Realistic Simulation of 3D Cloud - WSEAS · such as computer games, military training ... a method...

Realistic Simulation of 3D Cloud

HANG QIU1,2,3 LEI-TING CHEN1,3 GUO-PING QIU2 HAO YANG1,2,3

1 School of Computer Science & Engineering, University of Electronic Science and Technology ofChina, Chengdu, CHINA

2 School of Computer Science, University of Nottingham, Nottingham, UNITED KINGDOM3 Provincial Key Laboratory of Digital Media, Chengdu, CHINA

[email protected]

Abstract: -The digital creation of cloud is important for many applications in computer graphics, includingoutdoor simulations and the digital rendering of atmospheric effects. Unfortunately, it is still difficult tosimulate realistic cloud with interactive frame rates due to its peculiar microstructures and complex physicalprocess of formation. Realistic simulation of cloud turns to be one of the most challenging topics in computergraphics. In this paper, we present a method for simulating 3D cloud. The Coupled Map Lattice (CML) isadopted for the modeling of cloud, and the simulation of light scattering in clouds is achieved by using a seriesof spherical harmonics and spherical harmonic coefficients that represent incident-light distribution. Afrequency domain volume-rendering algorithm combined with spherical harmonics is applied to implement fastrendering of cloud scenes. Experiments demonstrate that our method facilitates computing efficiency, whileyielding realistic visual quality.

Key-Words: - Natural Scene, Coupled Map Lattice (CML), Spherical Harmonics, Frequency Domain, CloudRendering, Volume Rendering

1 IntroductionSimulation of natural phenomena has become animportant research field and one of the mostdifficult tasks in computer graphics. Cloud is anessential component of natural scenes, which playsan important role in various fields of applications,such as computer games, military trainingsimulations, flight simulations, virtual reality andspecial effects of movies. Unfortunately, like otheramorphous phenomena, clouds elude traditionalmodeling techniques with their peculiar pattern ofintricate, ever-changing volume-fillingmicrostructures. In addition, the visual aspect of acloud depends on complex light interactions.Simulating the effect of light propagation throughclouds is a time consuming and computationalintensive process. Moreover, the motion of cloud isextremely complex, which covers atmosphericflows, evaporation of water, water condensation andheat exchange. All aspects above-mentioned make itdifficult to generate visually convincing cloudsscene efficiently. Limited computational power andthe extreme complexity of physical process havecalled for tradeoffs between efficiency and realism.

In this paper, a method for simulating realistic3D cloud is proposed. Our goal is to look for theright compromise between realism and efficiency.

The major contributions of our work can be listed asfollows.

(1) To simulate the complex light scattering inclouds, spherical harmonics-based approach ispresented. A series of spherical harmonics andspherical harmonic coefficients are used to representincident light distribution. The values of sphericalharmonic coefficients are obtained by off-linesampling. This method can not only controlcomputation cost, but also meet the demands ofreality.

(2) Considering the existence of large-scale data,massive integrals and ever-changing viewpoint inthe scene, a frequency domain volume renderingalgorithm combined with spherical harmonics isimplemented, which improves the renderingefficiency effectively.

The rest of the paper is organized as follows.Section 2 briefly overview related work insimulation of clouds. Section 3 gives the overviewof our method. Section 4 depicts the modeling ofcloud based on CML, while Section 5 proposes anapproach for the lighting simulation based onspherical harmonics. Section 6 discusses cloudrendering based on frequencydomain volumerendering algorithm. Section 7 presents experimentsto demonstrate the efficiency of our method. Theconclusion of this paper is given in Section 8.

WSEAS TRANSACTIONS on COMPUTERS Hang Qiu, Lei-Ting Chen, Guo-Ping Qiu, Hao Yang

E-ISSN: 2224-2872 331 Issue 8, Volume 12, August 2013

2 Related WorkExtensive works made efforts to simulate realisticclouds. The related technologies can roughly beclassified into two categories: modeling andrendering. In this section, we give a briefly reviewof related work. The more specific survey can befound in [1].

