Visual-auditory Volume Rendering of Dynamic Quantum Chemistry

Molecular Fields

Evgeniya Malikova

, Valery Adzhiev

, Oleg Fryazinov

and Alexander Pasko

1,2

Bournemouth University, Bournemouth, U.K.

Skolkovo Institute of Science and Technology, Moscow, Russia

Keywords:

Volume Rendering, Visual-auditory Ray-casting, Signed Distance Fields, Multi-scale Visualisation, Molecular

Visualisation.

Abstract:

This work deals with a visual-auditory visualisation of dynamic heterogeneous objects represented by contin-

uous scalar ﬁelds obtained from quantum chemistry. The research concentrates on complex phenomena mod-

elling and rendering aspects and takes advantage of GPU implementation. The approach uses the constructive

HyperVolume for the multi-scale representation of the molecular phenomena. To propose an approach to the

visual-auditory rendering, we adapt the real-time interactive volume ray-casting to compute the optical and

auditory properties. We demonstrate the approach application for the visual-auditory rendering of dynamic

molecular structures.

1 INTRODUCTION

As computer simulations or experimental studies are

involved, scalar ﬁelds are used in many research areas

such as computational chemistry, medical data anal-

ysis and physical phenomena studies. We consider

an example of the analysis of the molecular struc-

tures that are dynamic objects with internal properties

and geometry changing in time. As the detailed and

accurate study of the properties of molecular struc-

ture can be computationally expensive, the analysis

of the molecular structures beneﬁts from simultane-

ous use of representations of various objects’ prop-

erties (Wahle and Wriggers, 2015) that are obtained

with different computational procedures. We consider

a particular case study of dynamic molecular struc-

tures obtained by the quantum chemistry simulation.

The modelling, rendering and visual analysis of

such multi-scale representations of the phenomena

are not straightforward. In Volume Rendering the

problem is addressed with the use of Multidimen-

sional Transfer Functions (TF) (Kniss et al., 2003)

and optical models with complex object-light interac-

tions (Wahle and Wriggers, 2015). Those techniques

are used to improve the quality of visual analysis and

to highlight features of interest. However, limitations

of the visual perception can not be avoided solely with

the enhancement of the optical model. The visual

system can be overloaded and perturbed due to the

fatigue of the user. An introduction of auditory sen-

sory stimuli is a well-known technique that is used to

address a problem of visual analysis limitations (Her-

mann et al., 2011). For scalar data analysis problem,

the works (Lodha et al., 1997) and (Gionfrida and Ro-

ginska, 2017) introduce the auditory analysis to ad-

dress the problems, where the visual analysis fails.

We suggest a simultaneous visual-auditory analy-

sis as a tool to address a problem of molecular struc-

tures complexity for a particular problem of the re-

sults of quantum chemistry problem study. The main

contributions of this work are the following:

1. We propose a uniﬁed approach to the visual-

auditory study of the physical phenomena the

molecular ﬁelds based on ray-casting.

2. We take advantage of HyperVolume (HV)

(Pasko et al., 2001) model for scene representa-

tion as a dynamic heterogeneous object with vi-

sual and auditory properties.

3. We consider the case study of the molecular struc-

ture, that is a result of quantum simulation, to per-

form simultaneous visual-auditory analysis to get

insight into the multi-scale representation of the

phenomena.

We demonstrate how the GPU implementation of the

constructive approach for HV scene can be used to ef-

ﬁciently perform simultaneous visual-auditory analy-

sis on the base of the ray-casting procedure.

Malikova, E., Adzhiev, V., Fryazinov, O. and Pasko, A.

Visual-auditory Volume Rendering of Dynamic Quantum Chemistry Molecular Fields.

DOI: 10.5220/0008957001930200

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 3: IVAPP, pages

193-200

ISBN: 978-989-758-402-2; ISSN: 2184-4321

193

2 BACKGROUND AND RELATED

WORKS

2.1 Volume Rendering of Scalar Fields

A scalar ﬁeld is a mapping f : x → ℜ,x ∈ ℜ

, which

associates any point in space with a scalar value. Vi-

sualisation of scalar ﬁelds usually employs Volume

Rendering technique that operates the initial data as

volumes that are stored in the texture memory.

