liquid penetration modeling for cloth dyeingmorimoto/pdf_video/07cae_dyeing.pdf · since dyeing...

Computational Aesthetics in Graphics, Visualization, and Imaging (2007)D. W. Cunningham, G. Meyer, L. Neumann (Editors)

Liquid Penetration Modeling for Cloth Dyeing

Y. Morimoto†1 and R. Tsuruno2 and K. Tomimatsu2

1Guraduate School of Design, Kyushu University2Kyushu University

AbstractThis paper presents a model of cloth dyeing using the characteristics of the thread and weave pattern. The

proposed dyeing model is based on Fick’s second law that defines the molecular transfer under translationaldiffusion [Fic85]. The algorithm in the proposed model calculates the dyeing distribution from parameters suchas the amount of dyeing, saturated amount, and pressure in each cell on a timeline. We improve the algorithmbased on Fick’s second law to consider a woven cloth structure and describe the proposed model of the structureof woven cloth as a two-layer cellular model. We then visualize the cloth using a simple 2D shading method ofasperity by using the color distribution on a dyed image of real woven cloth. In addition, we provide a method forproducing dyeing patterns without dyeing diffusion. The proposed method produces images that capture severalof the characteristics of dyeing observed in real dyed cloth.

Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation

1. Introduction

Dyeing is a traditional method of imbuing a cloth with color.It is a traditional art form that produces interesting patterns,not only according to the artist’s intent, but also unaccount-able physical factors. However, liquid penetration into clothis a complicated phenomenon from a scientific and physi-cal standpoint, and the pattern and color of dyed cloth is afunction of the physical properties of the dye and the fabric.In other words, dyeing cannot be completely controlled bythe fabric-dyeing artist. Predicting the actual result of dyeingusing graphics would be useful for designing cloth with ac-curacy, especially since the dyeing process is a troublesometask in reality. More people would be interested in the dyeingprocess if they could better predict the final product.

Most existing non-photorealistic rendering research hasexamined fine arts such as painting and drawing. In thisarea, images are generated with paper and canvas textures.Dyeing is an art equivalent to painting, with cloth as themedium instead of canvas or paper. In order to characterizedyeing, physical models of cloth dyeing and models repre-senting the texture of cloth are essential. Furthermore, wemust construct a design system to represent the art form of

† Chairman Eurographics Publications Board

dyeing, such as creating patterns on cloth with dye. There-fore, we propose a comprehensive model of these elements,which are necessary for the visual simulation of dyeing. Thepresent paper is organized as follows: The following sectionpresents related work. Sections 3 and 4 describe dyeing andthe visual characteristics associated with the technique. Sec-tion 5 describes dyeing simulation, and Section 6 presentsthe results of the present study. Section 7 then describes pro-gram usage, and Section 8 presents the conclusions of thepresent study and describes areas for future study.

2. Related Work

The methods for simulating painting tools and drawingstrokes are progressing in the area of non-photorealistic ren-dering (NPR). Some research in this area includes water-color painting and Chinese ink painting, both of which in-volve the diffusion and pigment density color using pa-per [GK91] [CAS∗97] [ZSyT∗99] [Lee01] [GK03] [CT05].Curtis et al. [CAS∗97] presented a method for watercoloreffects such as dry-brushing, intentional backruns, and flowpatterns. Their model simulates three phenomena: the flowof water on paper, the flow through paper fibers, and pigmentdeposition. They successfully simulated watercolor paint onpaper. Chu et al. [CT05] developed a novel method for rep-

c© The Eurographics Association 2007.

Y. Morimoto & R. Tsuruno & K. Tomimatsu / Liquid Penetration Modeling for Cloth Dyeing

resenting the real drawing of a fluid on absorbent paper withthe Lattice Boltzmann equation in real time.

There has been some research on methods, such as thebatik method, that can be employed for painting on cloth.Wyvill et al. [WvOC04] presented an algorithm for simu-lating the cracks found in batik. Their method can produceconvincing patterns that capture many of the characteristicsof the crack patterns found in real batik cloth. Also, Dragoet al. [DC04] performed simulations of the canvas used foreasel paintings. Their work represents real woven canvasesand considers weaving patterns and canvas aging. However,the texture of the cloth is not included in Wyvill’s algorithm,and the diffusion of paint in cloth is not considered in eitherDrago’s or Wyvill’s research.

