Clutter Reduction in Rendering of Particle (Atom) Trajectories with

Adaptive Position Merging

Bidur Bohara

and Bijaya B. Karki

1-3

School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, U.S.A.

Department of Geology and Geophysics, Louisiana State University, Baton Rouge, U.S.A.

Center for Computation and Technology, Louisiana State University, Baton Rouge, U.S.A.

Keywords: Trajectory Rendering, Clutter Reduction, Position Merging, Atomistic (Molecular) Visualization

Abstract: Visualization of position-time series data from molecular dynamics simulations of a material has to render

atomic trajectories, and relevant structural and dynamical information. Clutter/occlusion associated with

overlapping trajectories becomes serious even for moderate data sizes. We present an adaptive hierarchical

scheme for merging multiple positions along trajectories to significantly reduce the number of points/line

segments used for rendering. Our approach finds positions lying within a space window (cut-off distance)

from a reference position and merges them into a single position. The window is then moved in time order

with merging performed at each successive location. All original positions are thus processed to a reduced

number of new (merged) positions, which are further merged with the same or a different cut-off to obtain

even fewer positions. This hierarchical merging may continue several levels deep. Moreover, merging can

be performed subject to constraint of information, which is displayed (color-coded) along individual

trajectories. Both the trajectory geometry and underlying atomic structure become increasingly visible after

merging so the nature and extent of atomic arrangements and movements can be better assessed.

1 INTRODUCTION

Molecular dynamics (MD) simulations of real

material systems produce massive amounts of time-

varying positional data for constituent atoms or

molecules (Allen and Tidesley, 1987); (Peng et al.

2011). Visualization of such correlated data allows

us to gain insight into the structural and dynamical

behaviour of the material system under

consideration. Different approaches depending on

the nature of the atomic systems studied have

previously been used to visualize the scattered MD

data (see the Section 2). Two approaches for a rapid

navigation through the data are animation and

trajectories (Bhattarai and Karki 2009); (Li, 2005);

(Humphrey et al., 1996). Particle (atom) trajectories

allow a complete representation of position-time

series by rendering positions of all atoms at all-time

steps as points or line segments, so full simulation

information is contained in a single display. As

shown in Figure 1 (left), the main problem is that

trajectory rendering becomes too crowded because

there are simply many trajectories that are long,

distributed in 3D space, and overlapped with each

other. Note that the trajectories shown are unfolded

so they become continuous curves extending in the

space both inside and outside the simulation

supercell.

The challenge is how we can render the atomic

trajectories with a minimum clutter while preserving

the dynamical and structural information contained

in the data. The degree of trajectory crowdedness is

expected to increase with the size of the data, which

depend on the number of atoms and the number of

time steps. Though the clutter cannot be completely

avoided, it may be reduced to an acceptable level via

repetitive processing and analysis of the data.

Deciding whether to accept or reject the processed

trajectories may require a domain specific

knowledge. Various factors such as the geometrical

shape, spatial confinement, and other physical

properties of the trajectory are relevant.

Furthermore, the information about the geometric

arrangement of constituent atoms (i.e., atomic

structures) also needs to be rendered together with

the trajectories.

In this paper, we report an improvement in

rendering of the atomic trajectories from MD

264

Bohara B. and B. Karki B..

Clutter Reduction in Rendering of Particle (Atom) Trajectories with Adaptive Position Merging.

DOI: 10.5220/0004720102640271

In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications (GRAPP-2014), pages 264-271

ISBN: 978-989-758-002-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Visualization of molecular dynamics simulation data: atom trajectories and structure are rendered together. As

multiple positions along the trajectories are merged with our adaptive hierarchical merging (described in section 3), the

structure (consisting of Si-O polyhedra, H-O bonds, and floating Mg atoms) becomes increasingly visible (left to right).

simulations. We overcome the clutter/occlusion

problem associated with the trajectories by position

merging, encode useful information along the

trajectories, and superimpose the atomic structure.

While our approach should work for any MD data

set, here we deal with atomic systems that are

routinely simulated using the first-principles

molecular dynamics (FPMD) method based on the

fundamental equations of quantum mechanics. Two

atomic systems considered are hydrous silicate

(MgSiO

O) and silica (SiO

) liquids (e.g., Karki

et al., 2010). The first system consists of 84 atoms in

a supercell of length of 10.11Å and simulation run

of 60,000 time steps (with each time step being 1

femtosecond). There are about 5 millions of data

points in total. The second system consists of 72

atoms in a supercell of length of 10.32Å and

simulation run of 1.2 million time steps. There are

over 80 million data points in total. We consider

these data sets to be of moderate size in the sense

that the classical MD simulations based on pairwise

potential functions can handle very large systems

even exceeding one billion atoms (Nakano et al.

