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석사 학위논문
Master’s Thesis
수지상구조를사용한
파티클기반의눈시뮬레이션
Particle Based Snow Simulation Using Dendritic Structure
서 형 국 (徐 炯 國 Seo, Hyunggoog)
문화기술대학원
Graduate School of Culture Technology
KAIST
2013
수지상구조를사용한
파티클기반의눈시뮬레이션
Particle Based Snow Simulation Using Dendritic Structure
Particle Based Snow Simulation Using Dendritic
Structure
Advisor : Professor Junyong Noh
by
Seo, Hyunggoog
Graduate School of Culture Technology
KAIST
A thesis submitted to the faculty of KAIST in partial fulfillment of
the requirements for the degree of Master of Science in Engineering in the
Graduate School of Culture Technology . The study was conducted in
accordance with Code of Research Ethics1.
2012. 12. 27.
Approved by
Professor Junyong Noh
[Advisor]
1Declaration of Ethical Conduct in Research: I, as a graduate student of KAIST, hereby declare that
I have not committed any acts that may damage the credibility of my research. These include, but are
not limited to: falsification, thesis written by someone else, distortion of research findings or plagiarism.
I affirm that my thesis contains honest conclusions based on my own careful research under the guidance
of my thesis advisor.
수지상구조를사용한
파티클기반의눈시뮬레이션
서 형 국
위 논문은 한국과학기술원 석사학위논문으로
학위논문심사위원회에서 심사 통과하였음.
2002년 12월 21일
심사위원장 노 준 용 (인)
심사위원 여 운 승 (인)
심사위원 박 진 호 (인)
MGCT
20113286
서 형 국. Seo, Hyunggoog. Particle Based Snow Simulation Using Dendritic Structure.
수지상 구조를 사용한 파티클 기반의 눈 시뮬레이션. Graduate School of Culture
Technology . 2013. 20p. Advisor Prof. Junyong Noh. Text in English.
ABSTRACT
We propose a particle based simulation for snow, focusing on the rigid body behavior and fracture
effect of the snow. One of the most distinguishable features of the snow, compared to other granular
materials or fluids, is a combination of rigid body dynamics and powder-like behavior and fracture
effect on the cutting surface. Those features are caused by existence of ice bonds and a microstructure
of the snow which is in the shape of dendritic structure. We model the ice bonds with mass-spring
model and construct the dendritic structure by using minimum spanning tree. The dendritic structure
ensures the rigid body dynamics of snow. Also, the structure has property of fractal pattern so that
the snow model using dendritic structure ensures that the cutting surface of snow can show the fracture
effect. Our result shows that the dendritic structure ensures the rigid body behavior and generates
the fracture effect without modeling the fracture effect explicitly. Our method can be easily applied to
existing granular material simulation. We adopt granular material simulation using Smoothed Particle
Hydrodynamics(SPH) for base simulation. Our method is easy to implement, since the underlying
concept is simple.
