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2021,  3 (2):   142 - 155   Published Date:2021-4-20

DOI: 10.1016/j.vrih.2021.01.001
1 Introduction2 Related work2.1 Textile and physics science2.2 Textile appearance2.3 Physically-based wet clothes simulation2.4 Cloth modeling and simulation3 Liquid diffusion in structure textile3.1 Yarn, woven and textile3.2 Liquid transport in yarn and woven textile3.3 Imperfect textile modeling3.3.1 Diffusion connection3.3.2 Pilling3.3.3 Slippage3.3.4 Squeezing3.3.5 Imperfect TML structure4 Dyeing4.1 Imperfect liquid-driven diffusion5 Implementation5.1 Algorithm6 Experimental results7 Conclusions and future work

Abstract

The imperfect material effect is one of the most important themes to obtain photo-realistic results in rendering. Textile material rendering has always been a key area in the field of computer graphics. So far, a great deal of effort has been invested in its unique appearance and physics-based simulation. The appearance of the dyeing effect commonly found in textiles has received little attention. This paper introduces techniques for simulation of staining effects on textiles. Pulling, wearing, squeezing, tearing, and breaking effects are more common imperfect effects of fabrics, these external forces will cause changes in the fabric structure, thus affecting the diffusion effect of stains. Based on the microstructure of yarn, we handle the effect of the stain on the imperfect textile surface. Our simulation results can achieve a photo-realistic effect.

Content

1 Introduction
Textile stains are common in our everyday experience and are important for the fidelity of virtual clothing. Realistic and complex fabric dyeing effects, in film, games, industry, and other fields have a wide range of applications. Although artists can use hand-painted methods to design real and complex stains, the task is time-consuming and labor-intensive. In the current field of graphics research, there are lots of researchers focusing on the appearance of perfect fabrics material such as Kaldor et al., Xu et al., and Zhao et al., and some studies focus on the effect of stains in perfect woven fabrics, such as Morimoto et al., Zheng et al., but few people study the effects of stains with imperfect fabric structures[1-5]. This paper introduces the simulation technique of stain diffusion on fabrics with imperfect fabric structures. Our technology is based on the triple-layer model[5], which is specifically designed to simulate the true nature of dyeing behavior. We also use super sampling method at the textile broken yarn edge area to get a more accurate effect.
In our simulation, we simulated fabric structure and fluid diffusion separately. First, the textile structure was simplified and rebuilt to simulate the complex structure of the fabric by establishing connectivity between the two grids. Secondly, fluid diffusion is divided into two stages: fluid diffusion simulation and dye diffusion simulation. Liquid diffusion is driven by the capillary pressure of the yarn, and dye diffusion is driven by liquid diffusion and dye concentration in the liquid.
The main contribution of the paper is to make the simulation of a wide range of textile stain practical in computer graphics. Specifically, the contribution includes the following aspects:
(1) By adding diffusion properties methods, we could simulates common fabric structure damage characteristics, including extrusion, cutting and abrasion of fabric structure.
(2) The diffusion algorithm of the fluid in the TML is expanded from the diffusion along the yarn direction to the 2D plane diffusion, and the direction of diffusion is expressed by the method of diffusion probability.
(3) We provide a stable simulation system that can efficiently simulate the spread of stains on the surface of various fabric structures.
2 Related work
Visual simulation of fabric stains requires the use of research results in several different fields of study, including physical theory, textile science, chemistry, and computer graphics. Here, we briefly review the work related in these different areas.
2.1 Textile and physics science
Capillary force is the key to the diffusion of liquid in the fabric. The key to capillary strength depends on the surface tension of the liquid. Theory of those can be found in Sears et al., Hollies et al., and Hsieh Washburn predicted the movement of liquid in an ideal capillary tube[6-9]. Wiener et al. defined a thread as a formation of sufficient length, with a circular cross-section, in a constant filling, but without any variation in linear mass of the thread[10]. Zhang et al. proposed an equilibrium model for spontaneous liquid wicking into the longitudinal textile from an infinite liquid reservoir[11]. Takatera studied the liquid flow in fabric based on the principle of the capillary action, based on the capillarity theory[12]. Liu et al. investigated vertical wicking in twisted yarns, Mhetre measured the relationship between different textile materials and a given liquid[13,14]. These basic researches, for the follow-up research, have made a solid work.