The conventional Volume Rendering scheme sug-

gests the volume boundary (or scalar ﬁeld domain)

is deﬁned by a bounding box. The ray/volume inter-

section is computed to deﬁne the ray’s start and end

points and after the equations 1,2 are solved with the

ray-marching procedure (Fig. 1 (a)).

(a)

(b) (c)

Figure 1: Volume Rendering a) Schematic representation of

basic ray tracing for Volume rendering; b) Sphere-tracing

scheme (Hart, 1996); c) SDF accelerated Volume Rendering

on basis of sphere-tracing scheme.

In Volume Rendering a simple model of light in-

teraction with an object considers only emission and

absorption (J

onsson et al., 2014):

L(~x

ω ) = T (~x

,~x

)L(~x

ω )+

T (~x

,~x

)E(~x

)d~x

(1)

where L(~x

ω ) is an intensity at the point x

;

T (~x

,~x

) = e

−

(~x )d~x

is an attenuation of light

as it travels from the point x

to x

deﬁned in the

general case by an extinction coefﬁcient σ

(~x

) =

(~x

) + σ

(~x

) that takes into account absorption

and scattering (not considered in this model); E(~x

)

is a light contribution at the point x

, in other words,

the term describing emission process that can be writ-

ten as σ

(~x

) ∗ L

(~x

ω ).

The extended equation takes into account a single

light scattering (Max and Chen, 2010) and is also con-

sidered for an interactive Volume Rendering (J

onsson

et al., 2014):

L(~x

ω) = T (~x

,~x

)L(~x

ω)+

(σ

(~x

) ∗ L

(~x

+ σ

(~x

)∗

(~x

ω))T (~x

,~x

))d~x

(2)

where L

(~x

ω) represents the scattered radiance in

the direction

ω.

The shading and depth perception can provide an

addition to 3D shape cues and thus enhance visual

analysis and highlight the features of interest (Kniss

et al., 2003). The Blinn-Phong model (Levoy, 1988)

was an initial enhancement of the classical emission-

absorption model 1. This model is widely used in Vol-

ume Rendering to highlight features of interest such

as edges (J

onsson et al., 2014), although it was de-

signed for shading the surfaces and can produce dark

regions (Kniss et al., 2003).

Complex optical model computation like in the

equation 2 allows to signiﬁcantly enhance visual anal-

ysis quality (Wahle and Wriggers, 2015), however,

are still computationally expensive (J

onsson et al.,

2014) for the interactive and dynamic Volume Ren-

dering.

Computation of complex optical models for in-

teractive Volume Rendering takes advantage of mod-

ern graphics hardware (Schlegel et al., 2011). The

modern algorithms often employ the idea of splitting

the optical model computation into separate parts,

mainly concerned with the lighting conditions that

can be precomputed into textures independently and

updated on-demand (Kniss et al., 2003), (Schlegel

et al., 2011).

The other tool to address the complexity of stud-

ied phenomena in Volume Rendering is the Multidi-

mensional Transfer Function (TF) (Kniss et al., 2003).

TFs are used to address a problem of simultaneous

visual analysis of more complex objects represented

with two and more scalar ﬁelds describing various

object properties. In this research, we consider a

distance-based TF in Volume Rendering that high-

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

194

lights features of interest mostly determined by the

distance to reference structures (Tappenbeck et al.,

2006). Those type of TFs takes advantage of Signed

Signed Distance Field (SDF).

The Signed Distance Field (SDF) is a type of a

scalar ﬁeld, where the scalar value takes the value of

a distance to the surface dS of a solid object S(Jones

et al., 2006). The distance property of SDF allows for

efﬁcient ray-casting (Hart, 1996) and efﬁcient compu-

tation of complex light-object interactions in optical

model. Moreover, in this research, we will take ad-

vantage of the GPU implementation of the construc-

tive approach for the entire dynamic volume scene

modelling (Wang et al., 2011) based on SDF.

