations in the observations and introduces spurious visual correlations between the 

observations. Various solutions have been proposed to the overplotting problem, including the clustering and sub-setting of the observations [5, 14] or replacing the polylines with density representations [16, 19, 9]. Embedding such graphics in three dimensions 

provides an extra degree of freedom to separate observations, offering an opportunity to reveal a better view of correlations by visually 

“untangling” the overlap present in two dimensions. Several approaches to utilizing this extra dimension have been implemented in 

the past by other researchers: Wegenkittl et al. [25] extended parallel coordinates for dynamical systems trajectories by extruding the 

∗e-mail: nicholas.brunhart-lupo@nrel.gov 

†e-mail:brian.bush@nrel.gov 

‡e-mail:kenny.gruchalla@nrel.gov
 

§e-mail:sas@lava3d.com
 

polylines into the third dimension as a function of time. Johansson 

et al. [15] map vertical axes to the edge of cylinders each connecting to a single “focus” axes in the center. Streit et al. [23] extrude 

parallel coordinate line density into the third dimension. Multiple 

researchers [4, 22] have implemented versions of “parallel planes” 

where the single line-segment axes of parallel coordinates are replaced by pairs of axes arranged as a series of rectangles or planes. 

In this paper we adopt the notion of parallel planes into a fully 

interactive immersive virtual environment, and extend the notion of 

the interface to not only explore existing data, but to explore the 

system parameter spaces by interactively spawning parallel simulations directly from the immersive environment. The extension of 

the parallel coordinates from a surface into a volume alleviates the 

over-plotting problem and enables users to better spot correlations 

between observations; however, that feature separation can easily be obfuscated when projecting the three-dimensional construction back onto a two-dimensional display. Likewise, interacting 

with a three-dimensional parallel coordinate construction in a twodimensional projection becomes cumbersome at best. It is reasonable to suspect that an immersive environment would improve these 

visualizations. The three-dimensional stereo and motion parallaxes 

naturally increase the visibility of the separated lines, and users can 

directly interact with the visualization by brushing the coordinate 

planes with a virtual “brush” or “flashlight”, easily highlighting the 

observations temporarily of interest. Additionally, it has been hypothesized [8] that the egocentric perspective may actually improve 

spatial reasoning through embodied cognition (i.e., the natural body 

movement and body-relative spatial judgments provided by an immersive environment engages well-practiced automatic brain function acquired by what we have encountered and manipulated with 

our bodies as we move within and examine the world.) Specific 

to the visualization of statistical graphics, there have been multiple controlled user studies [2, 21, 10] that have shown benefits to 

visualizing statistical graphics in immersive environments. 

To support the exploration of complex high-dimensional parameter spaces, our immersive implementation of parallel planes is tied 

to a cluster of on-demand simulations that emit the multivariate 

time series. In the context of such exploration of the output from 

a simulation, an impediment to exploring correlations in its inputs 

and outputs through the parallel-coordinates technique occurs when 

the brushing of multiple axes for simulation-input dimensions results in filtering the dataset until no more simulated observations 

remain. This leaves the user without information regarding what 

output would correspond to the filter on input. When this occurs in 

practice, the next step would be to run additional simulations for the 

inputs domain of interest and then to restart the parallel-coordinates 

visualization with the expanded datasets. In our simulation-linked 

implementation, however, the brushing and selection actions on the 

simulation’s input variables trigger the launching of additional simulations corresponding to the visually selected portions of the input 

parameter space. As soon as the new simulations complete, their resulting observations are displayed in the virtual environment. This 

tight feedback loop between simulation and immersive analytics accelerates users’ realization of insights about the simulation and its 

output. 

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2 APPROACH

2.1 Parallel-Planes in an Immersive Environment

We map multivariate observations (x1,x2,..., xn) into threedimensional space by treating each observation as a line that intersects the rectangles representing coordinate axes at the observation’s coordinate values on those axes (see Figure 1). The intersections of the observations with a plane serves as a two dimensional 

scatter plot. Consequentially, the overall visualization of parallel 

planes can be thought of as a series of scatter plots where the same 

observations on each plot are joined by a polyline. The planes are 

embedded in the immersive environment somewhat like books on 

a bookshelf, with one of their axes pointing upward and the other 

axis pointing depth-wards. The names of the variables appear next 

to the corresponding axes of each plane. 

Figure 1: Representation of the observation (x1,x2,..., xn) using parallel planes in an immersive environment: the dashed polyline intersects each plane at the corresponding coordinate values. 