i
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Chapter 1. Introduction 1
Chapter 2. Related Work 2
Chapter 3. Base simulation 4
3.1 Smoothed Particle Dynamics . . . . . . . . . . . . . . . . . . . . . 4
3.2 Discrete Element Method . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 4. Dendritic Structure based Snow Model 5
4.1 Snow Particles Seeding . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Dendritic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Ice Bond Breaking Condition . . . . . . . . . . . . . . . . . . . . 7
4.4 Structure Reconstruction . . . . . . . . . . . . . . . . . . . . . . 8
4.5 Rigidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 5. Result 10
Chapter 6. Limitation & Future work 15
Chapter 7. Conclusion 18
References 19
Summary (in Korean) 21
ii
List of Tables
5.1 Scene description of experiments. ()* indicates the corresponding preprocessing time. . . 11
iii
List of Figures
4.1 Method overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2 Particle Seeding. The Particle types are divided into granular material particle and snow
particle. The snow particle is divided into seed particle and candidate particle. . . . . . . 6
4.3 Dendritic structure construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.4 Model for the ice bond. Two springs were used for representing ice bond. . . . . . . . . . 8
4.5 Isolated particles are reconstructed to dendritic structure when they are close to each other. 8
4.6 Each particle in dendritic structure can obtain appropriate velocity with rigidification
process so that they can behave like a rigid body. . . . . . . . . . . . . . . . . . . . . . . . 9
5.1 Broken snowman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Examples of seeding and construction of dendritic structure on snowman. . . . . . . . . . 11
5.3 The fracture effect of the snow. Top : Rendered image, Bottom : Not rendered image . . 12
5.4 Breaking Snowman-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.5 Breaking Snowman-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.1 Smooth surface reconstruction interrupt the detail of fracture effect. . . . . . . . . . . . . 15
6.2 Metamorphism of real ice bond. Ice bond goes through a metamorphism according to the
temperature and the time. [KS07] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.3 Stamping box. Since our method is based on incompressible granular material simulation,
volume fraction is not handled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
iv
Chapter 1. Introduction
Snow has a complex microstructure which consists of ice bonds between snow particles. At macro-
scopic level, snow is considered as continuous media, that is, the microstructure may sometimes no longer
be visible. However, microstructure of snow determines the bulk characteristics of the snow pack such
as settling rate, temperature distribution and its many additional mechanical properties [LBB∗02]. In
other words, microstructure significantly influences the behavior of snow at macroscopic level.
One of the most remarkable features of snow microstructure is an ice bond. Because of the ice bond,
snow particles cannot flow freely. Particles connected by ice bonds move together like rigid body. If
particles are not connected with each other by the ice bond, they will show general granular material’s
behavior. Another phenomena caused by the ice bond is fracture effect on snowpack. When an object
collides with the snow pack, cracked part shows rough surface, as the irregularly distributed ice bonds
are broken along the path of the object. It is important to represent these features for snow simulation;
rigid body like behavior, fracture effect.
Similar to the ice bond concept, many works have represented cohesion model on the granular ma-
terial simulation. Vinodh Vedachalam [VV11] and Rungjiratananon [RSKN08] added cohesion model to
molecular dynamics simulation, which is known as Discrete Element Method(DEM). The cohesion model
in those works use basic or modified spring force between neighbor particles. Alduan and Otaduy [AO11]
represented cohesion force maximizing strain rate dissipation based on granular material simulation using
Smoothed Particle Dynamics.
Those works shows some limitations for representing snow. The cohesion force acting like ice bond in
snow cannot ensure rigid body like behavior, because they did not consider the momentum conservation
of connected particles behavior. To behave like a rigid body, the particles moving together should have
appropriate linear and angular momentum. Granular material simulation can shows fracture like effect
a little due to cohesion. However, it is hard to represent the fracture behavior of the material matching
exactly that of dry granular media without explicit fracture modeling.
To emphasize the forementioned features of the snow, our method uses dendritic structure which
is a feature of microscopic level of snow. Dendritic structure is a typical multi-branching tree-like form
with fractal patterns which has self-similarity. Our method performs the following actions.
• Compute force with base granular material simulation.
• Check the ice bonds whether it break or stay.
• Examine the isolated particles whether the reconstruction will be happened.
• Create dendritic structure with particles connected by ice bonds.
• Rigidify the connected particles group by assigning appropriate linear and angular momentum.
We upsampled dendritic structure, and transplant to snow pack. We construct the dendritic struc-
ture with particles connected by ice bond, and rigidify that structure enforcing get same linear and
angular momentum. And dendritic structure has the fractal pattern, we can get fracture effect easily
just applying bond break condition [LG87].