2.2 Auditory Properties

The auditory model often takes advantage of simi-

larities in light and sound propagation (Takala and

Hahn, 1992). The acoustic rendering equation (Sil-

tanen et al., 2007) is a time-dependent version of the

general rendering equation (Kajiya, 1986) that is a

basis of the optical Volume Rendering models (Max

and Chen, 2010). The sound propagation and au-

ditory perception of this process to model auditory

feedback (McArthur et al., 2017) are open research

areas in augmented (Ribeiro et al., 2012) and virtual

(Begault, 1994) reality. Auditory stimuli are well-

known tools in molecular structures interactive study

(Liu and van der Heide, 2019) that is often consid-

ered as an alternative to haptic ones in the traditional

area of their application. The reason is that it does not

have to deal with haptic device limitations and allows

for mapping and perception of a much wider range of

properties (May et al., 2019).

The auditory study of volumetric structures as a

part of data analysis is an open research area (Gion-

frida and Roginska, 2017), (Malikova et al., 2019).

The interpretation of sound parameters for the au-

ditory analysis and control of the auditory represen-

tation of the phenomena can be not straightforward

(Hermann, 2018). Thus, the research in the area

mostly deals with the design of auditory mapping pro-

cedures for speciﬁc applications (Gionfrida and Ro-

ginska, 2017).

In this work, we take advantage of similarities in

the light and sound propagation to introduce an audi-

tory model based on sound wave generation as a result

of impulse propagation through the object. Thus, we

consider the ray-tracing technique for the simultane-

ous visual-auditory rendering of multi-scale phenom-

ena.

We discuss auditory feedback as distance-based

guidance or measurement procedure. For such pro-

cedures design, we consider the physical process

of sound propagation. Thus, the proposed auditory

model allows natural perception and interpretation of

the distance-dependent aspects of objects-sound wave

interaction. An auditory guidance procedure can be

used to inform of the spatial orientation and position

while interacting with virtual objects. A measurement

procedure allows tracking of small changes in fea-

tures of dynamic phenomena. As the visual system

can be fully engaged while performing a complex per-

ception task, the additional source of information pro-

vided through other sensory stimuli is needed (Hou

and Sourina, 2011). Thus, such auditory procedures

are quite important.

The conceptual framework for the introduced pro-

cedures is based on sound propagation the digital

waveguide approach to physically-based sound syn-

thesis (Cook, 2002). We consider the use of a basic

plucked string (Smith, 1992) model that allows au-

ditory tracking of even the small changes in the dis-

tance of sound propagation with a pitch characteristic

of sound.

3 OUR APPROACH TO

VISUAL-AUDITORY ANALYSIS

OF MOLECULAR FIELDS

Let us consider the case of the molecular structure

that is a result of quantum simulation as the two main

models are used for the phenomena analysis. The

most common geometrical representation of molec-

ular structures is the ”Balls and Stick” model (Berg

et al., 2002) (Fig. 2) (a). The model suggests that

atoms are represented with spheres and atomic radii

and distance between atoms approximate bonds be-

tween atoms and their types. Despite these simpli-

ﬁcations, this model is good for measurements and

monitoring of distance-related parameters.

Another model arises from quantum chemistry

calculations and concentrates on the analysis of more

complex abstraction for the representation of the

molecular structure (Shusterman and Strauss, 2001)

that usually suggests the necessity of simultaneous

analysis of two scalar ﬁelds. The shape of the Elec-

tron density ﬁeld is treated like molecule interaction

boundary as it deﬁnes a probability of an electron oc-

cupying an inﬁnitesimal element of space surround-

ing any given point. At the same time, its topological

analyses provide a deeper understanding of bonding.

The Electrostatic potential ﬁeld represents a charge

distribution, a property that allows predicting the be-

haviour of complex molecules. In the ideal case, the

Visual-auditory Volume Rendering of Dynamic Quantum Chemistry Molecular Fields

195

Figure 2: Selected frames of dynamic Volume Rendering of the chemical transformation from HCN to the HNC isomer. Balls

and Stick model (a) and quantum chemistry model (b).

user should be able to analyse both of those ﬁelds si-

multaneously (Shusterman and Strauss, 2001). Un-

like balls and sticks, this model allows for more ac-

curate analysis of the properties of a molecular phe-

nomenon such as bonding, although its computation

is expensive (see Fig. 2)(b)).