Brushing and selection of the observations are accomplished 

through the use of a virtual tool in the shape of a truncated cone, 

as shown in Figure 2. In the immersive environment, the base of 

the cone appears to be connected to the joystick controller (Figure 3) and the cone’s tip points in the direction that the controller 

points. In order to prevent the cone from obscuring the view of the 

observations, the cone has an opacity gradient from the tip, which 

is completely opaque, to the base, which is mostly transparent. The 

intersection of the cone with the parallel planes defines the selection and brushing region. Users can select small regions by pushing 

just the tip of the cone into a coordinate plane, and they can select 

larger regions by pushing the cone more deeply into the plane. The 

opacity gradient is tuned to ensure that the user can see the observations while they are using the tool to select them. Buttons on the 

control allow the user to select the intersection region, deselect it, 

or clear all of the selections in the environment. The observations 

passing through all of the selected regions of the planes have their 

polylines displayed as thin, opaque white tubes, whereas the observations that do not pass through all of the selected regions appear 

in transparent gray (see Figure 4). (The planes with no selected 

regions do not filter or exclude observations.) 

Additional buttons on the controller allow the user to scale, translate, and rotate the display. When displaying time series data, a time 

axis is displayed below and forward of the parallel planes. Buttons 

on the controller move the time step forward or backwards. 

The parallel planes visualization has many of the same strengths 

and drawbacks as traditional parallel-coordinates plots [13, 17]. In 

particular, the visualizations are more effective if the pairs of axes 

are chosen and the planes are ordered in an efficient manner [1]. 

In addition to simply brushing or highlighting the selected observations, when coupled to a simulation (instead of to a precomputed 

dataset), this parallel-planes visualization system can request additional simulations to be run for the selected regions of the input 

variables. (Input and output variables are distinguished on the display by the color of their names.) If the user keeps the controller’s 

Figure 2: The selection virtual tool, which is anchored in front of 

a physical joystick. The user can a select region of interest by intersecting the cone with a display plane. The simulation probability 

density of the selection can be manipulated with the joystick buttons. 

Figure 3: Joystick controller for the selector and other functions. 

selection button depressed, then a higher “density” of selection occurs: this higher density of selection appears as the thickness of the 

selection on the plane. When the button to request more simulations is pressed, the multivariate inputs to the simulation are chosen according to a probability distribution that is in proportion to 

the visual density of selection. This density-dependent response to 

simulation requests enables nuanced exploration of the simulation 

space. The visualizer typically creates a dozen simulation requests 

each time the simulation-request button is pressed. Pressing the 

button multiple times, or keeping it depressed, creates correspondingly more simulation requests. As soon as each new simulation 

completes, the visualizer displays the results of the simulations in 

the immersive environment. 

We have deployed this parallel-planes simulation-visualization 

system for the immersive environment in the Energy Systems Integration Facility at the National Renewable Energy Laboratory 

(NREL). Figure 5 shows its appearance in that environment. This is 

a two-surface environment with four blended stereoscopic HD projectors rear-projecting a 5m × 2.5m wall (a blended resolution of 

3456 × 1728) and two stereoscopic HD projectors front-projecting 

a 5m × 1.6m floor (a blended resolution of 3456 × 1080). The projected space is used in conjunction with an optical motion tracking 

system that tracks the position an orientation of the user, allowing 

the visualizations to respond in relation to the movement of the user. 

The visualizer was constructed using an in-house immersive 

graphics engine. This engine was written in C++ using the Qt 

framework, OpenGL, VRPN [24], and OpenMPI [6] on Linux. 

Crucially, the engine provides a distributed scene-graph and 

database integration. 

In addition to the aforementioned high performance visualizer 

for immersive virtual environments, we have also implemented a 

lighter weight parallel planes visualizer that deploys on laptop com2

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Figure 4: Photograph of the parallel planes in an immersive virtual environment with annotations describing the visualization and user interface. 

Figure 5: Appearance of parallel planes in an immersive virtual environment. (Photo by Dennis Schroeder / NREL) 

puters, DLP projectors, Google Cardboard, and the like. Even without the degree of immersiveness provided by a human-scale environment, the parallel planes technique provides significant advantageous in decluttering parallel-coordinates plots on these smaller 

displays. 

2.2 Visualization-Driven Simulation

Our primary motivation for linking simulation and immersive visualization is to speed the analytic process of developing insights 

from simulations. By tightly coupling the scenario-definition, simulation, and exploratory-analysis processes (Figure 6), analysts can 

rapidly test and develop hypotheses regarding the relationships between simulation inputs and outputs and can design scenarios (sets 

of simulation inputs) illustrating those hypotheses and insights. Immersive analytics adds a powerful “tangible” dimension to this hypothesis testing and scenario design, and opens possibilities for 

collaborative exploration and design of simulations. The rapid, 

concrete feedback between scenario design decisions and seeing 

their implications, combined with the shared visual record of previous design decisions and their implications, enables developing 

nuanced intuitions regarding relationships between the simulation 

input space and the simulation output space. 

