芸術科学会論文誌 Vol.11, No.4, pp. 118 – 128

炭酸水から生じる気泡のビジュアルシミュレーション
金森 由博 1) (正会員) 西川 武志 2)
Yonghao Yue2) (正会員) 西田 友是 2) (正会員)
1) 筑波大学

2) 東京大学

Visual Simulation of Bubbles in Carbonated Water1
Yoshihiro Kanamori1) Takeshi Nishikawa2)
Yonghao Yue2) Tomoyuki Nishita2)
1) University of Tsukuba
2) The University of Tokyo
kanamori@cs.tsukuba.ac.jp, {takeshi,yonghao,nis}@nis-lab.is.s.u-tokyo.ac.jp

概要
本論文では，炭酸水における気泡の生成，成長および運動の簡易なシミュレーション手法を提案する．気泡は，グラス，マドラー，炭酸水中の微小なほこりといった物体表面上の，小さな空気孔から発生することが知られている．気泡の数や生成速度は，物体の材質によって異なる．さらに物体の材質によって物体表面での気泡の挙動も異なる．プラスチックやアクリルといった材質の場合，気泡はゆっくりと表面を滑るように浮上するが，ステンレスのような材質ではそのような挙動は見られない．提案手法ではこのような差異を，空気孔の数を制御し，気泡に対する物体表面への付着力を導入することによって表現できる．炭酸水中の気泡は十分に小さいので，提案法では気泡を変形しない球体として扱う．格子法を用いて炭酸水の流れを計算することで提案法では気泡と炭酸水の対流を同期させている．さらに，複雑な気泡の挙動を再現するため気泡同士の衝突や融合も考慮している．

Abstract
In this paper, we propose a simple method for simulating the generation, growth and motion of bubbles in carbonatedwater. Bubbles are known to be generated at small air pockets on the surfaces of objects, such as a glass or a stirrer,
and on the microscopic dusts in carbonated water. The number of bubbles and their growth rates differ according to
the materials of the objects. In addition, the motion of bubbles also differs according to the materials; bubbles slowly
glide on plastic and acrylic surfaces whereas such motions cannot be seen on a stainless-steel surface. Our method
can represent such differences by controlling the number of generation points (i.e., air pockets) and applying adhesion
forces to make bubbles stick on the surfaces. Because bubbles in carbonated water are sufficiently small, our method
regards bubbles as non-deformable spherical particles. We simulate the flow in carbonated water using a grid-based
method, together with the two-way coupling technique between bubbles and the convective flow. Additionally, thecollisions and fusions among bubbles are also handled to reproduce the complex behavior of bubbles.
1 この論文は NICOGRAPH International 2012 に投稿した論文 [1] を芸術科学会論文誌に投稿するものである．