2.2 Textile appearance
The realism of cloth rendering has always been a hot and challenging direction. Recently, with the development of CV technology, virtual idols, high-precision realistic material display, virtual clothing design, and other needs have become more and more important. Daubert et al. presented BTF-like techniques to render fabrics, essentially based on replicating weaving or knitting patterns[15]. Xu et al., Zhao et al., Montazeri et al. and Schröder et al. successfully reconstructed the visual result of yarn and produced solid fabric rendering images[16-19]. Schröder et al. also propose a pipeline to estimate a parametrized cloth model from a single image[20]. Aliaga et al. presented a method focus in the scattering of individual cloth fibers and introduce a physically-based scattering model for fibers based on their low-level optical and geometric properties[21]. Castillo et al. also made a complete survey about fabric rendering in computer graphics[22].
2.3 Physically-based wet clothes simulation
Complex material simulation based on physics is one of the most popular in the area of computer graphics. Perlin introduced noise texture to simulate the surface imperfection visual effects[23]. Jensen et al. shown how to get the wet material effects[24]. Chen et al. explained weathering processes are the key to photo-realism[25]. Dorsey et al. shown fluid flowing through a porous medium to capture the appearance of stone by using Darcy's law[26]. Lu et al. synthesized the drying phenomena[27]. Chu et al. introduced a physically-based method for simulating ink dispersion in absorbent paper and Gu et al. and Lu et al. proposed techniques to measure, represent and render time-varying surface appearance[28-30]. Lenaerts et al. combined Darcy's Law and the SPH technique to simulate fluid flowing through a deformable porous material[31]. Fei et al. presented the interaction of liquid and textile from micro-scale to large-scale[32]. Zheng et al. introduced the diffusion of stains on fabrics of different materials through a Triple Layers Model (TLM)[5].
2.4 Cloth modeling and simulation
Modeling of fabrics can be divided into two ways: abstracting it into thin shell and yarn-based. Terzopoulos et al. treated the fabric as a thin shell and developed an elastic deformation model to capture its mechanics[33]. Breen et al. introduced mass-spring models to approximate the behavior of real woven fabrics[34]. Provot through the addition of strain limiting to model inextensibility[35]. Compared to the popular thin-shell model, Kaldor et al. simulated the dynamics of knitted cloth at the yarn level, enabling them to predict the large-scale behavior of yarn mechanics[36,37]. Cirio et al. introduced an efficient solution for simulating woven cloth at the yarn level by discretization of interlaced yarns based on yarn cross section[38].
3 Liquid diffusion in structure textile
3.1 Yarn, woven and textile
In textile research, a yarn is usually regarded as a complex structure consisting of tightly bundled fibers Wiener et al. which are coated with a loose fibrous layer, as is shown in Figure 1 [10]. The loose fibrous structure on the yarn surface is determined by the fibers that make up the yarn. Different yarns use different fiber materials, and the resulting weaving effect is different. The main difference is whether there is a fibrous effect on the surface of the yarn. This is because the length of the fibers is different.
In addition, the woven textile is made of warp and weft. The basic structure in the textile is formed by the cross knitting of the warped part and the weft part. Figure 2 shows the cross-distribution of twill fabric and yarn. When the yarn is used by external forces, it will produce deformation, and even damage in the structure, such as slippage, crease, pilling, wear, etc. Figure 3 shows three types of imperfect textile state.
The imperfect textile state has led to three changes in yarn:
(1) Change in the porosity rate in the yarn. The mass of each yarn feather does not change, so when the shape of the yarn changes significantly, its porosity will change with the occurrence of telescopic. That will affect liquid diffusion and dyeing.