Figure 6: Driving simulation studies from immersive visualization 

streamlines the simulation-analysis workflow. 

Within our parallel-planes visualization framework, three data 

spaces mediate the exchange of information between the immersive visualization and the simulation cluster (see Figure 7). The 

model metadata space provides information uniquely identifying 

the model to be simulated, the input variables and their ranges, 

and the output variables. The parallel-planes visualizer retrieves 

this information as it initializes its rendering. The simulation requests space stores requests from the visualizer for simulations to 

be run and it records the completion status of those simulations. The 

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simulation results space simply records the multivariate time series 

output by the simulations. In practice, the parallel-planes simulation framework implements these spaces as three MongoDB collections of BSON documents. This database-mediated communication 

and the employment of the tuplespace paradigm [7] for distributed, 

shared memory supports fully asynchronous exchange of information between the visualizer and the simulation cluster and leaves the 

two only very loosely coupled. Consequentially, this database is the 

only architectural point in common between the simulation and visualizer. In cases where a precomputed dataset or measured data is 

only available instead of a live simulation cluster, the visualizer can 

render those “simulation results” as if there were a live simulation 

backend. (Because of the static nature of the dataset and the lack 

of a live simulator, the requests from the visualizer would never be 

served by the simulator.) In cases of massive precomputed or measured datasets, the “simulation” activity can be replaced with statistical sampling of that primary dataset to create a subset requested 

for visualization. 

Figure 7: A simple database schema mediates asynchronous exchange of information between the visualizer and the simulators. 

As a proof-of-principle for this simulation-visualization system, 

we have implemented a general purpose simulation for system dynamics (SD) models serialized in the standard XMILE format [3]. 

The system dynamics (SD) simulation methodology, which emphasizes the representation of time-varying phenomena that involve 

internal feedbacks and responses to external influences, is well 

suited for interactive visual exploration. The mathematical and 

computational straightforwardness of SD, which relies on the solution of systems of coupled ordinary differential equations (ODEs) 

with Neumann (second type) boundary conditions, also lends itself to rapid computation of the outputs for simulation requests 

from visualization systems. The simulation has been deployed on 

NREL’s Peregrine supercomputer [18], running in conjunction with 

the ESIF immersive environment also at NREL. 

The simulation framework, whose components are outlined in 

Figure 8, consists of eight Haskell packages comprising about eight 

thousand lines of code that are deployable in heterogeneous computing environments of Linux, Windows, and Mac OS X machines 

or clusters where simulation load balancing relies on the aforementioned tuplespace mechanism. Communication between the computational units occurs using Erlang-style message passing. We 

used real-life SD models of varied complexity (dozens to thousands 

of equations) for verification and validation of the simulator’s correctness and accuracy. The resulting system scales such that hundreds of simulations can be simultaneously executed in response to 

users’ cues in the immersive visualization. In addition to being displayed in the visualization environments, the simulation results can 

be exported to statistical analysis packages or data files for further 

analysis. 

Figure 8: Sketch of major components in the architecture of the simulation framework. 

3	 EXAMPLE WORKFLOW FOR SIMULATION BY PARALLELPLANES VISUALIZATION

We now briefly demonstrate—to the extent possible using screenshots in print media—an example workflow for a parallel-planes visualization driving a simulation in response to a users’ brushing of 

the simulation input space. Figures 9 through 12 illustrate an example exploration for a very simple simulation with eight input variables (shown in the four leftmost planes) and two output variables 

(shown in the rightmost plane). Initially, the user selects a single region of the leftmost plane, which corresponds to a small rectangular 

range of the first two input variables. This triggers simulations to 

be run using that range for the first two input variables and where 

the other six input variables chosen uniformly at random: Figure 9 

shows the visualization once those simulations have completed. At 

this point, a user would probably want to explore a broader region 

of the input space. They might brush, as shown in Figure 10, a large 

region of the second plane from the right, triggering simulations for 

that range of the third and fourth input variables. In order to explore 

the rich set of correlations in the simulation output, the user might 

brush a portion of the rightmost output plane, highlighting the observations that lie both in the previously selected inputs and the 

particular output regions that has been selected: Figure 11 shows 

those simulations highlighted and the other simulations displayed 

faintly. In typical workflows, a user would move between brushing input variables to generate more simulation output (Figure 12) 

and brushing output variables to identify patterns in the data. This 

can be thought of as an iterative process of generating and testing 

hypotheses about the correlation of the outputs among themselves 

and between the inputs and outputs. Once solid hypotheses have 

been generated, a user might discard the simulation output and run 

a rigorously designed statistical experiment and then explore that 

using the parallel planes visualization. 