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1 Introduction
Water is so ubiquitous in our daily life that we unconsciously memorize its fascinating behavior. The demandsof creating realistic water animations have therefore beenquite high in computer graphics. Until recently, water
animations have been somewhat artificial in spite of the
progress of simulation techniques, because bubbles havebeen ignored to reduce the computational cost.
Recently, bubble simulations have gained attentions to
reproduce various phenomena including boiling [3] and air
trapping [5]. Cleary et al. [6] handled simulations of bubFigure 1: Photographs of objects in carbonated wables in carbonated water; however, their method suffersfrom the quite high computation cost, and cannot suffi- ter. Left: a wooden stirrer, right: a plastic spoon.
ciently reproduce the interesting behavior of bubbles around The amount of bubbles differs due to the difference
object surfaces, which is essential to represent the realistic of materials.
appearance of carbonated water.
Here, we describe the behavior of bubbles in carbonated water. Bubbles are known to be generated at small
surfaces (Figure 1, right). Our method handles the bubair pockets on the surfaces of objects, such as a glass or
bles’ motion due to the convection flow by representing
a stirrer, and on the microscopic dusts in carbonated wabubbles with particles and the flow with the Eulerian gridter. In this paper, such air pockets are called generation
based method [9], and computing the two-way coupling [10]points. The number and capacities of generation points
between the bubbles and the flow. The reality of the bublargely depend on the materials of objects, resulting in theble motion is further enhanced by handling the rebounddifferences of the amount and sizes of generated bubbles.
and fusion of bubbles when they collide. Unlike Cleary et
For example, bubbles are rapidly generated from a woodenal.’s model, our simple model is computationally inexpenstirrer due to the vast amount of generation points on its
sive, and thus suited for interactive applications.
porous surface (Figure 1). The duration in which eachbubble adheres to the surface also differs according to materials. Such difference of the duration yields various sizesof bubbles because bubbles keep growing by absorbing
over-condensed gases resolved in carbonated water. Af- Simulations of liquids including water belong to the mostter leaving the surface, bubbles rise along the convection important themes in the research of computer graphics.
flow caused by the stream of bubbles.
Here we elaborate on the related methods that handle theIn this paper, we propose a method for generating re- behavior of bubbles in liquids.
alistic animations of bubbles in carbonated water, with
Hong et al. [8] simulated deformations and coalescence
special interests in the behavior of bubbles around object of large bubbles by combining the Volume of Fluid (VOF)
surfaces, as described above. Our method controls the method and the front-tracking method. Song et al. [11]amount of bubbles by adjusting the number of generation used the Constrained Interpolation Profile (CIP) method
points on the object surface. Regarding the phenomenon to accurately calculate advection in the simulation of multhat bubbles adhere to object surfaces, the physical princi- tiphase flows. They handled bubbles that are generated
ple is not clearly known to the best of our knowledge. In- by the air trapped when objects are fallen into the water.
stead of seeking the faithful physical law, we simply model There are also several methods for bubbles generated via
the adhesion by introducing a friction-like force whose boiling of liquids [2, 3, 12]. All of these methods represent
magnitude is proportional to that of the normal force from bubbles with grids; in the case of small bubbles in carbonthe surface. Consequently, our method can represent not ated water, the methods require quite fine grids, and thus
only the different durations of bubble adhesion but also an become computationally expensive.
interesting phenomenon that bubbles climb along smooth2– 119–

Related Work

芸術科学会論文誌 Vol.11, No.4, pp. 118 – 128

Figure 2: Photographs of the surfaces of containers
containing carbonated water. Left: a glass, right: aplastic bottle, taken at the same distance. The sizesof bubbles also differ due to the difference of materials.

Müller et al. [13] used the Smoothed Particle Hydrodynamics (SPH) method to simulate the interaction between multiple fluids and state transitions including boiling. Their method can handle the deformation and coalescence of bubbles by representing both the air and liquids with particles. Greenwood et al. [5] dealt with thetrapped air as bubbles by approximating bubbles in liquids as spheres and simulating the generation of bubbles
using the particle level set method. Hong et al. introduced the two-way coupling of a grid-based method andthe SPH method, and represented the interaction between
rising bubbles and the water flow. Thürey et al. [14] accomplished simulations of the interaction between bubbles
and liquids represented with a height field in real time.
These previous methods do not target bubbles in carbonated water, and thus do not take into account the mechanism of their generation. Recently, Kim et al.[4] introduced a pratical simulation method for dispersed bubble
flow. Although their method does not target carbonatedwater as well as bubble collisions or merging, combining
it with our method will improve the motion of rising bubbles.
Cleary et al. [6] simulated the generation of bubbles incarbonated water using the SPH method. In their model,
the resolved gas in carbonated water is propagated by water particles via a diffusion process, and is provided to
the nucleation sites. Although their method can handle
highly dynamic animations as shown in their example ofAle poured into a glass, the use of a large number of particles makes their method quite expensive, as they reported
that a simulation takes more than ten days. Furthermore,their method neither handles the adhesion of bubbles onto
object surfaces nor the differences of sizes and generation
rates of bubbles according to the materials, as shown in
Figures 1 and 2.
Our method can handle such differences by introducing
adhesion forces that make bubbles stick on object surfaces.
Unlike Cleary et al.’s method, our method represents bubbles with particles and the water with a coarse grid together with the two-way coupling [10] of the two. Our
method is much simpler and less expensive than theirs.