2007).

2 RELATED WORK

Atomistic (molecular) visualization is one of the

most widely studied applications of computer

graphics and visualization (Bhattarai and Karki

2009); (Li, 2005); (Humphrey et al., 1996); (Grottel

et al., 2010); (Stone et al., 2011); (Zhang et al.,

2007). To gain insight into MD and FPMD

simulations, visualization has previously been

exploited in various ways depending on the nature of

the atomic systems studied. Few common examples

include VMD (Humphrey et al., 1996), Molscript

(Kraulis, 1991), XcrysDen (Kokalj, 1999), Atomeye

(Li, 2003), etc. In addition to rendering the atomic

configurations in various forms, they also support

animation and trajectories. To the best of our

knowledge, not much work was previously done in

manipulating the atomic trajectories.

Trajectory rendering is also relevant for other

movement-related data such as traffic network

consisting of roads and trails (Buchin et al., 2011).

Removing selected trajectories or portions of those

trajectories, and line simplification of highly curved

trajectories can help reduce the clutter to some

extent (Borcan, 2012). It is relevant to point out that

the pathline or trajectory technique is widely used in

vector visualization (Shi et al., 2007) with a lot of

efforts made on correct illumination and 3D

rendering of lines (Zockler et al., 1996), and

encoding the relevant information (Jones et al.,

2007). In the case of MD simulations, the input

position-time series directly represent the trajectory

data so trajectory rendering displays the spatio-

temporal behaviour of atomic system. Few ideas on

constraining trajectory rendering in space and time

have recently been explored (Bohara and Karki,

2012). Here, we present an improvement in

atomistic visualization by using adaptive

hierarchical (repeated) position merging based on

spatial proximity for trajectory rendering and by

superimposing instantaneous atomic structures.

3 POSITION MERGING ALONG

TRAJECTORY

Constituent atoms of a simulated material system are

expected to show non-uniform movements. This

ClutterReductioninRenderingofParticle(Atom)TrajectorieswithAdaptivePositionMerging

265

(a) (b) (c) (d)

Figure 2: Space proximity based two-level position merging along trajectory. Spheres represent space windows (cutoffs).

An original trajectory before merging (a), and the same trajectory after first merging (b), second merging (c) and smoothing

(d). Time is encoded along the trajectory (green to red).

means that the atoms spend longer time in certain

regions in 3D space than they do in other regions.

Positions in slow regions where atoms are perhaps

making oscillating (going back and forth) motions

form short and crowded portions of the trajectories.

A “proximity window” can be introduced based on

the assumption of such confined atomic movements

or localities so that positions lying in the window

can be merged together. This window can be

modeled as temporal proximity or spatial proximity.

It is important that the 3D geometry of the trajectory

be preserved during clutter reduction through

merging of multiple positions. This also means that

smaller amount of positional information is copied

to the video memory for rendering.

3.1 Basic Merging Algorithm

We first consider the temporal proximity, which

involves positions occupied by the concerned atom

over a finite time interval. A time window is defined

in terms of the number of successive MD steps, e.g.,

every 100 steps form a window. For each window,

we find a representative point by calculating the

mean (centroid) of all positions occupied at time

steps belonging to that window. Single position is

thus generated per window so the number of

windows (N

STEP

) gives the number of positions

to be rendered, where N

STEP

is the total number of

steps and N

is the size of the time window. Line

segments are drawn between two successive mean

positions to render the trajectories. The length of the

line segments can vary significantly since the atoms

move at different speeds at different time. Generally,

needs to be very large in order to reduce the

clutter in highly confined regions. This means that

line segments in extended regions (where the atoms

are moving fast without reversing directions) can be

unusually long so the time-window based merging

may not work well for the entire trajectory length.

Perhaps a more appealing approach is to apply

spatial proximity, which considers positions located

in the close vicinity of each other irrespective of

time when these positions are occupied by the

concerned particle. We define spatial proximity in

terms of a finite space window (cut-off distance) so

that all positions lying within such window are

considered for merging. The idea is to scan all time

steps to pick up positions whose distances measured

from the reference position are shorter than the cut-

off distance, and merge them together. The locality

being approximated is thus a spherical region of

radius equal to the cut-off distance (Figure 2).

Our position-merging algorithm for each

trajectory works as follows:

Step 1: Set the space window at the starting

(reference) position of an atom trajectory.

Step 2: Scan subsequent time steps to pick up

positions lying inside the window until an outside

position is encountered for the first time.