2.1 Modeling of CloudCloud modeling deals with the data used torepresent clouds in the computer, and how the dataare generated and organized. The methods for themodeling of cloud can be classified into two maincategories. One is procedural techniques and theother is based on physical simulation.

Schopik et al. [2] used volumetric implicit tomodel clouds, which has the beneficial attributes ofsmooth blending, simple computation. Nishita et al.[3] adopted fractals modeling method to representcloud. Texture sprite modeling approach isdeveloped in [4,5]. Above mentioned proceduraltechniques are computationally inexpensive, and thecloud shapes can be controlled by variousparameters. However, the adjustment of parametersis often conducted by trial and error, which haslimited extension.

The physically-based simulation methods aremore accurate when describing the shape of cloudand other attributes of cloud. Dobashi et al. [6]developed an efficient method for cloud simulationusing cellular automaton. Nevertheless, it is hard tosimulate complicated physics process. Miyazaki etal. [7] used Coupled Map Lattice, an extension ofcellular automaton, to simulate various types ofclouds. Harris [8,9] took the phase transition intoaccount when using Stam’s stable fluid solver [10]

for fluid dynamics. Unfortunately, due to its highcomputational demands, physics-based simulation isnot appropriate to real-time rendering.

2.2 Rendering of CloudRealistic rendering of clouds involves solving thecomplex interaction of light within the cloud andwith its environment. Interactive methods achieveefficient cloud rendering by ignoring most lightinteraction modes. As early as 1985, Gardner [11]has developed mapping technique to display clouds.Harris et al. [8,12] developed a fast renderingmethod for dynamic clouds. Both the motion andthe images of clouds are computed on the GPUusing 3D textures.

To improve realism, scattering of light should betaken into account. However, simulating themultiple scattering of light in a cloud would requirean unacceptable time to converge. Varioussimplifications have been proposed. Miyazaki et al.[13] considered single scattering of light andshadow-view slices-based rendering algorithm.Bouthors et al. [14, 15] analyzed light behaviour inplane-parallel homogeneous slabs and based on thisanalysis design a series of ad-hoc functions to obtainillumination in the rendered cloud. Most recently,Elek et al. [16] proposed an interactive algorithm. Itutilizes a temporally coherent illumination cachingprocess to amortize the simulation costs acrossmultiple frames.

3 Overview of Our MethodIn this section, we give an overview of our method.As shown in Fig.1.

Fig. 1 Simulation framework



In our method, the simulation process is dividedinto two phases. The main work of off-lineprocessing is to generate cloud data, pre-computeincident light and transform volume data to therepresentation of frequency domain. The work ofreal-time rendering processing is to carry outfrequency domain volume rendering. The details ofaforementioned two phases are amplified as follows.

(1) Off-line processing: firstly, the simulationspace is subdivided into lattices. Lattice data anditerations are initialized. Using Coupled Map Lattice(CML), the physical process of phase transition issimulated and cloud data can be generated. Tosimulate the interaction between light and cloud, weuse a series of spherical harmonics and sphericalharmonic coefficients to represent incident lightdistribution. At the same time, the cloud data arerendered to textures and the texture slices areconstructed. The volume data, which includespherical harmonic coefficients and density, can beobtained by iterative computation. At last, usingFourier transform to achieve the frequency domainrepresentation of volume data.

(2) Real-time rendering: according to the currentviewpoint, texture slices are extracted in frequencydomain and transformed to spatial domain data.Combining with phase function and transmissionlight, the final image in the direction of sight-linecan be achieved.

4 The Modeling of Cloud based onCMLIn nature, clouds are formed as a bubble of air isheated by the underlying terrain, causing the bubbleto rise into regions of low temperature. Then phasetransition occurs, that is, water vapor in the bubblebecomes water droplets (clouds). Obviously,atmospheric fluid dynamics is the most directapproach to model clouds. However, it requires agreat deal of computational cost.