3

Bubble Simulation

3.1

Overview

Our method represents bubbles in carbonated water with
non-deformable spheres, because each bubble in carbonated water is roughly one millimeter in diameter and canbe regarded as such [15]. Bubbles that adhere at generation points are also represented with non-deformablespheres.
We target the behavior of bubbles inside carbonated water and do not handle bubbles floating on the water surface, which we would like to deal with in a way similar to
Cleary et al. [6] in future work. Our method controls theamount of generated bubbles by adjusting the number ofgeneration points. Bubbles stay at their generation points
and keep growing when the external forces that attempt tomove bubbles are weak, and then start to move when theexternal forces become sufficiently strong. We reproduce
this phenomenon by introducing adhesion forces based on
the analogy of friction forces. The adhesion forces arecalculated so that their directions are opposite to the motion of bubbles and their magnitudes are linearly proportional to those of the normal forces from object surfaces.
The coefficients of adhesion forces affect the sizes of bubbles when they are released from the surface; larger coefficients help bubbles grow larger, while smaller coefficients
let them leave earlier. Note that we assume that carbon
dioxide (CO2 ) is sufficiently resolved in the water for thegrowth of bubbles.
Our method computes the water flow using the gridbased method by Stam [9] and handles the interaction between bubbles and the flow. Specifically, we use the two-– 120–

芸術科学会論文誌 Vol.11, No.4, pp. 118 – 128

Tangential
external force

way coupling technique [10] to represent the convection
flow caused by drifting bubbles as well as the motions ofbubbles influenced by the flow. Additionally, when bubbles collide, our method lets them repel or merge withused-specified probability.

3.2

Normal force
Normalexternal force
Adhesion force

The Behavior of Bubbles on Object
Surfaces

Our method randomly places generation points on the object surfaces with the user-specified density according to
the materials. For example, a porous object like a wooden
stirrer (Figure 2, left) are assigned with a large number ofgeneration points, while a plastic object (Figure 2, right)
not so many.
The duration in which each bubble sticks to the surface
varies according to the material of the surface, resulting
in different sizes and growth rates of bubbles. To represent this phenomenon, we introduce adhesion forces thatlet bubbles stick to the surface. To the best of our knowledge, the theory of the adhesion is not clearly known. Here
we introduce a simple model based on the considerationof external forces against bubbles; a bubble at a generation point is pushed onto the object surface by hydraulicpressure. According to Newton’s third law of motion, thebubble receives a normal force in the opposite direction of
the pressure. The bubble also receives a buoyancy force
from the surrounding water, and possibly a collision force
as well. To maintain the equilibrium against these external forces, we assume that the bubble receives an adhesion
force similar to a friction force, and its magnitude is linearly proportional to that of the normal force. Specifically,in our model, the bubble is assumed to receive what wecall a static adhesion force Fst in the stationary state;
Fst = −µ |N|

g
,
|g|

(1)

where µ is a coefficient for static adhesion, N is the normal force (illustrated as the green arrow in Figure 3) andg is the gravity. To decide whether the bubble stays at
the generation point or leaves there, we compare the magnitudes of the static adhesion force and the total external
forces in each time step of the simulation. Larger staticadhesion forces let bubbles stay longer at the generation
point and thus grow larger by absorbing the resolved gas,
while smaller forces let them leave earlier even when they
are relatively small. After leaving the generation point,

Glass
Bubbles

Carbonated water
Figure 3: Relationship between adhesion and external force. The blue arrow represents the total offorce from hydraulic pressure. The green, red andyellow arrows represent the normal force, the adhesion force and the horizontal component of the external force, respectively.

the bubble may immediately take off for the water surface from the object surface or glide up along the object
surface. Such behavior depends on the material of the object. For example, on plastic and acrylic surfaces bubbles
slowly glide, while on a stainless-steel surface they do not.
To represent such a phenomenon, we introduce a dynamic
adhesion force, similar to a dynamic friction force. Its
magnitude is also linearly proportional to that of the normal force;gFdy = −µ ′ |N| ,(2)|g|where µ ′ is a coefficient for dynamic adhesion. µ ′ is set
small for plastic or acrylic surfaces and large for stainlesssteel surfaces.

3.3 Grid-based Fluid Simulation
Our method simulates the water flow using a grid-based
method. The simulation space is subdivided into a coarse
grid, and the velocity of the fluid is assigned for eachgrid cell. The velocities are updated based on the NavierStokes equations in each time step;– 121–

∂u
∂t
∇·u

=

−(u · ∇)u + ν ∇2 u −

=

0,

1
∇p + f,ρ(3)(4)

芸術科学会論文誌 Vol.11, No.4, pp. 118 – 128

Water flow
velocity

Drag
force

Bubblevelocity
Bubble3.5

Bubble velocity
Water flow
velocity

Lift force

BubbleFigure 4: Illustrations of the drag force, the lift force
and the interactions between bubbles and the waterflow from left to right.

where u is the velocity, p is the pressure, ρ is the fluid
density and f is the external forces including the gravity.
We solve these equations using Stable Fluids [9].