There has also been some research on the methods for thevisualization of cloth. These studies attempted to representinterwoven threads and to model the interaction of light withthe threads of cloth in detail [WAT92] [XCL∗01] [SYO04].However, this level of detail is not always necessary and wetherefore focused on the structure of the cloth for diffusion.We therefore propose a very simple rendering method forcloth that is suitable for representing dyeing.

To simulate dyeing, it is necessary to consider the weavestructure of the warp and weft. In this research, we representdyeing by the interaction of weave patterns and the diffusionof dye.

3. Outline of Dyeing

The purpose of dyeing is to change the color of cloth, thatis, to bond dye tightly to fabrics. The key elements of dyeingare cloth, dye, and dyeing techniques, each of which consistsof numerous finer aspects.

Cloth is a fabric structure woven from threads, which arein turn composed of fibers. Since the dye diffuses along thesefibers in a cloth, the directional characteristics of the threadhave a marked affect on dye diffusion into the cloth. Thetwo-directional thread characteristics of woven cloth are re-ferred to as the weft and warp and the type of cloth is classi-fied according to its weave pattern. The most well knownweaving pattern is a plain-woven pattern. A plain weaveis the style of weave in which the weft alternates over andunder the warp. However, in addition to the weave pattern,there are other elements that affect dyeing, such as the inter-val between fabrics. Narrow intervals between fabrics pre-vent dyeing [Oki94] [Kur96] [Sak99] [Yos02].

Since dyeing techniques are important for determininghow dyeing is applied as an art form, we describe the fol-lowing common dyeing process using the example shown inFigure 1 and described below. 1) Prepare the cloth by clean-ing. 2) Prevent parts of the cloth from dyeing to create a pat-tern. The two techniques of tie-dyeing, which adds pressureto the cloth with folding and sewing, and batik, which cov-ers the cloth with wax, before the dying process. 3) Wet the

cloth with water. 4) Dip it in the dye compound. 5) Dry andopen it. 6) Wash the cloth to remove dye pigments which arenot firmly fixed into the fabrics, and 7) dry it. After drying,the dyeing process is finished.

Figure 1: Outline of the actual dyeing process. The imageon the left shows the cloth before dyeing (1), the centerimage shows the cloth after being tied (2), and the imageon the right shows the cloth after the entire dyeing process(3,4,5,6,7).

4. Visual Characteristics of Dyeing

In this section, we describe the visual characteristics of dye-ing caused by the following three physical elements.

1: The "dye stain shape" and "mottles" caused by the di-rectional characteristics of the dyeing of thread. The "dyestain shape" changes as the amount of dye changes. It ap-proaches a circular form as the amount of dye increases anda rhombic form as the amount of dye decreases. Figure 2 (a)shows the different shapes of dye stains depending on theamount of dye. In this figure, the amount of dye decreasesfrom right to left. "Mottle" refers to the extreme deep sec-tions of color around the edge of a stain and is strongly af-fected by the directional characteristics of the thread. Clothconsists of interwoven and piled weft and warp, which en-ables cloth to be described as a two-layered material. It isimportant to produce mottles in dyeing because the layersin cloth reduce the diffusive conditions between them. Thus,the two-layered cloth model can be used to represent mot-tles. Figures 2 (b) and 2 (c) show a magnified image of astain, and Figure 2 (c) shows a magnified image of a stainwith its gray values exaggerated.

2: An arrangement of square elements appears due to theshades of the threads: That is, the shades of threads withincloth look like an arrangement of square elements. We canalso see that characteristics in Figure 2 (b). These squareelements can fluff up the fabric and generate a fuzzy appear-ance.

3: Gradation is caused by pressure dispersion: There aresome dyeing techniques in which an application of pressureon cloth prevents it from dyeing and therefore makes pat-terns on the cloth. The pressure added on a part of the clothdisperses and smoothes the values of stain. Figure 2 (d) isa magnified image of dyeing with pressure. The pressuresmoothly disperses and creates a gradation of the color.



Figure 2: Characteristics of cloth dyeing.

5. Dyeing Simulation

In this section we describe the proposed methods for mod-eling cloth and dyeing diffusion and for the visualization ofthe above characteristic phenomena.

5.1. Cloth Model

In a previous study on NPR, paper and cloth were rep-resented using a two-dimensional model. There is an ad-vantage to reducing the computational cost in the two-dimensional paper model. In addition, since the model is ca-pable of simulating painting it is thus suitable as an artistictool. However, as described in Section 4, a two-dimensionalmodel is not well suited to representing dyeing characteris-tics. In the proposed model, we introduce a two-layered clothmodel in order to minimize z-axis factors.