(2) The connectivity of the yarn. When the yarn breaks, the connecting pipe inside the yarn is damaged. However, since each yarn is composed of dozens of fibers, there will be two forms at the break: A, clean and tidy break. B, the feather layer covered by the break.
(3) Changes in the surface structure of the yarn. The fibers on the surface of the fabric break, which will produce the phenomenon of outward plumes in the local area, causing the surface of the fabric to be covered by the plume layer.
3.2 Liquid transport in yarn and woven textile
When the liquid comes into contact with yarn and completes the wetting progress, the liquid spreading along the tubular void in the yarn structure is called in-yarn diffusion. The main factors affecting in-yarn diffusion are the free movement of the liquid in the yarn segment and the fluid flow driven by the capillary pressure gradient force. The following formula determines the maximum amount of liquid that can be contained in a yarn segment Mhetre[39].
W h = ρ l ( φ ) ρ s ( 1 - φ )
Where Wh represents the maximum liquid that can be accommodated in a yarn segment, φ is the porosity of the fabric, ρl is the density of the liquid, and ρs is the density of the fiber. φ, ρl , and ρs can be obtained from the textile science by looking up data. Porosity is a ratio that ranges from 0% to 100%. The higher the voids inside the object, the greater the ratio. There are many reasons for the porosity of the yarn, two of which are the key: (1) A complete yarn is bundled and woven by multiple fibers, so there will be woven voids inside. (2) The raw material of yarn is divided into natural yarn and polyester. Among them, natural yarns are mostly composed of cotton, linen, and wool. These fibers are short and curved, so it is easier to form voids in the yarn. Fabric density indicates the number of warp yarns and weft yarns in 1 inch2. In a piece of fabric, there are two types of density: warp and weft. Therefore, the porosity of a piece of fabric can be calculated from the weaving density of warp and weft threads and the porosity of a single yarn. Then through the porosity of the fabric, the water content of the liquid in a certain unit area can be calculated. When liquid passes through the yarn, some of the liquid stays because of the hydrophilicity of the fiber, a certain amount of liquid ε (ε< Wh, ε is determined by the intrinsic structure and material of the fiber) trapped in any wetting locations. Liquid diffusion happens when the liquid volume in the yarn segment is larger than ε. This is caused by the local capillary pressure differential P generated by the surface tension of the liquid:
P = 2 γ c o s θ / r
Where γ is the liquid surface tension, r is the inner radius of the fiber tube, θ is the contact angle.
Δ P = ( S 0 - S 1 ) P
Where ∆P is the pressure difference between the start and endpoints of the tube. The discrepancy of the liquid saturation calculates the capillary pressures of following yarn segments by Equ. 3 Sn is the yarn segment's saturation. The liquid in a yarn flows from lower capillary pressure regions to higher ones. Darcy's Law is an equation that describes the flow of a fluid through a porous medium and calculates the flow rate of Φ:
Φ = k r 2 Δ P μ L
Here L is the length of the tube, µ is the dynamic fluid viscosity, r is the radius of the tube radius, k is the permeability of porous material. Yarn permeability can be measured using methods such as Cirio et al.[38]. With the core knowledge of liquid-yarn interaction, we can study the transport of stain liquid in woven textiles and the diffusion of liquid-textiles, which are controlled by capillary pressure difference. As mentioned in Takatera, when the front of liquid flow in a warp meets a weft one, some liquid in the warp may be transmitted to the weft, and vice versa[12]. The effect is simulated by Zheng et al. method[5].
3.3 Imperfect textile modeling
When dressing in everyday life, the yarn structure may be damaged, such as broken, fork, curly fur, and other effects. These features are known in textile science as "Pilling" and "Slippage". Based on TLM, a complete yarn can be divided into three layers: a transition-layer consisting of loose feathers, an occlusion-layer consisting of outer loss fibers, and a tightly bound transport-layer consisting of internal fibers.
We have extended the parameter properties of TML to simulate the diffusion of fluids on imperfect fabrics.
