Creating Endless Water Flow Animation using Particle Data

Masanori Sotozaki

, Yoshinori Dobashi

1,2

and Tsuyoshi Yamamoto

Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Hokkaido, Japan

JST CREST, Tokyo, Japan

Keywords:

Particle-based Simulation, Endless Animation, Water, Natural phenomena, River.

Abstract:

In this paper, we propose an efﬁcient method for synthesizing water animation such as waterfall or rivers

using particle-based simulation. Recently, physically based simulation has become a popular technique to

create realistic animation of natural phenomena in many applications, e.g. commercial ﬁlms, movies and

games. Particularly, there is a growing demand on synthesizing realistic animation of ﬂuids, such as water.

However, realistic ﬂuid animation requires a high computational cost. Some applications requiring real time

performances, such as games, cannot afford such a high computational cost. In this paper, we propose an

efﬁcient method for creating endless animations of water ﬂow using particle data generated by ﬂuid simulation.

We store a set of dynamic particles in a database and use them repeatedly to produce endless animations.

1 INTRODUCTION

Computer graphics has become a popular tech-

nique and used in many applications, such as

movies, games, and commercial ﬁlms. In particu-

lar, physically-based simulation is often used recently

because it can create realistic animations of natural

phenomena by simulating actual physical processes.

Many physically-based methods have been proposed

for simulating ﬂuids such as water, smoke, ﬁre, and

so on. There are two main approaches for physically-

based ﬂuid simulation: grid- and particle-based meth-

ods. Grid-based methods uses grids to store physi-

cal quantities, such as velocities, at each grid point

(Stam, 1999), (Foster and Fedkiw, 2001). Particle-

based methods represent the ﬂuid with particles, cal-

culating the velocity and position of each particle

(M¨uller et al., 2003). Particle-based methods are pop-

ular for simulating water motion since it can handle

drastic deformations of water surface such as splash.

However, physically-based methods have some prob-

lems. One of the problems with physically-based sim-

ulations is its expensive computational cost.

In entertainment applications, it is often required

to create endless water sequences such as water-

falls, rivers, and fountains. To meet such a re-

quirement, advected textures techniques are some-

times used (Neyret, 2003). Noise functions are of-

ten used for dynamic water surface motion (Perlin,

1985). However, these approaches cannot generate

realistic movements since these are not physically-

based methods.

In this paper, the main contribution is an effective

approach for creating endless water animation. We

use particles created by particle-based water simula-

tion. In a preprocess, water ﬂow is simulated using

particles and the motions of the particles are stored in

a database. Our method uses the database to create

endless animations of water ﬂow. Our method has the

following three features:

• Since our method uses the particle database cre-

ated by the ﬂuid simulation, we can synthesize re-

alistic motion of water with high visual quality.

• Our method synthesizes endless water animations

from the particle dataset that are created for a

short period of time.

• Our method is efﬁcient since no ﬂuid simulation

is required once the particle dataset has been cre-

ated.

The rest of this paper is organized as follows. In

Section 2, we brieﬂy discuss some related work to

clarify the advantages of our method. Next, in Sec-

tion 3, we describe our proposed method. Some ex-

perimental results are shown in Section 4. Finally, in

Section 5, we conclude this paper.

2 RELATED WORK

This section describes some related work. First, we

describe particle-based ﬂuid simulation in Subsection

236

Sotozaki, M., Dobashi, Y. and Yamamoto, T.

Creating Endless Water Flow Animation using Particle Data.

DOI: 10.5220/0005746602340239

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 1: GRAPP, pages 236-241

ISBN: 978-989-758-175-5

 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reser ved

Particle-based

Simulator

particle data

placing

capturing box

Endless Water

Animation

Preprocess

reconstructing of

water surface

matching between

particle groups

emitting

particle groups

Endless

Particle Data

Run-time Process

particle group

Database

Particle Group1

Particle Group2

Particle Group3

g p

Database

Particle Group1

Particle Group2

Particle Group3

Figure 1: Overview of our method.

2.1. Next, we describe image-based methods for cre-

ating endless water animation in Subsection 2.2.

2.1 Particle-based Fluid Simulation

Using ﬂuid simulation can generate realistic ﬂuid an-

imation. Particle-based simulations are popular for

water simulation. M¨uller et al. proposed a particle-

based simulation called Smoothed Particle Hydrody-

namics (SPH) method (M¨uller et al., 2003). This

method discretizes the ﬂuid with particles, and solve

Navier-Stokes equations to calculate water motions.