We use a cellular model to represent the cloth. First, wemake a thread model by arranging the cells. Second, we con-struct cloth with thread models corresponding to the weavingpattern (Figure 3). The cells are then modeled as cloth, suchthat their size is equal to the width of each thread which hasa different diameter. We use a random distribution for the di-ameter of wefts and warps for a more natural representation.First, diameter w1 (for the weft) and w2 (for the warp) aredefined at the user’s discretion. Next, the proposed modeldecides all values of the diameter of each weft and warp in arandom range that is based on w1 and w2. The weft and warpare then constructed into a two-layer structure, as shown inFigure 3. We set these two layers in the cloth model and both

of them appear according to the weaving pattern. Also, wesimulate a woven cloth based on this cellular cloth model fordyeing and shading.

Figure 3: Cloth model. Blue color indicates weft. Yellowcolor indicates warp. Cloth cells are used to model theweave cloth pattern. Diffusion cells are used in the dyeingmodel in section 5.2.

5.2. Dyeing Model

We assume that the dye diffuses into the plain-woven cloth.Figure 3, cells that are dyed from pixel to pixel are defined asdiffusion cells. We assume that the cloth is wet in the modelaccording to an actual dyeing process, so its physical envi-ronment involves dipping the cloth into the dye.

In the dyeing system, the proposed cellular model de-cides whether each pixel belongs to the weft or the warp.Then, diffusion dyeing occurs on each pixel depending onits properties. We extend the diffusion equation to includeweaving patterns; this original equation is Fick’s second law,which represents the molecular transfer under the conditionof translational diffusion. We show the process of dye diffu-sion below.

1. We set the values of the parameters on all pixels.

<Parameters on a pixel>

• Concentration of physical quantity of dye:(c in weft, s in warp)

• Position in the weft or warp:(i, j)

• The number of time steps:(t)

• Interval time for one step:(Δt)

• Interval between pixels:(Δd for x and y-axis, Δz for z-axis)

• Diffusion coefficient:(Dc in weft, Ds in warp)

• Pressure:(Pc in weft, Ps in warp)

• The minimum saturation a pixel must have before it candiffuse to its neighbors when the cloth is dry to begin with:(ε)



• Adsorption rate:(a)

Pressure affects the diffusion coefficient and capacity as wedescribe below in this section. If ε is 0, we suppose that thecloth is wet in advance. There is another parameter that isadsorption rate a to stop the diffusion, which is a constantrate in all cells. These parameters represent the differencebetween wet to dry cloth.

2. The user indicates the dyeing areas by drawing or in-putting an image. We define the dyeing areas in a dyeingtable. Also, the user can indicate areas where pressure is ap-plied in a way that is similar to having pressure being appliedto the cloth. This pressure was defined using pressure tables,which indicate where each function is being applied. In ad-dition, these tables indicate the degree of pressure and theamount of dye. However, in the case of generating a stain,the user indicates a point on a screen. Then, the cells in acertain range are saturated according to the amount of dye.

3. If the process includes pressure on the cloth as a dye-ing technique, the pressure value is decided by the pressuredistribution as shown in Figure 4. First, RGB values aresmoothed by linear interpolation. Second, the values exceed-ing a certain value are set as maximum pressure 0.0, whereminimum pressure is 1.0. The max is 0.0, which indicatesthat no dye is bonded. The minimum RGB values are setas the minimum pressure, 1.0. For simplicity, the RGB val-ues between the maximum and minimum are converted topressure values in the 0.0 to 1.0 range to adjust the diffusioncoefficient such that a natural pressure dispersion is created.This process does not occur without adding pressure to thedesign.

4. Dye diffusion occurs in the threads. Dye compound isapplied where it is indicated in the dyeing table. The amountof dye is user defined and is also defined by converting theRGB values from the dyeing table. Next, dye diffusion be-gins, with diffusion based on the formula of Fick’s secondlaw:

∂φ∂t

= D∂2φ∂d

(1)

where D is diffusion coefficient, φ is a concentration of dif-fuse matter such as dye. And discretized form of Formula(1) is

φt+1i, j = φt

i, j +ΔtD(φt

i+1, j −φti, j)+(φt

i+1, j −φti, j)

Δd2 (2)