3.3.1 Diffusion connection
The diffusion model of TML assumes that the fabric weaving structure is complete, so fluid diffusion on the TML is along with the yarn structure and through the twisted ribbon connection points. However, when the weaving structure of the fabric is destroyed, the diffusion of the fluid no longer strictly follows its weaving structure, with a certain anisotropic and randomness. Therefore, we use diffusion connections in TML rather than fixed diffusion directions to simulate the diversity of diffusion connections on imperfect fabrics.
Diffusion connections are defined as the probability of diffusion of connections on nodes in the current TML, as well as the probability of adjacent nodes adjacent to each other in flat space. As shown in Figure 4, the distribution of diffusion probability changes greatly as the structure is destroyed.
3.3.2 Pilling
When the structure of the yarn surface is worn, the fiber structure of Yarn changes in three forms
(1) Yarn's tightly woven structure is damaged, resulting in the loss of the original direction of the stronger structure, the original internal connectivity of the capillary-tube was damaged or the direction changed. As shown in the first line in Figure 5. In this line, a is a good yarn structure, b is the damaged yarn structure, c is a good yarn structure shows the distribution of fluid diffusion connection, d is when the yarn structure is destroyed, the distribution of fluid diffusion connection becomes no longer structural.
(2) The loss fibers layer on the yarn surface is worn out directly to reveal its internal structure. The second line in Figure 5 shows this effect. In this line, a is a good yarn structure, b is the damaged yarn structure, c and d are together in the TLM way to represent the changes in the yarn structure. The yarn structure in figure transition-layer has been seriously damaged, and even transport-layer connectivity has also broken.
(3) The smooth, continuous fibers that are tightly bound on the surface of yarn break and fibers appear, and these fibers gradually converge to form fuzz balls. The third line in Figure 5 shows such examples. In this line, a is a good yarn structure, b is the destruction of the yarn structure, c and d is a common TLM way to represent the changes in the yarn structure. The yarn structure in the figure occlusion-layer has been seriously damaged, forming the outer layer of transition-layer or destroyed the transmission of transport-layer.
Summarize the above three situations: after the surface structure of yarn is destroyed, its originally maintained microstructure also changes, which will significantly affect the diffusion of fluid in the capillary yarn tube.
3.3.3 Slippage
Tightly constrained fibers are the basic structure of each yarn. When the yarn breaks, there are three different states: (1) All fibers are fastened; (2) Part of the fiber fracture, the production of hairy feathers; (3) All broken, the formation of irregular fractures, can produce fibrous. Figure 6 shows the three states above: a , b , and c . Figure 6d indicates that when weft yarn breaks, the deformation of the woven structure.
Slippage also affects the shape of warp yarn, diffusion connection, and TLM properties. After a bundle of yarn is broken, due to its structural characteristics, the yarn structure at the fracture will continue to loosen and gradually form a hairiness effect. These hairiness effects will significantly change the spreading properties of the yarn. According to Zheng et al.'s research, it can be known that when there is a thick and dense hairy layer on the surface of the yarn, it will have an obvious barrier effect and water storage effect on the diffusion of the liquid, and after the liquid dries up, it will form an accumulation of staining effects[5].
3.3.4 Squeezing
Squeezing will change the weave structure of the yarn, causing changes in connectivity and porosity. The degree of change is positively related to the amount of pressure. Squeezing not only changes the internal structure of the yarn but also forms a new capillary structure. The formation of this type of capillary structure is due to the interface gap formed between the edge of the extruded object and the fabric. Figure 7 shows this effect. In this figure, a shows the squeezing scene, b shows diffusion properties of each node on the fabric with squeezing effect, c shows the change in the yarn TML properties of the fabric node when the extrusion occurs.
3.3.5 Imperfect TML structure
Through the analysis in the above 4 sections, we added a simulation of fabric damage characteristics to the TML model structure. The TML method is extended by the following 2 methods:
(1) The diffusion probability of the 2D plane is used to simulate the connectivity of the yarn and the anisotropy of diffusion. Through this method, the following effects can be simulated:
a) A fluid diffusion channel formed by a complete yarn woven structure;
b) The yarn porosity changes caused by the cutting, loosening, and squeezing.