In our visual-auditory approach, we are employ-

ing both models in the analysis process keeping in

mind the dynamic nature of the phenomena. As a

case study, we analyse the dynamic reaction of the

transformation of HCN to the HNC isomer (see Fig.

2). We employ dynamic Volume Rendering for si-

multaneous visual analysis of changes in both scalar

ﬁelds of quantum chemistry model (see Fig. 2 (b)).

We consider the auditory analysis as a well-proven

tool for monitoring of small changes in dynamic char-

acteristics and employ it for simultaneous measure-

ments performed on the ”Balls and Stick” model (see

Fig. 2)(a). Below we will consider the HyperVol-

ume model for the multi-scale representation of the

phenomena and its further rendering to visual and au-

ditory stimuli.

3.1 HyperVolume Model

We use a HyperVolume (HV) model to describe a

studied phenomena through a tuple:

m(t) = (G(t),A

(t),A

(t)) : (F(X|t),S

(X|t), S

(X|t))

(3)

where G(t) is dynamic geometry described with func-

tion F(X|t); S

(X|t) and S

(X|t) are point attribute

functions S deﬁning optical A

and auditory A

prop-

erties of heterogeneous object.

Thus, we deﬁne a vector-valued function. The ﬁrst

component F is responsible for the object geometry

G. In our approach F is an SDF, which is obtained

from the input scalar ﬁeld by using signed distance

transform (Jones et al., 2006). The auditory properties

in the form of the generated sound wave are deﬁned

with S

(X) . The attribute S

(X) deﬁnes the results

of mapping to the optical properties such as colour

and opacity. Note that in the general case attributes S

are not scalars but vectors. For example, the colour

and transparency information in S

is normally repre-

sented as a four-component RGBA value.

In the case of the molecular structure, the dynamic

geometry G(t) is represented with electron density

ﬁeld isosurface as it is interpreted as a molecule in-

teraction boundary. The optical model S

(X) is used

for visual analysis of the quantum chemistry phenom-

ena representation. The auditory model S

(X) is used

to judge about the dynamic change of measured char-

acteristics performed on the basic ”Ball and Sticks”

model. In this case study, we consider its use for bond

length measurement.

The SDF-based ray-tracing is used for dynamic

visual-auditory rendering of multi-scale objects. We

use the constructive approach for modelling S

(X|t)

and S

(X|t) attributes of dynamic object m(t) (Pasko

et al., 2001) with SDF based geometry representation

for F(X |t) and implement most of visual-auditory

analysis pipeline on GPU (see section 4). Below we

consider optical and auditory models in more detail.

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

196

3.2 Optical Model for Ray-casting

The main target of the optical model S

(X) in equa-

tion 3 is to allow the user getting insight into the

molecular phenomena through colour and opacity. To

address the problem of complex phenomena repre-

sented with two scalar ﬁelds (Electron density and

Electrostatic potential) visualisation, we propose a

custom distance-based TF, that operates those two

ﬁelds simultaneously. We consider optical models

described with equations 1 and 2 for visual analysis

quality enhancement.

The emission-absorption 1 based S

(x) was not

particularly efﬁcient. We had to adjust the trans-

parency value to handle dark regions that made the

model look like a set of coloured isosurfaces (see

Fig.3(a)). The single scattering with a colour blending

allowed assessing both changes of the Electron Den-

sity isosurface shape and the Electrostatic Potential

distribution (see Fig.3(b)).

The results of conventional Volume Rendering for

various models S

(x), we have suggested for HCN

molecule case study, are presented in Fig. 3. Below

we will describe the proposed distance-based TF. The

use of SDF allows for optical model accelerated com-

putation of lightning and scattering.