– 1 –
Chapter 2. Related Work
Our method basically uses granular material simulation. There are two approaches for simulating
granular material: DEM and continuum methods. DEM model the granular material as small dynamic
particles advected by the contact forces between particles. The DEM was introduced by Cundall et
al [PC04]. for the analysis of rock-mechanics problems and then applied to soils [Cun71]. Many works in
rock mechanics field used this method to represent a rock as cemented granular materials [PC04] [DPH11].
In computer graphics field, Bell et al. [BYM05] used rigid compounds of spheres that have non-spherical
shape to model grains. Thus, the compound structures produce a considerable angle of repose which can
make sand piles stable. Rungjiratananon et al. [RSKN08] use DEM for representing sand interacting
with SPH water particles.
Continuum methods treat granular media as a continuous fluid. Zhu and Bridson [ZB05] modified
the Navier-Stokes fluid equation for friction forces to simulate granular media as a fluid. Their approach
identifies rigid parts in the material, and rigidifies those parts to obtain stable piles. Lenaerts and
Dutre [LD09] used a similar model with SPH discretization. They integrated granular materials and
fluids with two-way coupling. However, due to incompressibility assumption in fluid simulation, some
artifact which prevents the granular media from freely flowing occurs. To address this problem, Narain
et al. [NGL10] proposed another fluid-like model of granular materials replacing the existing fluid-based
model’s assumption of incompressibility with a unilateral constraint. Alduan et al. [AO11] adapted
unilateral incompressibility to predictive-corrective incompressible SPH(PCISPH) algorithm with minor
modifications adding cohesion. Their approach does not suffer from artifacts caused by Eulerian grid.
Ihmsen et al. [IWT12] proposed a Lagrangian simulation framework which can obtain high visual detail
with low computational cost. Their approach calculates the friction and pressure forces on a coarse scale
base simulation. Spatially fine-scaled set of particles is coupled to particle set in coarse simulation so
that the method can make highly detail result.
Comparing DEM with continuum-based methods, DEM require prohibitive computational cost for
large-scale scenarios or fine-grained materials. However, continuum-based methods enable the choice of
the simulation resolution as a trade-off between efficiency and quality due to regular computational do-
main. Most snow scenes requires large simulation domain. Our method adapt the SPH-based continuum
method proposed in the work of Alduan and Otaduy [AO11].
Dendritic structure is a typical multi-branching tree-like form which is very common in nature:
lightning, cracks, tree, snowflake, frost. Dendritic structure has a natural fractal pattern [Lib05]. One
of the most common and classic methods to generate dendritic structure is diffusion-limited aggrega-
tion(DLA) [WJS81]. Kim and Lin [KL03] used DLA to visualize simulation of ice growth. Cha et
al. [CPHN12] adapted DLA to identify a flow region for viscous fingering effect. The quality of results
obtained by DLA method is very high and realistic. However, this method cannot determine shapes in-
tended by user. If the structure changes, whole domain of DLA simulation requires recalculation causing
high computational cost.
There are other methods for generating dendritic structure. One of those methods is the path
planning algorithm. Long and Mould [LM09] proposed a new procedural method based on the path
planning algorithm for dendritic stylization where an input image can be embedded into a dendritic
– 2 –
structure. Similar to the path planning approach, minimum spanning tree(MST) is used for modeling
the dendritic structure in medical or biological field [HAI]. Path planning and MST both are algorithms
which scan all nodes in the graph and specify the particular edges of that graph. These approaches have
many advantages compared to DLA. Although quality of the result is lower than DLA, path planning
and MST can determine the end nodes enabling the users to obtain intended shape with very low
computational cost. In our method, the dendritic structure should be reconstructed at each time step
due to particle advection. We construct a graph which treats particle position as an end node. We make
a dendritic structure by MST with the graph.
– 3 –
Chapter 3. Base simulation
Our method adopt Alduan and Otaduy [AO11] for our basic granular material simulation which use
two dynamics for particle advection: DEM and SPH.