Defines the one-dimensional molecular motion under thecondition of translational diffusion. Dye diffusion is basedon one-dimensional diffusion on the thread to be affected bythe dimensional characteristics of the thread. In addition, thediffusion can be assumed to affect crossing threads. There-fore, we improve formula 2 so as to consider the diffusion to

the crossing threads:

ct+1i, j = ct

i, j+

Δt

{D1

(cti+1, j−ct

i, j)+(cti+1, j−ct

i, j)Δd2 +D2

(sti, j−ct

i, j)Δz2

}

(3)

where D1 is the diffusion coefficient in the same thread anddirection as the thread of interest, D2 is the diffusion coef-ficient in the cross thread in the z direction. We can repre-sent various weaving patterns using the above formula, asillustrated in Figure 5. Furthermore, we define the diffusioncoefficient Dc,Ds randomly. This is different from the diffu-sion coefficient D in the original diffusion equation, whichis a constant. However, Dc,Ds varies with position and theproperties of the cloth. Since the diffusion coefficient varieswith location in a real cloth, each pixel is assigned a differentvalue. Also, the diffusion coefficient is affected by the degreeof pressure because pressure prevents diffusion. Therefore,we can compute Dc,Ds by setting:

D1 =(

Dci+1, j+Dci−1, j+Dci, j

3

)(Pci+1, j+Pci−1, j+Pci, j

3

)(4)

D2 =(

Dsi, j+Dci, j

2

)(Psi, j+Pci, j

2

)(5)

Dc and Ds are set according to the diameter of each thread.The capacity of dyeing of a cell depends on the pressurevalue. Therefore, dye diffusion does not occur at all if thepressure value is 0.0 in the proposed system. Also weavepatterns affect Dc and Ds by multiplication with arbitrarydecimal figure when position of the weft of warp in z-axis ischanging.

In the proposed dyeing model, we do not set the amountof water and dye; instead, we set the concentration of thephysical quantity of dye c and s. This means that water sat-urates the space where the dye is nonexistent. In the case ofdyeing dry cloth, we estimate dyeing using the same model,but assume that the water is air and add a rule for the surfacetension of the liquid that stops the diffusion where the cellhas insufficient dye. We represent the absorption of dye onfabrics by fixing absorption on a timeline at a constant rate.Also, the proposed model represents dyeing unevenness. Adifferent diffusion coefficient for the bias of the fabric den-sity and molecular concentration is used for dyeing uneven-ness. We use random numbers to determine the diffusion co-efficients for each thread (Figure 2 (e)).

The following is an example of the properties we employwhen we use a drop of dye on dry cloth with this model. Weset double capacity of dye in cells inside the area of a circlewith a radius of 30 pixels. We then apply the proposed dye-ing model with properties such as those shown in Table 1 (1)to produce the result shown in Figure 10 (a). Conversely, thestain produced by of a drop of dye on a wet cloth producedusing the properties shown in Table 1 (2) is shown in Figure10 (c).



properties Case (1) Case (2)

ε (percent) 0.5 0.0Dc,Ds (cm2/s) from 0.2 to 0.35 from 0.2 to 0.35Δd (cm) 0.8 0.8Δt (s) 0.5 0.5a (percent) 0.0001 0.0001Result

first radious 30 (pixels) 30 (pixels)final radious 48 (pixels) 58 (pixels)final timestep 2800 (times) 2000 (times)computational time 4 (minutes) 3 (minutes)

Table 1: There are examples of properties to make dyeingstains on the dry and wet cloth and their data of the results.The result of properties (1) is Figure 10 (a) as on the drycloth. The result of properties (2) is Figure 10 (c) as on thewet cloth. In this case, 2800 timesteps is worth 23 minutesat the actual time. Final timestep and computational time of(2) is up to the user.

Figure 4: Relationship between pressure and dyeing diffu-sion. (a) Dyeing table used as the set dyeing area. (b) Pres-sure table used as the set pressure area. We describe the dye-ing system using these tables in Section 7. (c) is (b) afterbeing Gauss filtered. (d) and (f) indicate the dispersion ofdyeing and pressure. (f) shows the pressure with smoothing,and (d) shows the pressure without smoothing. In (d) and (f),red indicates the areas of maximum pressure, blue indicatesthe areas of medium pressure, and green indicates the areasbeing dyed. (e) is the resulting image of dye diffusion for (d),and similarly (g) is the resulting image of dye diffusion of (f).