Step 3: Merge/map all positions found in the step 2

to single position.

Step 4: Start at the first position not yet picked up

(new reference position), and do the steps 2 and 3.

Step 5: Move the window in the time order with

merging performed at each successive location

(repeating the step 4) until the end.

Thus, all positions are processed to generate a

reduced set of new (merged) positions. If successive

positions are well separated because either the cut-

off distance is too small or atoms move too fast,

merging is not effective at all and every window

contains single but original position. On the other

hand, if atoms have covered small distances because

either atom are slowly moving/oscillating or the cut-

off distance is too large, an arbitrarily large number

of positions can be found in the window under

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266

consideration to map to a single position. Note that

processing atomic positions in the time order

ensures the correct geometry of the trajectories while

merging nearby positions as much as possible.

3.2 Adaptive Hierarchical Merging

After the first run of position merging using a cutoff

distance, the clutter though it might have already

reduced considerably is still not at an acceptable

level and merged positions are still too close. So it

may be desirable to apply additional merging with

the same or larger cutoff. The next level merging

then considers all new positions derived in the

previous merging by placing a space window (of the

same or bigger size) at the first merged position.

Figure 2 illustrates two-level merging. As in the

original merging, all positions lying within the

current window at each successive location are

picked up and merged. It is likely that the positions

even after the second merging are still closely

spaced, and/or again it may be desirable to apply an

even larger cut-off. A third/higher level merging is

then performed for the positions, which have

undergone merging more than once. This adaptive

hierarchical processing will continue until the

number of repeatedly merged positions does not

decrease anymore. This situation arises relatively

fast if the cut-off distance is constant from the one

level to the next. However, if the cut-off distance is

increased progressively, the merging process may

continue over many levels. The user has to specify

when to stop either by not increasing the cut-off

further or by visually assessing the crowdedness and

correctness of the trajectories being increasingly

approximated with multilevel position merging.

Merging is expected to be sensitive to

information that we want to display (color code)

along the trajectories. Examples of useful

information include the distance travelled by atom,

time spent, coordination states, bond events, merge

count, mean squared error, etc. Such information is

computed during merging process from original set

of positions and appropriately mapped to the merged

positions. Information extraction for coordination

states involves the positions of nearby atoms.

Atomic coordination ሺܥ

ఈఉ

௜

ሻ is the number of the

nearest neighbour atoms of the same species (



) or

other species (



) around a given atom of species



Coordination is of multivariate type as it can take

multiple values for a given window. Our approach to

impose a coordination constraint while merging is

that successive positions within a space window are

merged only if they are in same coordination state.

A position with different coordination state than the

previous positions will start a new space window for

merging next sequence of positions of the same

coordination state. It is expected to result in more

crowded trajectories than original merging.

3.3 Trajectory Rendering

To visualize the particle (atom) trajectories, we

render a series of connected line segments for each

trajectory by using the original positions (no

merging) or new (merged) positions at different

levels of merging. The user may choose to display

single trajectory for a selected atom or a subset of

trajectories corresponding to an atomic species or a

group of atoms (e.g., SiO

unit), or trajectories for

all constituent atoms.

Successive positions generated by the final

hierarchical level merging are well separated (by

more than the cut-off distance) so trajectories are no

longer smooth and can be visually distracting. This

becomes more serious when larger cut-offs are used.

We perform a piece-wise smoothing of line

segments by generating cubic and quadratic Bézier

curves. A subset of merged positions along the

trajectory is used as control points in the Bézier

equation to generate the local curves. Additional

information about the material system in question

can be extracted on the fly and encoded along the

trajectories using a color map.

4 RESULTS AND DISCUSSION

How much the trajectories are cluttered/crowded

depends on the size of the data and the nature of the

atomic movements. Here, we present our case

studies by visualizing complete position-time series

of two material systems (silicate and silica liquids)

mentioned earlier.

4.1 Effects of Space Window Size

For a given data set, the size of space window (cut-

off) applied controls the degree of clutter reduction

to a great extent. Larger the cut-off, more positions

merged along the trajectories and less crowdedness

(Figure 3). However, too wide space windows can

cover multiple localities and new positions produced

by merging process may be too few to approximate

the trajectory geometry to any acceptable level

(Figure 3, right). There is a trade-off between cut-off

(clutter measure) and the trajectory geometry.