3.1 Smoothed Particle Dynamics
SPH smoothes quantities over a neighborhood with radius h by using a kernel W to weight the
contributions according to the distance xij between two particles i and j. An estimation of a quantity of
ith particle qi is accomplished by equation
< qi >=∑j
mj
ρjqjW (xij , h) (3.1)
where mj is the mass of particle j and ρj its density.
3.2 Discrete Element Method
DEM method is also a particle-based simulation method, which was originally used for rock me-
chanics problem. When a collision between the particle i and j occured, it calculates the normal and
tangential contact forces. With those contact forces, particles are advected. The force of normal direction
is modeled in terms of spring and the force of tangential direction is modeled as a friction.
Fn = ks(d− ||xi − xj ||)~vnormal
||~vnormal||(3.2)
Ft = kt~vtangential||~vtangential||
(3.3)
where Fn is the normal contact force, Ft is the tangential contact force, ks is the spring constant, d
is the sum of radius of particle i and j, xi and xj are position of each particle, ~vnormal and ~vnormal are
the relative velocities of normal direction and tangential direction, kt is the coefficient of friction.
3.3 Simulation
If the density of a particle ρi is higher than critical density ρmax, the particle is advected by SPH. It
means that the particles which have high density receive considerable amount of pressures from neighbor
particles so that make the particles freely flow. On the other hand, DEM dynamics work on particles
which have lower density than ρmax, treating as elastic spheres.
– 4 –
Chapter 4. Dendritic Structure based Snow Model
Figure 4.1: Method overview.
Whole process of our method is shown in Figure 4.1. There are many physical factors which
determine the properties of snow. Most of all, the microstructure of snow plays a significant role in
determining the characteristics of snow [LBB∗02]. Thus, we drastically simplify the snow models focusing
on the microstructure of snow to allow efficient implementation. Our method needs a pre-processing
which is consists of 2 steps. First, we have defined two types of particle and seed those particles to
whole domain as described in Section 4.1. Second, after the particle types are determined, we construct
the dendritic structure using MST, see Section 4.2. After the pre-processing is performed, our method
enters into simulation step. During the simulation step, if the particles which are not snow particle
receive a considerable amount of pressure, it means that the particles go through the phase change, thus
we change the type of those particles to snow particle and reconstruct the dendritic structure including
the particles, see Section 4.3. Then, we check the ice bonds whether they are broken by the external
forces using mass-spring model as described in Section 4.4. We rigidify the particles which consist of the
dendritic structure and update the velocity and position of the particles, see 4.5.
– 5 –
Figure 4.2: Particle Seeding. The Particle types are divided into granular material particle and snow
particle. The snow particle is divided into seed particle and candidate particle.
4.1 Snow Particles Seeding
We have defined 2 types of particle for modeling the snow.
• Granular material particle : Granular material particle represents the particle which is not con-
nected to any particle. Thus, granular material particle ensures the powder-like behavior of snow.
DEM and SPH dynamics work on this type of particle. It also can be a snow particle if the particle
receives considerable amount of pressure force.
• Snow particle : Snow particle represents the particle which is connected to other particles. The
dendritic structure consists of snow particles. Snow particle ensures the rigid body-like behavior
of snow. Snow particle type is divided into two subtypes, which are Seed particle and Candidate
particle. Seed particles are roots of the dendritic structure. Candidate particles are nodes of the
structure. It can be a granular material particle if the ice bond is broken.
At first, whole particles in domain are granular material particle. We determine the portion of snow
particles by a user parameter γ. Among the snow particles, we also determine the ratio of seed particle
to candidate particle by parameters α, β. By controlling the parameters, users can determine the ratio of
the rigid body motion to powder-like motion which will be represented in the result scene. This process
is shown in Figure 4.2.