(2) By adding structural failure points to the TML model to simulate the changes in the weaving and surface structure of a single yarn, including:
a) The damage or formation of the hairy layer caused by the abrasion of the yarn structure;
b) Yarn fracture and section fiberous layer formed by loose Yarn;
c) Squeezing causes the originally loose fiberous layer space to be compressed tightly.
4 Dyeing
4.1 Imperfect liquid-driven diffusion
The dye carried by the liquid eventually changes the color of the fabric. Therefore, the simulation of stains produced during the dyeing process can be used by Zheng et al.[5] proposed methods. To be exact, dye diffusion includes three processes: liquid-driven diffusion, concentration-driven diffusion, and the dyeing process.
In addition to these effects, we discuss the dyeing effects on imperfect fabrics such as dyeing precipitation. When the liquid moves to the end of the yarn, due to the gradual destruction of the capillary structure, the liquid diffusion effect is reduced, and along with the evaporation of the liquid, a precipitation point of the dyed particles is gradually formed. In Figure 8, we showed the process of stain spreading and stain settling. During the process from a to c , the liquid spreading to the end of the yarn disappears due to evaporation, and the dyed particles are thus deposited, forming a gradually thickening dyeing effect. The first row is the simulated effect diagram, and the second row is the schematic diagram of the calculation. In the second row, each grid represents the calculation node in the TML model. The dark blue points are dyed particles and the white points are solvents.
5 Implementation
5.1 Algorithm
We define the variables used in the algorithm:
In the first step, we abstract the fabric as an M(m×n) grid, as shown in Figure 2.
In the second step, we preprocess the diffusion probability data in this M grid. According to the fabric material properties, damage types, abrasion strength, and external pressure specified by the artist, the node's probability of connectivity C mn, fiber layer thickness F mn, porosity P mn and maximum liquid flow L mn at each node are calculated separately, as shown in Figure 9 and Figure 10. The calculation methods are as follows:
Porosity and maximum liquid flow:Adjust the porosity of the node according to the fabric material of the current node and the external extrusion. When the external pressure on the node increases, the porosity of the node, the thickness of the fibrous layer and the probability of connectivity all decrease, and vice versa, those diffusion properties are maintained. When the porosity changes, the maximum fluid flow rate in the yarn changes in proportion to it.
Description table of key variables used in the algorithm
Variable Description
C mn probability of connectivity at the node
F mn fiber layer thickness at node
P mn porosity at the node
L mn maximum liquid flow at the node
D mn color fastness at node
Y mn liquid-yarn wetting progress at node
S mn liquid saturation at node
E mn evaporation ratio at node
Probability of connectivity:According to the current node's woven structure and wear strength, the probability of connectivity between itself and the surrounding 8 nodes is calculated (Figure 11c), and the connectivity is stored in C mn. As shown in the second picture shown in Figure 6 and Figure 11.
Fiber layer thickness:Update the fiber layer thickness value of the current node according to the fabric material type and the wear strength of the yarn. As shown in the second and third rows in Figure 5.
Through the above calculation, we have obtained a piece of fabric diffusion probability data that can express the damaged fabric.
In the third step, we use the following algorithm.1 to calculate the process of stains spreading on imperfect fabrics:
Algorithm.1 The main iteration loop:
for Each warp and weft direction do:
for Each Node in M do:
update Y mn by Zheng et al[5];
LiquidDiffusion();
DyeDiffusion();
end for
end for
Algorithm 2 describes the process of fluid diffusion and evaporation on the fabric.
Algorithm.2 LiquidDiffusion:
calculate liquid diffusion for all C mn do:
calc. L mn by wicking pressure by Equ. 2:
P = 2 γ c o s θ / r
update liquid diffusion by Equ. 4:
Φ = k r 2 Δ P μ L
end for
do liquid evaporation;
Algorithm 3 describes the process of stains spreading on the fabric with fluid diffusion and precipitation dyeing.