3.4

We can observe repulsion and coalescence of bubbles when
they collide, especially when they are gliding on an object surface. Our method detects collisions of bubbles,
and then stochastically determines whether they repel orcoalesce into one. The probability is specified by the user.
When bubbles are merged, our method erases collided
bubbles and creates a new bubble whose volume is the total of those of collided bubbles and whose position is thecentroid of them. The radius of the new bubble is calculated according to its volume.
When bubble particles i and j repel, the following repulsion force Fc is added to bubble particle i, and also
added to bubble particle j in the opposite direction;

where mi and ri are the mass and the radius of the bubble particle i, ui is the water velocity at the position of
bubble i, which is linearly interpolated from the velocities
at surrounding grid points. kdrag is the coefficient for the
drag force and kli f t is the coefficient for the lift force. vi
is the velocity of bubble particle i and ωi is the vorticity
at the position of bubble particle i. Conversely, the flow isaffected by the bubbles as well; the total force among bubbles near each grid cell is calculated, and then its inversedirectional force is added as an external force in Equation
(3).

Fc

=

∆x

=

mi (kcol ∆x + kdamp vn ),xi − x j((ri + r j ) − |xi − x j |),|xi − x j |

(7)
(8)

where kcol is the stiffness coefficient, kdamp is the damping
coefficient and vn is the normal component of the relative
velocity.

Interaction between Bubbles and Wa3.6
ter Flow

We compute the interaction between bubbles and the water flow using the two-way coupling technique [10]. See
Figure 4 for illustrations. The flow provides drag and lift
forces to bubbles. The drag forces Fd work so that bubbles
move along the flow. The lift forces Fl let bubbles follow
vortices in the flow.
mi(5)
Fd = −kdrag |vi − ui |(vi − ui ),ri
Fl = −kli f t mi (vi − ui ) × ωi ,(6)Interaction among Bubbles

The Motion Equation for Bubbles

In this section, we summarize the external forces applied
to bubbles and the motion equation for the bubbles.
A bubble receives a buoyancy force Fb due to the difference of densities against water;
Fb = (mi − ρliqVbub )g,(9)where ρliq is the density of carbonated water, Vbub is thevolume of a bubble. While a bubble is inside carbonatedwater, it keeps growing by absorbing the resolved gas in
the amount proportional to its surface area.
In summary, the total of the external forces Fall for a
bubble is the summation of the buoyancy force (Equation(9)), the repulsive force from collision (Equation (7)), thedrag and the lift forces from the water flow (Equations (5)and (6));
Fall = Fb + Fc + Fd + Fl .

(10)

In addition, our method adds the dynamic adhesion forces
to gliding bubbles (Section 3.2). Our method then updates
the velocity and position of the bubble according to the– 122–

芸術科学会論文誌 Vol.11, No.4, pp. 118 – 128

law of motion using the total forces;
dvi
dt
dxi
dt

=

Fall
,
mi

(11)

=

vi ,

(12)

where mi is the mass of bubble particle i.

4

Results

This section shows the results of 2D and 3D simulations
using our method. The implementation was written in C++
using OpenGL. All experiments in this paper were conducted on a PC with an Intel Core i7 extreme 975 3.33GHz
processor and 3GB RAM. As for rendering, the 2D results are displayed by representing bubbles with texturemapped quads. The 3D results are rendered using an offline renderer POV-Ray.
Figure 5 shows gliding motions of bubbles on surfaces
with different materials. The motion of each bubble differs due to the differences in the coefficient of dynamic
adhesion (Section 3.2). In this simulation results, the bubble on the surface that has a lower coefficient of dynamic
adhesion moves faster.
Figure 6 shows the 2D simulation results of the interaction between bubbles and the water flow, assuming thata wooden stirrer is placed obliquely in the tilted rectangle
area. The top and middle rows of Figure 6 show the results with and without interactions between bubbles andthe water flow, respectively. The difference of bubbles’
motion can be observed as shown in the areas with red circles. Figure 7 shows the results with different amounts andsizes of bubbles. The top result of Figure 7 contains 5,000
generation points while the bottom one 500. The computational times for each time step (without rendering) are
1.6 milliseconds for the top and 1.1 milliseconds for thebottom, respectively. The coefficients for static adhesion(Section 3.2) are 0.001 for the top result and 0.04 for thebottom result, respectively. The smaller coefficient in the
top yields smaller bubbles and the faster growth rate thanthose in the bottom. Figure 8 shows a comparison between
a photograph and the result combining 2D simulation anda background image. The corresponding accompanying
video demonstrates that visually plausible animations canbe obtained using our method. There are 1,000 generation
points on the grape image area. The coefficient of staticadhesion force is 0.06.