0 ≤ γ ≤ 1 (4.1)
α+ β = γ (4.2)
4.2 Dendritic Structure
Our method uses the MST to construct the dendritic structure with snow particles classified in
previous seeding process. Following steps are shown in Figure 4.3. First, we need to generate graphs
with snow particles to apply the MST algorithm. We examine the neighbor candidate particles near the
seed particles. We create all connections(edges) between the seed particle and the candidate particles
that have the distance shorter than l. We assume that the ice bonds are not generated if the distance
– 6 –
Figure 4.3: Dendritic structure construction.
between particles r is longer than l. Thus, we include the edges which satisfy the condition r < l to
the graph, and exclude the edges which are r ≥ l from the graph. We assign weight values to all edges
which are in inverse proportion to the distance. It implies that the closer distance may cause the more
probability of ice bond generation. We also examine the other neighbor candidate particles near the
candidate particles which are selected before. Then, we create all connections repeatedly between the
candidate particles that have the distance shorter than l. In this way, we check the every snow particle.
After this process, there might be some candidate particles which are not connected to any other. We
change the type of those particles to granular material particle. Second, we select the edges that make
lowest total weight value of the graphs. We adopt the Prim’s algorithm [Pri57] to construct the MST.
Finally, we can obtain the shape of dendritic structure and connection information between the snow
particles. With this information, our method can examine the mass-spring force on the ice bond which
is used as a criterion for the existence of ice bond.
4.3 Ice Bond Breaking Condition
D.O. Potyondy and Cundall [PC04] proposed a mass-spring model to represent the bonds between
rock particles. The bonds behave as a beam in their approach. We adopt this method to decide the
maintenance of ice bonds. Our method uses two springs for an ice bond with normal direction and
tangential direction. Sum of the exerted forces on a particle is calculated before in Section 3. If the
normal component of total force exceeds the maximum normal force σmax or the tangential component
of total force exceeds the maximum tangential force τmax; then the ice bond breaks, and it is removed
from the dendritic structure. We mark the isolated particle as a separated particle.
Fn = kn∆Un (4.3)
Ft = kt∆Ut (4.4)
σmax < Fn : Break (4.5)
τmax < Ft : Break (4.6)
where Fn is the normal force, Ft is the tangential force, kn is the spring coefficient of normal direction
– 7 –
Figure 4.4: Model for the ice bond. Two springs were used for representing ice bond.
spring, kt is the spring coefficient of tangential direction spring, ∆Un is the relative displacement of
normal direction between the particles, ∆Ut is the relative displacement of tangential direction between
the particles, σmax is the maximum normal force, τmax is the maximum tangential force. Eq. 4.5 and
Eq. 4.6 indicate the breaking condition. The ice bond will be broken if breaking condition is satisfied.
In our method, snow particles are connected with dendritic structure, and the structure has fractal
pattern. Fractal pattern has a property of fracture. Thus, if the ice bonds consisting of the dendritic
structure are broken, the part where a deformation happened on dendritic structure shows the fracture
effect.
4.4 Structure Reconstruction
After the ice bonds are broken, the isolated particles may be reconstructed according to the position
of each particle or just behave as a granular material particle showing powder-like behavior. We assume
that if isolated particle is not far away from another isolated particle, those particles can be reconstructed.
We examine the distance between each isolated particles and reconstruct a dendritic structure with
isolated particles within length L from other particle. 4.5
With this process, the isolated particles which are not reconstructed ensure the powder-like behavior
of snow, and the reconstructed particles ensure the rigid body behavior of snow.
Figure 4.5: Isolated particles are reconstructed to dendritic structure when they are close to each other.
– 8 –
4.5 Rigidification
The particles consisting of the dendritic structure need to be rigidified for rigid body behavior.