Algorithm.3 DyeDiffusion:
for all C mn do:
calc. dye diffusion by liquid-driven;
do dye deposition;
end for
6 Experimental results
In Figure 12, we simulated the change in the stain spreading effect of the fabric due to squeezing. Figure 12a and Figure10a' are real collected data. It can be seen from real experiments that more stains are formed at the squeeze area, which affects the diffusion effect of stains from the free area across the squeeze area. Figure10b, Figure10c, Figure10d is a continuous simulation effect, in which the blue area is the stain and the red area is the fabric area squeezed by the heavy object. Figure10b', Figure10c', and Figure10d' are the performance of the same process. The red box highlights the stain precipitation formed at the extrusion and the diffusion effect affected by the extrusion.
Figure 13a, Figure 13b, and Figure 13c show the diffusion process of stains after the fabric is cut, and Figure 13a', Figure 13b', and Figure 13c' are real collected data. It can be seen that at the cutting fracture, the dynamic effect of fluid diffusion and stain precipitation can be better represented by the simulation method.
By adding multiple diffusion attribute features, we can model the diversity of the fabric, thereby achieving more complex and real diffusion effects. Figure 14a is the result of stains spreading on a well-structured fabric. Figure 14a' is the result of stains spreading on imperfect fabrics. These two pieces of fabric come from the same complete fabric. Through comparison, it can be found that due to changes in the structure of the fabric, the diffusion result of stains has changed from uniform diffusion to uneven diffusion, and there is an obvious uneven stain precipitation effect. Figure 14b, Figure 14c and Figure 14d use the Zheng et al. method to simulate the diffusion process of stains on a fabric with a complete structure[5].
The second row of Figure 14 use our method to simulate the diffusion process of stains on an imperfect fabric, and include the effects of slippage, squeezing and pilling on the fabric.
The third row of Figure 14 shows the effects simulated using only the slippage effect, but because the overall structure of the fabric is complete, so the results of diffusion also tend to isotropic.
The fourth row of Figure 14 shows the important effect of the squeezing effect on diffusion results, especially in the Figure 14c''' stage, when the diffusion of liquids is temporarily blocked at the edge of the pressure.
The last row of Figure 14 shows how pilling affects liquid diffusion: diffusion is hindered by the aggravation of the fiber layer, but as the fluid immerses the fiber layer, a uniform and complete diffusion effect is eventually formed.
Table 2 lists the computational simulation resources and performance consumption used in our DEMO. In our algorithm, the performance we need is proportional to the sampling direction and the required size that the diffusion properties need to be calculated. When the structure of the fabric is imperfect, the more iterative calculation directions, the greater the performance consumption.
Description table of key variables used in the algorithm
DEMO Grid Size Total Farams Connection attributes Timing
Zheng2019[5] 256×256 3000 3 300s
Demo1 256×256 3000 5 420s
Demo2 256×256 4500 5 550s
Demo3 256×256 6000 9 1400s
7 Conclusions and future work
The wear and tear of fabric is a common occurrence in daily life, and it is also an important but easily overlooked phenomenon in fabric real-life rendering. The damage of the fabric will change in material, physics and so on, and this paper focuses on the change of material effect caused by the interaction between the fluid and the broken fabric.
Since the fluid diffusion channel formed by the weaving structure becomes diverse due to the destruction, it is no longer feasible to simulate the diffusion of fluid on the fabric by simplifying the yarn to tube. In this paper, we use the diffusion properties method to simulate how stains spread in the imperfect fabric weaving structure, and we can obtain simulation results close to the actual effect.
In this paper, the structure of the fabric is simplified, taking into account only simple flat and twill fabrics, for the complex satin and three-dimensional braided fabrics, there is no modeling, which is our follow-up to the direction of in-depth study. Those complex weaving structures will lead to more diverse changes in the shape of the yarn, which will also affect the effect of fluid diffusion.

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