Koshizuka et al. proposed Moving Particle Semi-

implicit (MPS) mehod for handling incompressible

ﬂuids (Koshizuka and Oka, 1996). Zhu et al. devel-

oped a method called Fluid-Implicit-Particle (FLIP)

which combines grid and particle based simulations

(Zhu and Bridson, 2005). This method reduces er-

rors by using particles for the advection process in

ﬂuid simulation. Recently, many methods have been

proposed to improve the SPH method. Becker et al.

proposed a method that enforces incompressibllity for

SPH simulation (Becker and Teschner, 2007). So-

lenthaler et al. improved SPH to take long time

steps (Solenthaler and Pajarola, 2009). M¨uller et al.

proposed Position Based Dynamics (PBD) method

(M¨uller et al., 2007). Macklin et al. proposed Po-

sition Based Fluids (PBF) using PBD for particle-

based simulation (Macklin and M¨uller, 2013). This

is suitable for parallelization using Graphics Process-

ing Unit (GPU). Nugjgar et al. proposed creating end-

less water surface animation using Markov-Type Vec-

tor Field (Nugjgar and Chiba, 2013). This method

employ surface model, our method employs particle

database approach.

2.2 Image-based Methods

While ﬂuid simulation generates realistic animation,

one of the problems is its high computational cost.

This is especially problematic for creating highly re-

alistic images by increasing the number of particles.

An alternative approach to the ﬂuid simulation is to

use videos of real water ﬂow. This subsection dis-

cusses some of those methods using videos. Bhat et

al. proposed the method generating seamless endless

animation (Bhat et al., 2004). This method is able

to synthesize and edit endless 2D animation using 2D

video input. Okabe et al. proposed ﬂuid video synthe-

sise method from single view image with ﬂuid video

databases (Okabe et al., 2011). Since this method

uses 2D images, so it cannot handle free viewpoints.

Many methods that reconstruct water surfaces from

images were proposed (Yu and Quan, 2013), (Li et al.,

2013), (Ihrke et al., 2005), (Hilsenstein, 2005). How-

ever, these cannot express dynamic animation such as

splash since 2D images do not have geometric infor-

mation. Since our method uses simulated particles,

we can handle arbitrary viewpoints and dynamic mo-

tions of water.

3 OUR METHOD

The proposed method is suitable for creating steady

ﬂows, such as river and waterfall. Figure 1 shows an

overview of our method. As shown in Figure 1(a), we

ﬁrst creates the particle dataset by ﬂuid simulation us-

ing the SPH method in a preprocess (Subsection 3.1).

3.1 Database Construction

The database of particles is constructed by running

the particle-based water simulation as a preprocess.

Creating Endless Water Flow Animation using Particle Data

237

Our method assumes steady ﬂows such as streams

and is not suitable for such a situation where water is

poured into a glass. While simulation is running, we

divide the particles into a set of groups, which we call

particle groups. In the following, we explain how the

particle groups are generated by using a 2D example

shown in Figure 2. In order to simulate water ﬂow,

a particle emitter is placed at a position where the

water ﬂow begins. We also set a terminal boundary

where particles are forcibly eliminated (see Fig. 2).

The water ﬂow is then simulated by computing the

motions of the particles between the emitter and the

terminal boundary. In order to create particle groups,

a capturing box is placed at a user-speciﬁed position

as shown in Fig. 2. At each time step of the simu-

lation, our system checks the number of particles in-

side the capturing box. If the number exceeds N

min

the particles in the box form a particle group. N

min

speciﬁed by the user. The trajectories of the particles

are recorded until they reach the terminal boundary.

We repeat these processes until the number of parti-

cle groups reaches a user-speciﬁed number, M. In the

following sections, let us denote i-th particle group by

, where i = 0,1,· ·· ,M − 1.

particle emitter

terminal boundary

capturing box

Figure 2: Creating particle groups.

3.2 Similarity between Particle Groups

Our method creates endless animation of water ﬂow

by repeatedly selecting a particle group and emitting

the particles in the selected group. Our method selects

the particle group sequentially based on the similari-

ties between particle groups. This section explains the

computation of the similarity between a pair of parti-

cle groups.

The similarity D

between two particle groups S

and S

is calculated in the following way. We use the

distributionsof the particles at the time step when they

are in the capturing box. Although the numbers of

particles in these groups are not necessarily the same,

we assume that they are same. When the numbers

䝟䞊䝔䜱䜽䝹䝉䝑䝖㻌㻜㻌

䝟䞊䝔䜱䜽䝹䝉䝑䝖㻌㻝㻌

䝟䞊䝔䜱䜽䝹䝉䝑䝖㻌㻞㻌

䝟䞊䝔䜱䜽䝹䝉䝑䝖㻌

(a)

(b)

(c)

(d)

Figure 3: Creating endless water animation.

are different, we apply a clustering algorithm to one

of the groups containing larger number of particles so

that the number of clusters becomes the same as the

number of the particle of the other group. Next, we

compute a perfect matching between the particles in

and those in S

such that the following cost function

is minimized.