We adopt the method of Carlson et al. [CMT04] which enforces grid cells of rigid body to obtain the
rigid motion. In our approach, the grid cells are replaced to particles. Sum of the momentum (lin-
ear and angular) of each snow particle in dendritic structure implies the total momentum of the rigid
body. We redistribute the total momentum of dendritic structure to each particle by satisfying following
equations. 4.6
x =
∑imixi∑imi
(4.7)∑i
mi~vi = (∑i
mi)~V (4.8)∑i
mi~ri × ~vi = (∑i
mi)w (4.9)
~vi = ~V + (~ri − x)× w (4.10)
Zhu and Bridson [ZB05] adopted rigidifying equations to represent rigid body-like fluid motion in
grid-based simulation. In our approach, we modified the those equations for particle-based simulation.
Eq. 4.7 indicates center of mass, Eq. 4.8 and Eq. 4.9 indicate total momentum of particles in dendritic
structure, Eq. 4.10 is used to obtain appropriate velocity of each particle. After the redistribution of
total momentum, snow particles in dendritic structure can behaves as one rigid body.
Figure 4.6: Each particle in dendritic structure can obtain appropriate velocity with rigidification process
so that they can behave like a rigid body.
– 9 –
Chapter 5. Result
Figure 5.1: Broken snowman.
We implemented our method on the granular material simulation using SPH [AO11]. Our imple-
mentation adopt PCISPH solver for calculating SPH forces of particles. We rendered the particles with
surface reconstruction method introduced by Zhu and Bridson [ZB05]. This technique offered more
smooth result for tracking surface of particles. All of our simulations were run on a single Intel i7 3.4
GHz CPU with 8 GB of RAM. Table 5.1 shows the number of particles and the computational time
consumed in our results. The preprocessing time to perform initialization phase in Figure 4.1 required
a few seconds. However, since our method use MST to construct the dendritic sturucture which has
time complexity of O(ElogV ) where E is the number of edges and V is the number of vertices, the
preprocessing time increased according to the number of snow particles. 5.2
– 10 –
Table 5.1: Scene description of experiments. ()* indicates the corresponding preprocessing time.
SceneNumber of particles Average time per frame
Boundary Snow Base simulation Snow solver
Snowman 210125 35824 9.6 1.06(0.83)
Stamping box 16820 11552 4.51 1.34(0.31)
Figure 5.2: Examples of seeding and construction of dendritic structure on snowman.
After initialization step, snow solver required a few seconds during the simulation time. However,
even though the number of snow particles in ’Stamping box’ is less than ’Snowman’, computational cost
is higher than ’Snowman’. This is due to reconstruction process in Section 4.4. There were more snow
particles which are reconstructed in the ’Stamping box’ scene. Thus, the computational cost of snow
solver depends on the number of reconstructed snow particles.
Figure 5.4 and Figure 5.5 is the ’Snow man’ scene. While the red ball is breaking the snowman, we
can observe the rigid body motion of snow in this Figures. Also, we can observe the fracture effect on
the cutting surface due to irregular destruction of dendritic structure in the Figure 5.3.
– 11 –
Figure 5.3: The fracture effect of the snow. Top : Rendered image, Bottom : Not rendered image
– 12 –
Figure 5.4: Breaking Snowman-1.
– 13 –
Figure 5.5: Breaking Snowman-2.
– 14 –
Chapter 6. Limitation & Future work
Our method has a couple of limitations. Our method adopted the method of surface reconstruction
introduced by Zhu and Bridson [ZB05] to obtain the surfaces of particles. It is clear that the dendritic
structure contribute to show fracture property of snow(see the bottom of 5.3), however, we recognized
that its property of smootheness interrupt the detail of fracture effect.(see 6.2) The fracture effect on the
snow should be more sharp. We may solve this problem by introducing the new surface reconstruction
method. The new method should conserve the sharp detail of snow at the cutting surface while not
bumpy as blobby method. To achive this goal, we may obtain the isosurface of particles in coarse scale,
and add the detail of particles obtained in fine level We plan to resolve this problem further in the future.