3.2.1 Transfer Function

To deﬁne a distance-based TF, we consider the Blinn-

Phong model and use the SDF object geometry deﬁ-

nition. The proposed TF highlights the shape of Elec-

tron Density Field and to allows judging on the value

of the Electrostatic Potential Field. We employ the

specular and diffuse shading to provide highlights of

both scalar ﬁelds and especially closer to the ”atom”

regions.

As described in (Levoy, 1988), a numerical optical

model for colour at i-th voxel C

= C(x

) for a parallel

light source is:

= c

· k

+ k

· d(x

)

(

N(x

) ·

L ) + k

(

N(x

) ·

H )

] (4)

where

N(x

) is a surface normal at voxel x

location,

L is a normalised vector in the direction of the light

source,

H is a normalised vector in the direction of

maximum highlight; c

is a component of colour par-

allel to the light source; k

are constants used in

a linear approximation of the depth-queuing; d(x

) is

perpendicular distance from the picture plane to the

voxel location x

The ambient, diffuse, specular coefﬁcients k

are vary at different parts of the volume and are

Figure 3: Volume Rendering of the HCN molecule. Render-

ing with introduced TF and the following optical models: a)

without scattering; b) with basic single scattering.

controlled by the SDF value of the Electron Density

Field in order to highlight how colour is distributed on

selected isosurfaces. We multiply the opacity value

of the TF by the coefﬁcient controlling the isosurface

highlight o

: o

= o

d(x

)

max

· |

d(x

)

max

· π · f |, where f is a

number of isosurfaces; d

max

is a maximum value of

the distance ﬁeld; o

is a basic coefﬁcient that is the

maximum o

value can take. If o

is greater than a

certain threshold value we apply surface shading with

and k

values equal to o

3.3 Auditory Model for Ray-casting

The proposed approach allows the visual-auditory

analysis of both quantum chemistry and ”Balls and

Sticks” representations. The optical property S

(X)

allows judging on phenomena through colour and

opacity. The sound perception has the potential to

provide a wider range of auditory entities for inter-

pretation such as pitch, volume, duration, rhythm, etc.

We employ the physical process of sound propaga-

Visual-auditory Volume Rendering of Dynamic Quantum Chemistry Molecular Fields

197

tion to directly construct a sound wave representation.

We consider the task of auditory analysis through the

pitch of the dynamic length changes in NC bond for

the dynamic chemical reaction of transformation from

the HCN to the HNC isomer.

The atoms of ”Balls and Sticks” model are repre-

sented as SDF spheres Sp

,Sp

with sufﬁciently

small radii. We take advantage of an ideal string

model to render distance property of NC bond to

sound wave and judge about the bond length through

the pitch. The process is schematically presented in

Fig. 4 and is described as follows.

Figure 4: Rendering to auditory stimuli. Schematic repre-

sentation of ray-casting the length of NC bond and mapping

it into the sound with the ideal string model.

We adapt the travelling wave solution for an ideal

plucked string (Smith, 1992) for introduced auditory

model. The result of an initial impulse of the plucked

string travelling wave y(x,t) can be represented as a

sum of the right going y

(x − ct) and left going y

(x +

ct) waves (see Fig. 4 (b)).

The travelling waves are simulated through the de-

lay lines. Once the initial waves are generated as a

result of a string picking, they travel along the string.

Thus, the time impulse needs to pass the distance till

it is reﬂected. The propagation process is aurally per-

ceived through the pitch: l = 2 ∗ R/p, where R is a

sampling rate, string length l and p is a perceived

pitch. We perform auditory analysis to judge on small

changes and we use the ray-casting procedure to com-

pute the sound wave.

4 IMPLEMENTATION

The HV model is described through a construction

tree. The leaves are initial scalar ﬁelds data loaded

to GPU memory as 3D textures, and the nodes are op-

erations similar to the initial idea presented in (Pasko

et al., 2001). The conventional TF is considered as

the ”node of operation” within the construction tree

of the HV model.