Coupled Map Lattice (CML) is a dynamicalsystem that models the behaviour of non-linearsystems. It is easy to implement and computationalcost is small. Therefore, we applied CML toimplement the modeling of cloud.

As shown in Fig. 2. The simulation space issubdivided into lattices. The number of lattices is

zyx NNN .

Each lattice point ),,( zyx contains a set of

properties for simulating the physical state of cloud.The set of properties can be expressed as:

},,,{),,( EwwvzyxP lv (1)

where ),,( zyxv is the velocity vector.

),,( zyxwvis the water vapour. ),,( zyxwl

depicts the

water droplets, while ),,( zyxE is the internal energy.

Fig. 2 The generation of cloud data

We adopt CML to simulate the formation ofcloud. During the simulation, the distribution of thestate values in each lattice are calculated andupdated at every time step. Let P be the state value

for current time step. The state value P in the nexttime step can be calculated by P .

Similar as [7], we considered the factorsincluding viscosity and pressure effects, advection,diffusion of water vapour, thermal diffusion,thermal buoyancy and phase transition.

Velocity field is affected by viscosity andpressure. To avoid complex computation andsimulate the influence of viscosity and pressure onvelocity field, the z component of the velocity v

for the next time step ( zv ) is calculated as:

xp

xvzz

divVgradk

zyxvkzyxvzyxv

)(

),,(),,(),,(

(2)

where zv is the z component of velocity v for

the current time step.vk is the viscosity ratio and

pk

is the coefficient of pressure effect. Thecomputations of x and y components are in the

similar way.The buoyancy effect is simulated by the

following equation:

)],1,(),1,(

),,1(,,1

),,(4[4

),,(),,(

zyxEzyxE

zyxEzyxE

zyxEk

zyxvzyxv bzz

）（ (3)

wherebk is the coefficient affecting the strength

of the buoyancy force.Diffusion of water vapour and thermal diffusion

are simulated as follows:



*( , , ) ( , , ) ( , , )vv v w vw x y z w x y z k w x y z (4)

),,(),,(),,(* zyxEkzyxEzyxE E (5)

vwk is the diffusion coefficient for water vapour.

( , , )vw vk w x y z depicts the diffusion effects.

Ek is the

coefficient of thermal diffusion.vw and

E represent the difference of water vapour andtemperature per time.

Affected by viscosity field, advection, diffusionand buoyancy, water vapour value in each lattice istransported to the adjacent lattices. When theamount of water vapour reaches to the maximumamount of water vapour, phase transition thatgenerates water droplets (clouds) happens.

5 Lighting Simulation based onSpherical HarmonicsTo achieve realistic performance, interactionsbetween light and cloud must be considered. Innature, the colour of a cloud depends on the lightthat cloud received and the position of theviewpoint.

The incident light intensity of a cloud iscomposed of sunlight, sky light and reflected lightfrom earth [3]. As shown in Fig. 3, when incidentlight spreads in cloud, it will be affected bytransmission and multiple scattering. Transmissionis only related to the attenuation of light intensity.However, multiple scattering affects both theintensity and propagation direction of light. Theintensity of emergent light is formed bytransmission light and scattering light.

Fig. 3 Light spreading inside cloud

Riley et al. [17] used angular distribution, whichrepresented by convolution, to simulate multiplescattering. This method considered only the forwardportion of multiple scattering, and it is still semi-empirical. Some other researchers, represented byDobashi [6, 19] and Miyazaki [18], simplified thecomplicated integral calculation to polynomial.Although these approaches can achieve real-timeperformance, the display results are not satisfied.

Compared with the above-mentioned methods, inthis section, we present a trade-off approach.

5.1 Basic PrincipleTo simulate the multiple scattering of light in cloud,the incident light distribution, which includestransmission light and scattering light, is calculated.To improve clarity in the following sections, wedefine some symbols. As shown in Table 1.