5.3. Visualization of the Dye and Cloth

Basic color by amount of dye: Applying the algorithm fromSection 5.2 produces the dispersion of the amount of dye.The algorithm can decide the basic color of the pixels. Weassign the basic colors using the highest and lowest colorvalues of a real image of dyeing with linear interpolation. Inorder to represent the dye, other color values can be added

x

zx

Figure 5: Connection between the warp and weft in the dif-fusion equation. The blue cells indicate the weft, and the yel-low cells indicate the warp, In addition, i and j indicate theposition in XY coordinates.

to determine the color from the real image of dyeing. Thepigment change associated with dye stains appears in thisway.

Cloth shading and fluff of fabrics: We present a sim-ple method for the shading of dye on cloth. Figure 6 (a) isa magnified image of real dyeing and Figure 6 (b) is a con-tour drawing of the average value of RGB in Figure 6 (a).The part of this image corresponding to the cell can be rep-resented with the hyperelliptic figures seen in Figure 6 (c).For each cell, we set the color distribution as in Figure 6 (c)based on the amount of dye. Figure 7 (a) is the image afterapplying the proposed dyeing model and Figure 7 (b) is theimage after applying the proposed shading model.

Weaving yarns are made from many small pieces of fluff.The fluff of fabrics makes the outline of the threads lookblurry and soft. In the proposed texture model, we use animage smoothing processing technique to make the contoursof the weaving yarns vague to represent the texture of fluff,as shown in Figure 7 (c). By selecting weave patterns, we canproduce various cloth textures, examples of which are shownin Figure 8. In addition, real cloth images can be used as thetexture with the proposed model. In this case, it is necessaryto indicate the weft and warp areas using another image.

6. Results

Figure 9 shows a comparison of real and computer-generatedstains on dry cloth with the proposed cloth shading model.These images in Figure 9 show the results according tocomputer-generated characteristics of dyeing as Figure 2 inSection 4. The color distributions for of the each stain typesare similar and both have a mottled appearance at the fringe.However, the dark edge and uneven arrangement of threadsin the real stain are not achieved in our results and we willattempt to resolve this in future. Figure 9 (a) is a comparisonbetween real and generated stains for the directional charac-teristics with an amount of dye. The outlines of the stains aresimilar for each amount of dye, suggesting that the proposeddyeing diffusion model is effective. Figures 9 (b) and 9 (c)show the characteristics associated with mottles and textureof the cloth. The proposed dyeing model with cloth patterns



Figure 6: Sading model.

Figure 7: Visualization of dye and cloth.

Figure 8: Visualization of dye and cloth. Cloth textures pro-duced by the proposed model. Each image has its smallestbasic pattern on the bottom-right corner. Yellow cells indi-cate weft. Blue cells indicate warp.

is effective for making mottles and cloth textures. Figure 9(d) shows the results associated with dry pressure distribu-tion; there was color gradation of dye for pressure and dif-fusion. Figure 10 shows comparisons of real and computer-generated stains on dry and wet cloth with a real cloth image.

7. Program Usage

In this section, we describe the process associated with gen-erating dyeing images with the methods presented above.

Dyeing table: We can use an image in the proposed dye-ing model to indicate the location of a diffusion area. Suchan image is referred to as a "dyeing table", which is usedto generate dyeing-like images. Figure 11 (c) is created us-ing the dyeing table. First, we draw patterns such as Figure11 (b) by referring to the real tie-dyeing image Figure 11(a). Then, the RGB values of Figure 11 (b) are converted tothe amount of dye needed to generate the dyeing-like patternFigure 11 (c).

Pressure table: Figure 9 (d) is the result of simulatingdyeing with a pressure table that is a left image of Figure 12.The dye is distributed on four side of the cloth. In this way,we present a dyeing system that generates patterns with theprotection against dyeing as indicated by the pressure table.

Simple Tie-dyeing Simulation: When the user wants a

Figure 9: Characteristics of computer-generated stains,showing, (a) different shapes of dye stains depending on theamount of dye. (b) magnified image of mottled areas. (c) con-trast enhanced image of (b). (d) dyeing gradation by pres-sure.