∑

i, j

||x

− x

, (1)

where x

and x

are positions of the corresponding

particles i and j in the matching between S

and S

respectively. This problem is equivalent to the min-

imum assignment problem. Our method solves this

problem using Hungarian method (Kuhn, 1955). We

use the minimum cost as the similarity D

3.3 Creating Endless Animation

We explain our method for creating endless anima-

tion of water ﬂow by using Figure 3. Figure 3 shows

a two-dimensional example for simplicity and uses

GRAPP 2016 - International Conference on Computer Graphics Theory and Applications

238

seven particle groups, S

, S

, ..., S

. We use similarity

as the transition probability matrix and create the

endless animation by randomly choosing the particle

groups using D

First, our method emits particles in S

(see Figure

3(a)). We then select a particle group from the rest of

the particle groups by using a random number obey-

ing D

∑

so that a particle group similar to S

is likely to be selected. In Figure 3 (b), S

is selected

and the particles in S

are emitted. As shown in Fig-

Figure 4: River results using our method.

ure 3(b), the particles in S

and S

are overlapped in

order to reduce the discontinuity between the parti-

cle groups. The next particle group is again selected

in the same way by using a random number obeying

∑

. The endless water animation is created

by repeating these processes.

(a)

(b)

(c)

Figure 5: Blending particle groups. The top(a) and mid-

dle(b) ﬁgures show particles simulated with different con-

ditions. The bottom ﬁgure shows particles created by blend-

ing particles in (a) and (b).

3.4 Blending Particle Groups

This section describes a method for synthesizing wa-

ter ﬂows by blending two sets of particle groups that

are created by water simulations under two different

conditions.

Let us explain the method by using Fig. 5, where

the water ﬂow shown in Fig. 5(c) is synthesized by

blending particles shown in Figs. 5(a) and (b). Let us

denote the two sets of particle groups, G

and G

, cre-

ated by using the two results shown in Figs. 5(a) and

(b), respectively. We ﬁrst translate the positions of the

particles so that the capturing boxes for G

and G

are

at the same position. Then, the water ﬂow is synthe-

sized by switching the particles in G

to the particles

Creating Endless Water Flow Animation using Particle Data

239

in G

at the position of the capturing box. In order to

achieve smooth transitions, a particle group in G

switched to a particle group in G

that is most sim-

ilar to the particle group in G

in terms of the cost

function expressed by Eq. 1. The positions of the par-

ticles are linearly blended between the corresponding

particles.

3.5 Reconstruction of Water Surfaces

The water surface is reconstructed in the following

way. We assign a kernel function for each particle.

We use an isotropic kernel function (M¨uller et al.,

2003). A grid covering all the particles is then gen-

erated and we accumulate the kernel functions of all

the particles into the grid. The water surface is ob-

tained by computing isosurfaces by using the march-

ing cubes method (Lorensen and Cline, 1987). How-

ever, when using this method, the discontinuity be-

tween the particle groups would be visible. As de-

scribed in the previous section, the successive parti-

cle groups overlap to avoid this problem. The ker-

nel functions of the particles in the overlapped region

are blended together so that the discontinuity is less

visible. Figure 6 shows an example of water surface

reconstruction.

Figure 6: The example of water surface reconstruction.

4 RESULTS

This section shows results using the proposedmethod.

The examples shown in this section are calculated

on a PC with Intel Core

i5 2.7GHz(CPU) and

8GB memory. We use a commercial software (Re-

alFlow2013, ) for creating the particle groups. Table

1 shows the calculation time. The images are rendered

by Autodesk Maya 2016(Maya2016, ).

Figure 4 shows an example of a synthetic river

generated by using proposed method. The number

of particles is approximately 20,000. Twenty parti-

cle groups are created. The capturing box is placed

Table 1: Calculation times for the two examples. T

is the

calculation time for creating 200 frame particle data. T

CPG

is the time for creating a single particle data. T

CEA

is the

for creating endless animation of 1,000 frames and T

BPG

the time for blending two particle groups consisting of 566

particles.

Snece T

CPG

CEA

BPG

River 157s 0.001s 13.773s —

Pipe 218s 0.001s 8.463s 664.573s

in front of the particle emitter. This example demon-

strates that our method successfully creates endless

water animation

Figure 7 shows another example created by blend-

(a)

(b)

(c)

Figure 7: Water ﬂow in the curved pipe. (a) is created by

computing motions of particles in the curved pipe. (b) is

created by computing particles in the straight pipe with an

obstacle in the middle. (c) is created by blending particles

in (a) and (b) using our method.

GRAPP 2016 - International Conference on Computer Graphics Theory and Applications

240

ing particles simulated with two different conditions.

Fig. 7(a) and (b) show the two sets of the particles

and Fig. 7(b) shows the particles created by blending

the particles in Figs. 7(a) and (b).

5 CONCLUSIONS AND FUTURE

WORKS

In this paper, we have proposed the method for creat-

ing endless water animation using simulated particles.

We also proposed the method for blending particles

simulated under different conditions. The proposed

method can create high quality animations with low

cost by re-using the particle groups repeatedly.

There are several possible future works. First, we

would like to extend our method to other natural phe-

nomena, such as ﬁre and smoke. Since our blending

method cannot handle more than two sets of the parti-

cle groups, we improvethe method to handle multiple

sets of particle groups.

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