We take advantage of the modern CUDA graph

API (NVIDIA, 2019) to describe such construction

trees and render them to textures on-demand with the

updated parameters. The ﬁnal 3D textures represent

the HV model m(t) and the lighting conditions. Those

textures are sampled during the conventional Volume

Rendering and auditory feedback computation (see

the example in Fig. 5). The GPU data ﬂow model al-

lows integration of image processing techniques that

can be implemented as graph nodes applied to tex-

ture volumes with CUDA graph API. Currently, we

have considered a basic case of ”host” implementa-

tion with Image Processing Toolkit (ITK) (Johnson

et al., 2015), to extract the centres of SDF spheres

,Sp

that represent the atoms of the molecule

from scalar ﬁelds.

The ﬁnal visual-auditory scene is presented as a

set of objects S = (HV,SDF

,L), where HV are Hy-

perVolume representations in a form of a tuple de-

scribed above; SDF

is a set of the SDF geometry in

the scene; L are the precomputed lighting conditions

for the scene. This representation naively supports

further extension with interactive procedures that pro-

vide auditory feedback. The further extension can be

introduced on the same basis of SDF geometry mod-

elling and ray tracing.

The different parts of the scene in Fig. 5 repre-

sentation are evaluated in advance, stored as textures

and updated on-demand (see section 2.1 for details).

The proposed approach handles the rendering of both

surfaces and volume objects in a similar way. Thus,

the entire scene is procedurally modelled, stored and

rendered on GPU. Below we describe the obtained re-

sults for dynamic visual-auditory molecular phenom-

ena study.

5 RESULTS

We analyse the dynamic reaction of the transforma-

tion of HCN to the HNC isomer (see Fig. 2) through

the obtained visual-auditory image of the phenomena.

The initial data is a sample data from the GAMESS

software package (M.W.Schmidt et al., 1993) that de-

scribes an HCN initial saddle point state before the

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

198

Figure 5: The CUDA implementation scheme of the HyperVolume model construction tree for the the process of HCN to the

HNC isomer reaction.

HNC isomer reaction and the ﬁnal state - HNC iso-

mer (see Fig.2(a,b)). The results of visual-auditory

rendering are presented in the accompanying video.

We use the auditory feedback for measurements per-

formed on the molecular structure.

As an example, we use it to highlight a process

of small changes of CN bond length in HNC iso-

mer reaction dynamic process (Fig. 2(a)) and judge

about the dynamic change of distance through the

pitch. The process is schematically presented in Fig.

4 (b). The pitch changes from lower to higher values

as the distance becomes smaller. At the same time,

we judge visually on dynamic change within quantum

chemistry representation of the molecular phenomena

through the dynamic Volume Rendering.

6 CONCLUSIONS AND

DISCUSSION

This paper presents a novel approach to the scientiﬁc

visualisation of complex physical phenomena such as

dynamic molecular ﬁelds based on the visual-auditory

Volume Rendering. The proposed solution is based

on the techniques used for multi-scale, heterogeneous

objects modelling and rendering. The main features

of the approach are HyperVolume model for visual-

auditory scene representation and ray-casting to vi-

sual and auditory stimuli.

We have addressed a particular problem of anal-

ysis of molecular ﬁelds that are results of quantum

chemistry simulation. Taking this case study as an ex-

ample, we have demonstrated how the visual-auditory

analysis based on the presented approach can be used

to get insight into dynamic multi-scale phenomena as

solely visual analysis can be challenging. We have

implemented our approach on GPU, demonstrated its

ﬂexibility and considered the representative case stud-

ies. The approach allows GPU data ﬂow for visual-

auditory Volume Rendering.

The SDF technique has applications in image pro-

cessing tasks and is an essential part of computa-

tionally expensive interactive procedures, like colli-

sion detection. The proposed approach has the poten-

tial to combine the heterogeneous objects modelling

procedures and the conventional image processing on

GPU. The proposed approach further extension will

also consider the interactive visual-auditory rendering

tasks that target the enhancement of molecule editing

and other interactive exploration procedures.

So far we have considered the basic optical model

and have taken into account only single scattering.

Rendering of more complex auditory and optical

models is the area of future research. Exploring multi-

scale object shapes and internal properties through the

perception of the spatial 3D sound is on our agenda.

Visual-auditory Volume Rendering of Dynamic Quantum Chemistry Molecular Fields

199

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