Second limitation is that we did not consider the porosity of snow. In the case of real snow, it is
a porous material which contains air spaces between snow particles. Due to this property, snow can be
compressed when it has interaction with other object. However, we adopted granular material simulation
using SPH which has constraint of incompressiblity. Thus, we could not represent the volume fraction
of snow. 6.3 If the snow particles are considerably lumped each other, our method can show plausible
result like Snowman.
Another limitation is that we did not consider the metamorphism of ice bond. The size and com-
plexity of ice bond are changed during the metamorphism. [KS07] , Figure 6.2 To handle more complex
phenomena, out method should reflect the chainging of the ice bond connection with metamorphism.
Since the researches are vividly working in snow physics field, we plan to investigate this issues further
in the future.
Figure 6.1: Smooth surface reconstruction interrupt the detail of fracture effect.
– 15 –
Figure 6.2: Metamorphism of real ice bond. Ice bond goes through a metamorphism according to the
temperature and the time. [KS07]
– 16 –
Figure 6.3: Stamping box. Since our method is based on incompressible granular material simulation,
volume fraction is not handled.
– 17 –
Chapter 7. Conclusion
In computer graphics field, most researches on snow are focused on fluid-like feature like snow
avalanche. However, the snow shows a combination of rigid body dynamics and powder-like behavior
and fracture effect on the cutting surface. Those phenomena are caused by microstructure of snow which
is shape in the dendritic structure consisting of ice bonds. We proposed a new snow simulation method
emphasizing the rigid body behavior and fracture effect of snow. By introducing the microstructure of
snow to the exsisting granular material simulation, our result can obtain these features. The particles in
dendritic structure are rigidified by appropriately redistributing the total angular and linear momentum.
Our method can control the rigidity of snow by offering userparameters so that the snow in our simulation
can show various behavior from freely flowing to rigid body. The dendritic structure also has a property
of fractal pattern which has self-similarity with recursiveness. Thus, we can obtain fracture effect by
simply breaking the ice bonds in dendritic structure.
Our method can be easily applied to existing granular material simulation. The dendritic construc-
tion is executed by MST which has efficient time complexity. This makes the computational overhead
negligible on the base granular material simulation. Our method is easy to implement, since the under-
lying concept is simple.
– 18 –
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Summary
Particle Based Snow Simulation Using Dendritic Structure
우리는 눈의 강체적 특성과 균열 효과에 초점을 맞춘 파티클 기반의 눈 시뮬레이션을 제안한다.
다른 분체나 유체와 비교하여 가장 눈에 띄는 눈의 특징 중에 하나는 강체의 움직임과 가루의 움직임
그리고 절단면에서의 균열 효과가 함께 나타난다는 점이다. 이러한 특징들은 눈에 있는 얼음결합과
수지상 구조를 이루고 있는 눈의 미세구조 때문에 발생한다. 우리는 매스 스프링 모델을 이용해 얼음
결합을 모델링하고, 최소 신장 트리를 사용해 수지상 구조를 표현하였다. 수지상 구조는 눈의 강체적
움직임을 보장한다. 또한 수지상 구조는 프랙탈 구조를 이루고 있어, 이 구조를 이용해 눈을 모델링
함으로써 눈의 절단면이 균열 효과를 보일 수 있다. 우리의 결과물은 수지상 구조가 강체적 움직임
을 보이도록 하고, 외부적인 모델링 없이도 균열효과를 표현 할 수 있음을 보여준다. 우리의 연구는
현존하는 분체 시뮬레이션에 쉽게 적용 될 수 있다. 우리는 기본 시뮬레이션으로 Smoothed Particle
Hydrodynamics(SPH)를 사용한 분체 시뮬레이션을 차용하였다. 우리의 연구에 깔려있는 근본적인 개
념은 간단하여 쉽게 구현할 수 있다.
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감 사 의 글
엄마! 나 집에 갈 수 있어요 ㅠㅠㅠ
아부지, 차좀 승용차로좀 굽신굽신
어머니 아버지 생각이 제일 먼저 나네요.. 잠시 눈물좀 훔치고.