Figure 9 shows results of 3D simulations, captured every 30 time steps. There are a cylindrical glass and a blue
glass ball. The ball has 500 generations points on its surface. We assume that there are no generation points on thewall of the cylindrical glass. Bubbles stay at their generation points for a while due to the static adhesion forces.
Then, bubbles glide up along the surface. Regarding theattached bubbles, we let them slightly intrude into the object surface to represent their adhesion. To show the glide
motions more clearly, we show in Figure 10 a near-viewof another 3D simulation with the generation points reduced to 50 and other parameters remained the same as
Figure 9. When the total external forces become larger
than the static adhesion forces, bubbles leave their generation points and then glide up along the object surface. The
computational time for each time step (without rendering)is 79 milliseconds.
Note that we cannot compare our results with those ofprevious methods in the same condition because, to thebest of our knowledge, no previous methods focused on
the generation and growth of bubbles on a surface. In
terms of computational time, our method is much moresuited to interactive applications than Clearly et al.’s method.
Regarding parameter tuning, the coefficient for static adhesion force and the number of generation points are important to represent the differences of surface materials, as
demonstrated in Figure 7.

5

Conclusions and Future Work

This paper has proposed a simple method for simulating
bubbles in carbonated water, focusing on their behavioraround object surfaces. Our method controlled the amountof bubbles generated from object surfaces by adjusting thenumber of generation points. To represent various sizes
and on-surface gliding motions of bubbles, our method introduced static and dynamic adhesion forces, which makethe bubbles stick on the surfaces. Our method also handled collisions and fusions among bubbles, and the twoway coupling between bubbles and the flow in carbonatedwater.
For future work, we would like to verify the physicalvalidity of our method and represent more realistic behaviors of bubbles, including floating bubbles on the surfaceof liquids.

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Figure 5: Sequence of different motions of bubbles
on the surfaces. In each image, brown partitions are
surfaces and the coefficient of dynamic adhesion isdifferent in each partition (1.0, 0.6, and 0.3 from left
to right, respectively). Bubbles on the more rightside rise faster because bubbles receive less dynamic
adhesion forces which are proportional to the coefficient of dynamic adhesion.

References[1] Kanamori, Y., Nishikawa, T., Yue, Y., Nishita, T., Visual Simulation of Bubbles in Carbonated Water, Proc.
of NICOGRAPH International 2012 (2012).

Figure 6: Top: 2D simulation results with interactions between bubbles and carbonated water flow,
middle: 2D simulation results without interactions[2] Fujisawa, M. and Miura, K., Animation of Ice Melt- between bubbles and carbonated water flow, bottom:
ing Phenomenon with Phase Change Based on TherThe velocity field of carbonated water flow.
modynamics, Transactions of Information Processing
Society of Japan, 48, 1480–1488 (2008).

[3] Kim, T. and Carlson, M., A simple boiling module, In
Proc. of SCA ’07, 27–34 (2007).
[4] Kim, D. and Song, O. and Ko, H.-S., A practical simulation of dispersed bubble flow, ACM Transactions
on Graphics (Proc. of SIGGRAPH 2010), 29 (4), 1–5(2010).
[5] Greenwood, S. T. and House, D. H., Better with bubbles: enhancing the visual realism of simulated fluid,
In Proc. of SCA ’04, 287–296 (2004).
[6] Cleary, P. W. and Pyo, S. H., Prakash, M. and Koo, B.
K., Bubbling and frothing liquids, ACM Transactions
on Graphics (Proc. of SIGGRAPH 2007), 26 (3), 97(2007).
[7] Enright, D., Marschner, S. and Fedkiw, R., Animation
and rendering of complex water surfaces, ACM Trans-