Table 1. Definition of Symbol

Symbol Definition

Direction

nx

Position of cloud particle

( , )nL x The intensity reflected from position

nx in

direction

inin LL~

/Incident light intensity/sample of incident lightintensity

outL Emergent light intensity

backL Background transmission light intensity

( )mlc

Spherical harmonic coefficients

( , )P

Phase function

sK Dissipation coefficient

C Polynomial

Approximate value of backward scatteringlight at position

nx

( , )LP Phase function. Its reference point is light

source

5.1.1 Representation of Incident LightDistributionIncident light distribution depicts the incident lightintensity of cloud particles under the influence oftransmission and scattering.

We use spherical harmonics [20] to representincident light distribution, which can be expressedas follows:

ml

ml

mLlin YcL

in

,)( )()(

(6)

)(

inL is the incident light intensity in direction

.mlY ,

is spherical harmonics that can be

traditionally represented as:

0),(cos

0),(cos)sin(2

0),(cos)cos(2

),()(

00 mPK

mPmK

mPmK

YY

ll

ml

ml

ml

ml

ml

ml

(7)

where l R , [ , ]m l l . (cos )mlP is associated

Legendre polynomials. mlK is a polynomials that

related to l and m . ( )mlY

can be calculated by

transforming it to spherical coordinates. That is to



say we can use equation (6) to calculate the incidentlight intensity in any directions when the value of

spherical harmonic coefficient mLl in

c )( could be

obtained. Therefore, we store a set of sphericalharmonic coefficients for each cloud particle torepresent the incident light distribution of eachcloud particle. The spherical harmonic coefficientcan be calculated by using a series of samplingvalue )(

~

inL :

dYLc mlin

mLl in

)()(~

)( (8)

5.1.2 Choice of Sampling EquationIn our approach, the sampling object is the incidentlight of current cloud particle in various directions.We divide the incident light into three differenttypes: direct sunlight, forward incident light andbackward incident light. As shown in Fig. 4.

Fig. 4 Composition of incident light

Sampling is time consuming. To reduce thecomputation cost, we adopt different samplingapproaches according to different types of incidentlight.

(1) Direct sunlight. It provides the most incidentenergy for cloud particle by transmission andscattering. We use a revised light transport modelfor sampling, which can not only guaranteecalculation precision, but also reduce the calculationtime.

(2) Forward incident light. It affects the intensityof incident light by scattering. We ignore theinfluence of transmission, and adopt the simplifiedlight transport model to calculate.

(3) Backward incident light. Compared with thetwo types of incident lights above mentioned, itsintensity is weaker. We put forward an approximatesimulation by adopting a constant term.

Through sampling calculation of three types ofincident light, the sampling data of cloud particle invarious directions can be achieved, thus m

Ll inc )(

can be

obtained.

5.1.3 Calculation of Lighting based on GPUTo benefit from GPU processing, we adopt render totexture (RTT) technique. The density and spherical

harmonic coefficients are organized to textures. Aseries of spherical harmonic coefficients of eachcloud particle are achieved by iterative calculation.Thus, the incident light intensity of each cloudparticle can be obtained.

5.2 Revised Light Transport Model based onSpherical HarmonicsTo simulate the complicated scattering, the lighttransport model is usually applied:

dsDsTsgDTLxLD

n 0

),()(),0(),0(),( (8)

),0(

L is the incident radiance.

),0(),0( DTL

indicates incident light that reaches

current particle by transmission in direction

. ),( DsT is the transmittance.

dsxLxPsxKsg s )),((),,())(()(4

(9)

)(sg represents the attenuation of intensity

),(

nxL at nx

in direction

due to the scattering of

current particle. At the same time, the scattered lightfrom other particles enhanced its intensity.

In order to use the light transport model above-mentioned to implement sampling calculation invarious directions, we make light transport modelequivalent to view-independent incident light modeland view-dependent emergent light model.