The choice of the space cut-off requires domain

ClutterReductioninRenderingofParticle(Atom)TrajectorieswithAdaptivePositionMerging

267

Figure 3: Effects of the space window (cutoff) size on the trajectory geometry. One H trajectory (top row) and one Si

trajectory (bottom row) are processed using four different cutoffs. On increasing cutoff from left to right, the trajectories

become simpler with local features disappearing more and more. The final trajectory (right) in each case fails to preserve

the overall geometry. The color encodes time information along the original and processed trajectories.

specific knowledge and some pre-processing of a

given position-time series data (such as radial

distribution function and mean square

displacement). Our adaptive approach allows the

user to adjust the space cut-off by considering a few

factors such as the number of trajectories, the shape

and extent of trajectories, the desired level of clutter

reduction, and the degree of trajectory

approximation. For instance, if a single trajectory

(one selected atom) or a few trajectories (atoms

forming a structural unit or cluster) are visualized, a

small cut-off may reduce the associated clutter to an

acceptable level. However, if many (corresponding

to all atoms of one species) or entire trajectories are

rendered, relatively large cut-offs are needed.

4.2 Visualization of Trajectories

A detailed visualization of trajectories of hydrous

silicate (MgSiO

) and pure silica (SiO

) liquids

shows us that the atomic movements involve two

types of motion: extended portions of the trajectories

represent rapid continuous motion whereas the

crowded portions represent confined (oscillating)

motion. The atoms jump from one confined region

to another in relatively short time interval.

For the hydrous system, each trajectory of each

species (H, Mg, Si, and O) is obtained by rendering

60,000 successive positions occupied by the

corresponding atom. Here we display 16 H

trajectories obtained by processing about one million

positions in the total (Figure 4). They start from the

respective initial atomic positions all lying within

the supercell and they eventually extend beyond the

super-cell reaching as 3 or 4 times the supercell

length. Note that H atoms are the most mobile

species. It is difficult to trace these trajectories

except in the outermost regions. Also, any atomic

structures such as initial configurations shown by

atomic spheres can hardly be seen. The H

trajectories are approximated using our adaptive

position merging approach with a cut-off 1.5Å and

five levels of merging (Figure 4). This process

suppresses local wiggling features and reduces the

number of positions along the trajectories.

Individual trajectories can be seen almost

everywhere and all atomic spheres are visible.

During visualization process, the user can explore

the complete trajectory geometry with the aid of

operations like rotation, translation, scaling, and

highlighting.

The atoms in the silica liquid are very slow

covering relatively small distances even over much

longer simulation duration. In other words, the

atoms are trapped locally most of the time. The Si

trajectories obtained by rendering one million

positions per atom are highly confined to narrow

regions and they extend very little outside the

supercell (Figure 5). Different trajectories tend to

form distinct regions displayed with different colors

but these regions overlap among each other. It is

difficult to assess the shape and extent of these

trajectories because the geometric structures are

almost invisible. Our adaptive hierarchical position

merging approach is expected to be useful.

4.3 Performance Analysis

The effectiveness of position merging along the

trajectories can be assessed by counting the number

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268

Figure 4: Trajectories of 16 H atoms (each colored differently) in hydrous silicate liquid after hierarchical merging.

Figure 5: Trajectories of 24 Si atoms (each colored differently) in silica liquid after hierarchical merging.

of final (merged) positions used for trajectory

rendering, examining the geometries (shape and

extent) of individual trajectories, and having a

measure (qualitative) of clutter reduction in

visualization of trajectories and atomic structures.

Key factors relevant for this assessment include

space window size (cut-off distance), hierarchical

merging level, and also imposed information

constraint. Here, we present a performance analysis

considering two cases: weak merging (with a narrow

space window) and strong merging (with a wide

space window) for each species trajectory for both

material systems.

As shown in Table 1, the effects of window size

(or cut-off) are substantial. For H trajectories,

merging with a cut-off of 0.8Å involves 5

hierarchical levels and yields 16,450 final points

compared to about 1 million original positions. The

visibility of the trajectories improves considerably

and some atomic spheres start to appear. When a

larger cut-off of 1.5Å is used (again with 5

hierarchical levels) the number of final positions

drops to 3,170 – a reduction by a factor of 300 with

respect the original positions. The individual

trajectories and underlying atomic structure become

visible. For O trajectories, the number of final

positions drops from about 9,000 (weak merging) to

1,770 (strong merging), compared to 2.6 million

original positions. Similarly, the number of final

positions drops by a factor of 4 and 6 between the

two cases of merging for Mg and Si trajectories,

respectively. A relatively larger effect is seen for Si

trajectories because most of them are more confined.