Figure 10: Computer-generated and real stains on dry andwet cloth. Here, computer-generated stains are producedwith a real cloth image, showing, (a) generated image of astain on dry cloth. (b) real image of a stain on dry cloth. (c)generated image of a stain on wet cloth. (d) real image of astain on wet cloth.

specific dyeing and pressure distribution, they can constructdyeing and pressure tables and produce the tie-dyeing im-age with the proposed system if it is possible to predict thetables. Figure 13 is an example of this process using a tradi-tional Japanese pattern called seikaiha. Figure 14 shows thesimulation of seikaiha along the time step. However, this ex-ample is simple, and it is easy to predict dyeing and pressuredistribution. However, numerous dyeing techniques are dif-ficult to predict and systems that can be used to predict theoutcome of a dyeing pattern using either dyeing and pres-



sure tables from the geometry of the cloth, or from the dye-ing techniques that were employed during dying is our futurework.

8. Conclusion and Future Work

We have presented the dyeing model with an improved dif-fusion equation that can be used to consider weaving pat-terns, uneven diffusion coefficients, and different pressuresfor a tie-dyeing simulation. In addition, the improved diffu-sion equation presented herein cannot handle a wide range ofdiffusion coefficients because it is not robust. Consequently,the proposed model could be improved with more physi-cal details such as gaps between the yarns. The extent ofcoloring calculated from the dye amount could also be de-fined physically with a suitable color coordinate system. Itis difficult to consider the appearances of gaps or the detailsof cloth texture associated with dyeing in the present sys-tem. These physical improvements would simplify the deci-sions required by the user when using the proposed dyeingsystem. In addition, the proposed dyeing model should bephysically justified. Additional future improvements couldinclude increasing the speed of the proposed dyeing modeland assigning the resolution of the cells according to level ofdetail of the cloth, adding mixed colors to the model, and soon. The rendering of the cloth could be improved by mod-eling the light interaction with the threads and 3D cloth ge-ometry. Further research must be conducted to evolve theproposed model so that it can interactively handle three-dimensional configurations for the art of patterning cloth bydyeing. Adding dyeing techniques such as batik and brush-ing could also improve the completeness of the proposeddyeing system.

References

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[DC04] DRAGO F., CHIBA N.: Painting canvas synthesis.Vis. Comput. 20, 5 (2004), 314–328.

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Figure 11: Images for the dyeing table. (a) real tie-dyedcloth. (b) dyeing table constructed from (a). (c) proposeddyeing model with the dyeing table (b).

Figure 12: The image on the left is the pressure table forFigure 9(d). The image on the right shows a real dyeing tech-nique used to press the cloth, which results in Figure 2(d).

[Kur96] KUROKI N.: Senshoku Riron Kagaku (DyeingTheory Science). Maki Shoten (in Japanese), 1996.

[Lee01] LEE J.: Diffusion Rendering of Black Ink Paint-ings Using New Paper and Ink Models. 295–308.

[Oki94] OKITSU F.: Shibori no Kukuri to Some (Dye andTie in Tie-dyeing). Rikogaku Sha (in Japanese), 1994.

[Sak99] SAKAKIBARA A.: Nihon Dento Shibori noWaza (Japanese Tie-dyeing Techniques). Shiko Sha (inJapanese), 1999.

[SYO04] SAEKI M., YAMAGUCHI K., OKUMURA M.:Representation of fabric texture mapping technique usingsurface reflection characters and thread pattern. vol. 57,J.Tex.Mach.Soc.Japan(in Japanese), pp. T73–T80.

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[WvOC04] WYVILL B., VAN OVERVELD K., CARPEN-DALE S.: Rendering cracks in batik. In NPAR ’04:Proceedings of the 3rd international symposium on Non-photorealistic animation and rendering (New York, NY,USA, 2004), ACM Press, pp. 61–149.

[XCL∗01] XU Y.-Q., CHEN Y., LIN S., ZHONG H.,WU E., GUO B., SHUM H.-Y.: Photorealistic ren-dering of knitwear using the lumislice. In SIGGRAPH’01: Proceedings of the 28th annual conference on Com-puter graphics and interactive techniques (New York, NY,USA, 2001), ACM Press, pp. 391–398.

[Yos02] YOSHIKO W. I.: Memory on Cloth:Shibori Now.Kodansha International, 2002.

[ZSyT∗99] ZHANG Q., SATO Y., YA TAKAHASHI J.,MURAOKA K., CHIBA N.: Simple cellular automaton-based simulation of ink behaviour and its application tosuibokuga-like 3d rendering of trees. The Journal of Visu-alization and Computer Animation 10, 1 (January - March1999), 27–37. ISSN 1049-8907.

Figure 13: Simulation and comparison of tie-dyeing.

Figure 14: Simulation of tie-dyeing along time step (t) in theimages.


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