5.2.1 Equivalent Representation of LightTransport ModelWhen parallel light reaches cloud, cloud particlesreceive different intensity of incident light invarious directions. Therefore, view-dependentincident light distribution is formed. As shown inFig. 5 (a), even if the viewpoint changes, theincident light distribution of particle will not bechanged. For the emergent light, its intensityincludes background transmission light andscattered light. The intensity of light that receivedby viewpoint will be changed according to theposition of viewpoint. As shown in Fig. 5 (b).

(a) View-independent (b) View-dependent

Fig. 5 View-independent incident light distributionand view-dependent emergent light



The equation (8) is made equivalent to two parts:calculation of incident light and calculation ofemergent light .As shown in equation (10) (11):

dsdsxLsxPsxKDsT

DTLxL

D

insn

ninnin

4

)),((),),(())((),(

))(,0(),0(),((10)

dsdPsxLsxKDsT

DxTLvuL

s

Vinsn

vuVbackVout

),()),(())((),(

),(),0(),,( , (11)

Equation (10) obtains intensity of incident lightin various directions by background transmissionlight and scattered light of surrounding particles.The core of equation (10) is to calculate multiplescattering model, which is implemented in off-lineprocessing by using spherical harmonics.

Equation (11) uses incident light distribution,which obtained by equation (10), to calculateintensity of emergent light in direction of sight line.According to the relationship between emergentlight and the position of viewpoint, we use equation(11) in real-time processing.

5.2.2 Spherical Harmonic-based Sampling(1) Direct sunlightTo achieve sampling value of incident

light ),(~

Lnin xL in light source direction, we

construct the recursive form of equation (10):

dxLPK

xCxL

LninLs

Lnnin

)),((),(

))((),(

1

4

1

(12)

),(),())(( 111 nnLninLn xxTxLxC

(13)

))(( 1 LnxC

can be calculated according to the

result of the previous iteration. ),(

LP is phase

function. Its reference direction is equivalent to thedirection of light source. We use the orthogonalityof spherical harmonics to achieve the final samplingequation as follows:

ml

nm

Llm

PlsLnnin xccKxCxLIN

,1)()(1 )())((),(

(14)

dYxPc mln

mPl )(),()(

(15)

(2) Forward incident lightFor the forward incident light, only the scattering

lights of the adjacent particles are considered.Therefore, the computational model can berepresented as:

dsdsxLsxPsxKDsTxLD

innnin

4

)),((),),(())((),(),(~ (16)

The recursive form of equation (16) can beexpressed as:

])),((),),(()(

),()[,(),(~

4

111

11

dxLxPxK

xLxxTxL

ninnns

ninnnnin(17)

According to the orthogonality and rotationinvariance of spherical harmonics, equation (17) canbe rewritten as:

mln

mLl

mPlnsnn

ninnnnin

xccRxKxxT

xLxxTxL

inL

,1)()(,11

11

)()()(),(

),(),(),(~

(18)

,LR represents the new coefficient after rotation.

(3) Backward incident lightBackward incident light has little contribution to

the intensity. We adopt a constant value to

simulate it.In conclusion, the final equation that depicts

incident light distribution can be expressed asfollows:

)]()(),(~

)(),(~

[4)()(

ml

backward

ml

forwardnin

Lm

lLninnm

Ll

YYxL

YxLN

xcin

(19)

N is the total sample number. Equation (19) canbe used to calculate view-independent illuminationmodel.

5.3 ImplementationWe adopt RTT technique to reiterate the SHcoefficients for each cloud particle. The calculationprocess is divided into two phases: CPU processingand GPU processing. As shown in Fig. 6.

Fig. 6 Calculation flow



(1) CPU processingFirstly, based on RTT technique, the lattice data

are translated into 2D texture slices. The first textureis set to be the data source of the first iterativecalculation.

Each texel of texture corresponds to a cloudparticle. The spherical harmonic coefficients anddensity are stored in RGBA channels. As shown inFig. 7.