To date, in our trials of the simulation-linked parallel-planes 

technique, we have found the user experience to be best when simulation response times are less than thirty seconds. Slower responses 

can be made acceptable to users, however, if visual cues such as 

markers registering the presence of simulations-in-progress annotate the input planes: essentially, these markers are promises to the 

user that their requests have been acknowledged and are being simulated. Depending on the immersive environment, tens of thousands of observations can be displayed effectively without causing 

severe over-plotting. “Zooming in” on fine structure in the results is 

particularly effective in large immersive environments because the 

user can walk right up to the data in question and brush it to make 

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Figure 9: Initial exploration of a example simulation. Simulations 

have only been run for a small portion of the input space, shown by 

the selected rectangle in the leftmost plane. In this example, the four 

leftmost planes show input variables and the rightmost plane shows 

output variables. 

Figure 10: A continuation of the exploration in Figure 9, where additional simulations have been triggered by selecting a large region in 

the second-from-left plane. 

the observation visible throughout the display. 

4 SUMMARY AND PROSPECTS

This software presents a user-provided multivariate time-series 

dataset or simulation as an interactive three dimensional visualization analogous to the two-dimensional statistical graphic commonly called a “parallel coordinates” plot. Each variable of the 

input dataset is represented by the horizontal or vertical axis of a 

plane floating in virtual three dimensional space. Furthermore, each 

observation of the input dataset is represented by a polyline connecting the observation’s coordinate values on the planes. Users 

can select, or “brush”, regions of the planes and see highlighted 

the observations that intersect the brushed regions. This interactive 

visualization allows users to explore the correlation between variables in the observations and the distribution of observations among 

the variables. When used in conjunction with a simulation cluster, 

this software can provide a form of “simulation space exploration” 

similar “computational steering”, but in the context of ensembles of 

simulations rather than within a single simulation. 

The technology described in this paper is under active use for 

simulation analysis and also under active development aimed to 

make it more effective. In particular, the use of a large, immersive space does not completely alleviate the problem of overlapping observations, it simply lets larger datasets be used before it 

becomes a problem. One approach is to allow the user to thin 

out the data in the display, particularly where it is highly redundant. To further relieve the problem of overplotting or occlusion 

Figure 11: A continuation of the exploration in Figure 10, where the 

previously run simulations are filtered by a small range of output parameters brushed as the selected region in the rightmost plane. 

Figure 12: A continuation of the exploration in Figure 11, where many 

more simulations have been run, but this larger dataset is brushed as 

it was in Figure 11. 

between the lines connecting points on the parallel planes, we propose to explore an adaptation of the edge bundling techniques introduced by Holten and Van Wijk [11] and applied to traditional 

parallel coordinates by Rubel et al. [22] and Palmas et al. [20]. We  ̈

also have experimented with alternatives representations to parallel planes, one promising one among which is a “parallel forest” 

layout. The “trees” in the parallel forest are simply the individual parallel-coordinate axes; these are arranged in the immersive 

space like trees in a forest, but the locations are carefully chosen to 

conform to a two dimensional graph layout based on the statistical 

correlation between variables. Although the parallel forests have 

somewhat lower information density than the parallel planes, they 

may provide a more intuitive and inviting, but less abstract, view 

for users who are not already familiar with parallel coordinates. 

The axes in parallel forests can also be annotated with information 

such as histograms of marginal distributions. 

Our ongoing work also links this simulation-visualization system 

with ancillary visualizations and controllers. The loose coupling 

of the visualization and the simulations allows for the inclusion 

of other visualization clients and other controllers. For instance, 

we have successfully linked web-browser-based two-dimensional 

parallel-coordinate controllers/visualizers to the same simulation 

clusters while the immersive visualization is active. This allows 

collaborations where some users are locally brushing and exploring 

the simulation space, but where the output from the simulations that 

their exploration launches are available to all other users, whether 

they are using the immersive parallel-planes, laptop-based visualizations, or other client software. In fact, tools for the design of 

experiments, such as R, can also be linked into the collaborative 

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space, so that structured batches of simulations can be requested 

according to statistically sound principles and then shared among 

the visualization clients. To further enhance group collaboration 

in a shared space such as immersive environments, we propose to 

investigate the use of computer-vision distinguishable physical objects (fiducials) to represent coordinate axes and brush regions on 

the axes to allow multiple analysts to work with the same visualization at the same time in a shared space. A final amenity for 

collaborative use of this approach is to allow users to “bookmark” 

and share the brushing configuration and/or “snapshot” and share 

the simulations created. 

ACKNOWLEDGEMENTS

This work was supported by the U.S. Department of Energy. The 

research was performed using computational resources sponsored 

by the Department of Energy’s Office of Energy Efficiency and 

Renewable Energy and located at the National Renewable Energy 

Laboratory. This work was initially supported by the Laboratory 

Directed Research and Development (LDRD) program at the National Renewable Energy Laboratory. 

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