Position merging along atomic trajectories for

silica liquid is much more sensitive to window size

than that for hydrous silicate liquid. A weak merging

along Si trajectories using a cut-off of 0.5Å saturates

at the 8

level and generates around 57 thousands

positions, compared to the original 24 million

positions. The number of reduced (final) positions

drops to around 4 thousands with somewhat larger

cut-off (0.7Å). The overall reduction in the number

of positions needed for trajectory rendering is by a

factor of about 6,200. Thus, a much smaller set of

processed positions, which represents only 0.016 %

of the original positional data are rendered thereby

dramatically reducing clutter in rendering of Si

trajectories. Since O atoms cover longer distances,

we use larger cut-offs of 0.8Å (weak merging) and

1.2Å (strong merging). The weak merging yields

ClutterReductioninRenderingofParticle(Atom)TrajectorieswithAdaptivePositionMerging

269

Table 1: Number of atomic positions, original and after merging, of individual atom species in hydrous silicate liquid (top

part), and silica liquid (bottom part) for weak merging (small cut-offs) and strong merging (large cut-offs). Number of

positions after first level merging at corresponding cut-off is presented inside the parentheses. The last column represents

the number of positions for a constrained merging with large cut-off.

Original Weak Merging Strong Merging

Cutoff Levels Positions Cutoff Levels Positions Constrained merging

H 960,000 0.8 5 16,450

(24,710)

1.5 5 3,170

(7,160)

15,630

(16,830)

Mg 720,000 0.5 4 6,818

(7,975)

1.0 4 1,585

(2,520)

14,000

(14.015)

Si 720,000 0.5 4 2,920

(4,540)

1.0 3 510

(740)

1,975

(2.115)

O 2,640,000 0.8 5 8,945

(14,125)

1.5 4 1,770

(2,615)

5,480

(6,170)

Si 24 millions 0.5 8 57,420

(507,490)

0.7 5 3,865

(12,055)

51,530

(75,110)

O 48 millions 0.8 8 93,880

(989,570)

1.2 6 3,150

(12,290)

Figure 6: Trajectories of H atoms with color-coded coordination information with respect to O atom (red: singly

coordinated, yellow double coordinated), before (left) and after (right) constrained merging with cut-off of 1.50Å.

little less than one hundred thousand positions, and

the strong merging case yields much fewer positions

(3,000 positions) for reduced trajectory, which

represent about 0.0066 % of the original positional

data and results in a much improved visibility.

The number of hierarchical levels needed to

saturate merging varies somewhat depending on the

space cut-off and atomic species. This number spans

the range of 3 to 5 for two cases (weak and strong

merging) considered for all species of hydrous

silicate. The number is higher (5 to 8 levels) for Si

and O trajectories of silica. Hierarchical merging

tends to continue deeper for the cases of highly

confined trajectories. The number of new (merged)

positions along trajectories decreases as merging

goes deeper the merger hierarchy. As shown in

Table 1, the numbers of positions differ significantly

between the first level and the final level of

hierarchical merging in both weak and strong

merging.

Finally, we consider the sensitivity of position

merging to a coordination information constraint

(Figure 6). As shown in Table 1, fewer levels are

needed to saturate merging in the hierarchy, and the

number of final positions generated by merging

along H trajectories, with H-O coordination as

constraint, increases from around 3,000 (for original

merging) to above 15,000 for a cut-off of 1.5Å.

Similar increases in the number of final positions

were found for other cases.

5 CONCLUSIONS

We have presented an improvement in atomistic

visualization of position-time series data obtained

from molecular dynamics simulations of real

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270

materials by rendering both the atom (particle)

trajectories and instantaneous structures. To reduce

the clutter caused by the crowded trajectories, we

perform adaptive hierarchical merging of multiple

positions along the trajectories. According to our

approach, the multiple positions to be merged at

each level are picked up using a proximity window,

which is defined in terms of space window (distance

cutoff). Our analysis shows that the number of

effective positions needed to render the trajectories

decreases dramatically under merging (with/out

information constraint) and the processed (reduced)

trajectories show significantly reduced clutter. We

can further enhance the visualization process by

encoding additional information (time, 3D position,

coordination number, and merge count) along the

trajectories. Improved trajectories allow us to better

assess the nature and extent of the corresponding

atomic movements. In particular, they suggest that

atoms move via discrete jumps (hopping-like

motion) in addition to continuous forward motion.

More importantly, the underlying atomic structures

become visible with all trajectories rendered. While

moderate-size data sets containing several millions

of data points (atomic positions) were considered in

this study, we anticipate to extend the proposed

position merging to larger data sets produced by

large-scale molecular dynamics simulations.

ACKNOWLEDGEMENTS

This work is supported in part by a grant from

National Science Foundation (EAR 1118869).

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