우왕좌왕 하던 저를 끝까지 포기하지 않으시고(?) 많이 가르쳐주시고 지도해주신 태권이형 정말 감사
드립니다. 옆에서 형과 함께 작업하면서 연구자로서 갖추어야할 자세, 관점등에 많은 것들을 배우고
생각해 볼 수 있었습니다. 연구가 잘 진행되지 않을 때 저와 함께 술도 한잔 하며 연구관련 코멘트도
많이 해주시고 이럴 때 일수록 자기관리 잘해야 한다며 운동도 함께 해준 승훈이형 감사합니다. 형
덕분에 미립자단위까지 Discritized되었던 정신을 수습하고 연구를 무사히 마칠 수 있었습니다. 함께
연구문제에대해많은이야기를나눠주고도움을많이준지환이형감사합니다. 문화기술대학원에와서
랩 설명회 때 ’열정’있는 사람이면 오라고 해주셨던 유미누나 감사드립니다. 누나가 그 때 그런 말씀
안하셨으면 저는 어떻게 됬을까요? 제 연구주제에 대해 많은 관심과 좋은 코멘트들 많이해주신 박진호
교수님 감사드립니다. 보잘 것 없는 논문임에도 불구하고 좋게 봐주신 여운승 교수님 감사합니다. 곁
에서 긍정의 기운을 마구 뿜어내준 경한이도 고맙다. 항상 많은 것을 보고 배우고 느끼게 해주는 우리
VM식구 여러분 감사드려요
무엇보다 나이를 잊은 열정과 그에 못지않게 나이를 잊은 외모를 갖추신 교수님. 항상 학생들에게 비전
과 희망을 제시해주시는 우리 교수님. 처음 랩에 들어왔을 때 교수님께서 하신 말씀이 아직도 기억에
남습니다.
”무엇을 공부하던 간에 문제를 정의하고 그것을 풀어나갈 수 있는 과정을 배워라. 그리고 그것을가지
고 남들을 설득할 수 있는 방법을 배워라.”
졸업연구를 진행하면서 교수님의 이 말씀이 계속 머리에 맴돌았습니다. 그리고 서서히 그러한 것들을
배워나가면서 연구라는 것이 쉽지는 않지만 정말 재미있는 일이라는 것을 알게 되었습니다. 항상 자신
의 생각을 남에게 정확히 전달하고 그것을 설득할 수 있도록 이끌어 주셔서 정말 감사합니다. 덕분에
제가 앞으로 하고 싶은 것이 무엇인지 이번 연구를 진행하면서 알 수 있었습니다.
Visual Media Lab을 세계 최고의 연구실을 만들기위해 앞으로 나아가시는 노준용 교수님! 정말 감사합
니다.
그리고 마지막으로 항상 저를 응원해 주시는 부모님, 동생 보아에게 감사의 말씀 전합니다.
P.S:존재자체만으로힘이되는녀석들 -김종우김종태김재준박무열박성현안건배준희 Tooth Fairy
– 22 –
Curriculum Vitae
Name : Hyunggoog Tryndamere Seo
Date of Birth : July 3, 1986
E-mail : [email protected]
Educations
2011. 3. – 2013. 2. Graduate School of Culture Technology, KAIST (M.S.)(Advisor.Junyong Noh)
2005. 3. – 2011. 2. Computer Science, KAIST (B.S.)(Advisor.Kieung Kim)
2002. 3. – 2005. 2. Chungmyung High School
Career
2010. 1. – 2010. 11. Programmer & Director, RG Soft
Academic Activities
1. Seunghoon Cha, Hyunggoog Seo, Jinho Park, Jonghyun Hwang, Junyong Noh An efficient dif-
fusion model for viscous fingering, Korea Computer Graphics Society 2012 , Jeju (Korea), June.,
2012.
– 23 –