Fig. 7 Cloud data storage structure

In the following calculation process, thespherical harmonic coefficients are updatedaccording to the iterative calculation results.

(2) GPU processingFirstly, using equation (19), spherical harmonic

coefficients of current texture are calculatedaccording to the information of the first texture. Theresults of the first iteration are set to be the inputdata for the following iterative calculation. Thisprocedure can be repeated, until all the textures areprocessed.

6 Cloud Rendering based onFrequency Domain Volume RenderingThe most popular rendering techniques for 3D cloudsimulation include splatting [6, 7] and slice-basedvolume rendering [8, 9, 17]. These methods take fulladvantage of parallel capability of GPU and achievehigh rendering speed. However, when viewpointchanges, the volume clouds need to bereconstructed, the computation cost can not beignored.

Considering the ever-changing viewpoint,integral calculation and massive cloud data in cloudscene, frequency domain volume rendering [21, 22]is a feasible approach. Nevertheless, traditionalfrequency domain volume rendering algorithm lacksof depth information. Therefore, we present afrequency domain volume rendering methodcombined with spherical harmonics to look for theright compromise between realism and efficiency.

6.1 Frequency Domain Volume RenderingAlgorithmThe traditional frequency domain volume renderingalgorithm is based on Fourier projection slicetheorem. Once a volume data is Fouriertransformed, an image for any viewing direction canbe obtained by extracting a 2D slice of the 3Dspectrum at the appropriate orientation and theninverse Fourier transforming it [21, 22]. As shownin Fig. 8.

Fig. 8 Frequency-domain volume rendering

The implementation of frequency domainvolume rendering includes two steps:

(1) Pre-processing step. 3D spatial data aretransformed into the frequency domain, which canbe expressed as:

dxdydzezyxfwvuF zwyvxui )(2),,(),,( (20)

(2) Real-time rendering step. A parallelprojection of ),,( zyxf can be computed by

evaluating ),,( wvuF along a plane defined by the

arbitrary orthonormal vectors. Each point of theplane corresponds to a function value:

)(),( vuFP vuvu

(21)

At last, taking its inverse 2D Fourier transformyields the projection.

The primary motivation of frequency domainvolume rendering is that, once the forward 3Dtransform is computed as a pre-processing operation,we can compute projections at arbitrary anglesquickly by working with 2D manifolds of the data infrequency domain. Its essence is linear integralalong some directions.

6.2 Frequency Domain Volume RenderingAlgorithm Combined with SphericalHarmonicsIn real-time rendering phase, equation (11) is usedto obtain the light intensity in direction of sight line.As shown in equation (11).



Set

dPsxLsxKDsTA Vinn

),()),(())((),(

Equation (11) can be expressed as:

dsADxTLvuLs

vuVbackVout ),(),0(),,( ,

(22)

Obviously, )),((

sxLinis represented by a series

of spherical harmonic coefficients mLl in

c )(.

),( , DxT vu

is optical depth, which can be calcuated

as follows:

s

sdttx

eDxT)(

))(,(

(23)

is density. depicts albedo. All of them are

set to be constant values. Thus, we only need tocalculate:

dxdydzewvuF zwyvxui )(2),,( (24)

(1) Depth information supportTraditional frequency domain volume rendering

lacks depth information. Totsuka et al. [22]provided an approach to overcome this drawback.However, it is time consuming. In our method, weadopt a function ))(( s related to density to

approximately substitute ),( DsT . Thus, in equation

(22), dsAs can be depicted as:

dsdPsxLsxKs Vin

s

),()),(())(())(( (25)

(2) Phase function supportFirstly, we transform equation (25) into the

following form:

dssxcVcVsxKs mLl

mPl

sin

)))]((()([))(())(( )()(

(26)

where )))((( )( sxcV mLl in

is the spherical harmonic

coefficient vector corresponding to incident lightdistribution. )( )(

mPlcV

is the spherical harmonic

coefficient vector corresponding to phase function.Equation (26) can be formed as:

)()))]((())(())(([ )()(m

Pls

mLl cVsxcVsxKs

in

(27)

The essential of equation (27) is to calculateemergent light intensity accumulation of all thesampling points in direction of sight line. Thus, thephase function of each sampling point is the same.Each sampling point in the integral path has thesame )( )(

mPlcV

. Therefore,

))((...))(())(( )(2)(1)( nm

Plm

Plm

Pl scVscVscV

(28)

Equation (27) can be depicted as:

s

mLl

mPl

s

mLl

mPl

l m s

mLl

mPl

dssxsxcVcV

sxsxcVcV

sxsxcc

in

in

in

)))(())((()(

)))(())((()(

))(())((

)()(

)()(

)()(

(29)

where ))(())(())(( sxKssx

.

From a physical standpoint, the essential of ourmethod is to make the incident light distribution ofeach particle in the integral path equivalent to thetotal incident light distribution of a single particle.As shown in Fig. 9.

Fig. 9 Physical meaning of phase function-supported frequency domain volume rendering

7 Experiments and DiscussionsWe use OpenGL on C++ platform to implement themethod presented in this paper, and carry out relatedexperiments on PC. The computer configurationused for experiments is Windows XP operatingsystem, Intel Pentium 2.6GHz CPU, 2G memory,and NIVDIA 9800GT graphics card.

The performances of our rendering method areshown in Fig.10, which have little perceivable lossin image quality.

(a)



(b)

Fig. 10 The snapshots of cloud simulation

To testify the influences of lattice number andinterpolation algorithm on the rendering efficiency,we carried out a series of pressure tests. Firstly, weconstructed three scenes. The lattice number inabove-mentioned three scenes are set to 888 ,

161616 and 323232 respectively. Based on tri-linear interpolation and high order interpolation, weanalyze rendering efficiency. The fly-through pathis predefined. We sampled 2000 frames in eachscene respectively, and achieved the average framerate. Fig.11 shows the result.

For tri-linear interpolation, when the number oflattice is 888 and 161616 , with the increase ofcloud number, the rendering efficiency decreasednot evidently. When the cloud number is 10, therendering speed is 50fps and 45fps, respectively.With the increase of lattice point, the renderingefficiency decreased. Benefit from frequencydomain volume rendering, the computational costcan be controlled effectively. When the number oflattice is 323232 and the number of renderingcloud is 10, the rendering speed is still 20fps.

(a) Rendering efficiency with tri-linear interpolation

(b) Rendering efficiency with high order interpolation

Fig. 11 Rendering efficiency with different cloudresolution and interpolation algorithm

For high order interpolation, with the increase oflattice point, the rendering efficiency decreasedquickly. When the number of lattice is 323232

and the number of rendering cloud is 4, therendering speed is still 20fps.

8 ConclusionRealistic simulation of cloud is a challengingproblem in the field of natural phenomenasimulation with wide applications. In this paper, wehave proposed an effective method for simulating3D cloud. The interactions between light and cloudare considered, and achieved by using a series ofspherical harmonics and spherical harmoniccoefficients to represent incident-light distribution.To improve rendering speed, a frequency domainvolume-rendering algorithm combined withspherical harmonics is presented.

Obviously, the method proposed in this paper isnot considering flying through or inside the clouds.Furthermore, our method is not very suitable foranimation of clouds. In the near future, we wouldlike to extend our algorithm to handle the dynamicsimulation of cloud.

Acknowledgement:The authors wish to thank the anonymous reviewersfor their thorough review and highly appreciate thecomments and suggestions, which significantlycontributed to improving the quality of this paper.

This work is supported by National HighTechnology Research and Development Program ofChina (No. 2012AA011503), Project on theIntegration of Industry, Education and Research of



Guangdong Province (No. 2012B090600008) andthe pre-research project (No. 51306050102).

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