actions on Graphics (Proc. of SIGGRAPH 2002), 21(3), 736–744 (2002).
[8] Hong, J.-M and Kim, C.-H, Animation of bubbles inliquid, Computer Graphics Forum (Proc. of Eurographics 2003), 22 (3), 253–262 (2003).
[9] Stam, J., Stable fluids, In Proc. of SIGGRAPH ’99,
121–128 (1999).
[10] Hong, J.-M., L, H.-Y., Yoon, J.-C., and Kim, C.-H.,
Bubbles alive, ACM Transactions on Graphics (Proc.
of SIGGRAPH 2008), 27 (3), 1–4 (2008).
[11] Song, O.-Y., Shin, H. and Ko, H.-S., Stable but
non-dissipative water, ACM Transactions on Graphics(Proc. of SIGGRAPH 2005), 24 (3), 81–97 (2005).

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Figure 8: Comparison of a 2D simulation result anda photograph. Left: a simulation result, right: a photograph.

Figure 7: The amount of bubbles differ according todifferent materials of the object. The size of bubbles
differ according to the coefficients of static adhesion
force. The top and bottom simulation results have
5,000 generation points with µ = 0.001 and 500 generation points with µ = 0.04, respectively.

[12] Mihalef, V., Unlusu, B., Metaxas, D., Sussman, M.
and Hussaini, M. Y., Physics based boiling simulation,
In Proc. of SCA ’06, 317–324 (2006).
[13] Müller, M., Solenthaler, B., Keiser, R. and Gross,M., Particle-based fluid-fluid interaction, In Proc. of
SCA ’05, 237–244 (2005).
[14] Thürey, N., Sadlo, F., Schirm, S., Müller-F, M. and
Gross, M., Real-time simulations of bubbles and foamwithin a shallow water framework, In Proc. of SCA ’07,
191–198 (2007).
[15] Gërard, L.-B., Uncorked: The Science of Champagne, Princeton University Press (2004).

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Figure 9: 3D simulation of bubbles rising in a cylin- Figure 10: Bubbles glide on the surface of the spherdrical cup.
ical object.

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Yoshihiro Kanamori

Yonghao Yue
Yoshihiro Kanamori received his B.S., M.S., andPh.D. degrees in computer science from the University of Tokyo, Japan, in 2003, 2005, and 2009, respectively. Since April 2009, he has been an assistant professor at the University of Tsukuba. His research interests center in computer graphics including rendering and visual simulations. He now studies image edting techniques for reproducing realworld phenomena. He is a member of IIEEJ and Yonghao Yue is an assistant professor at the Department of Complexity Science and Engineering,
IPSJ.
Graduate School of Frontier Sciences, the University of Tokyo, Japan, since 2011. He is also an assistant professor at the Department of Information Science, School of Science, the University of Tokyo,
Japan, since 2012. His research interests center incomputer graphics, including realistic image synthesis, global illumination, Monte Carlo techniques andTakeshi Nishikawa
physically-based simulations. He received his B.S.,
M.S. and Ph.D. degrees in Computer Science fromthe University of Tokyo, Japan, in 2005, 2007 and2011, respectively. He is a member of ACM, IIEEJ,IPSJ and ITE.

Takeshi Nishikawa received his M.S. in Sciencefrom the University of Tokyo, Japan in 2010. His
research in the University of Tokyo focused on computer graphics. He now works for SOFTBANK
CORP.

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Tomoyuki Nishita

Tomoyuki Nishita is a professor in the Departmentof Complexity Science and Engineering (also in the
Department of Information Science) at the University of Tokyo, Japan since 1998. He received his
BE, ME and Ph.D in Engineering in 1971, 1973, and1985, respectively, from Hiroshima University. He
taught at Fukuyama University from 1979 to 1998
He was an associate researcher in the Engineering
Computer Graphics Laboratory at Brigham Young
University from 1988 to 1989. His research interests center in CG including lighting/shading models(radiosity), natural phenomena, real-time rendering,geometric modeling, and non-photorealistic rendering. He is one of the pioneers of radiosity method.
Dr. Nishita received Research Award on Computer
Graphics from Information Processing Society ofJapan in 1987, and also received Steaven A. Coonsaward from ACM SIGGRAPH in 2005. He was apresident of The Institute of Image Electronics Engineers of Japan in 2009-2010.

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