3D simulation of double-needle bar warp-knitted clustered pile fabrics on DFS

2.1 Knitting process and design

The production process of double-needle bar warp-knitted clustered pile fabrics primarily includes knitting on a double-needle bar warp-knitted machine, a pile splitting process, and subsequent finishing steps. First, the pile guide bars are knitted on the front and back needle bars using the double-needle bar warp-knitted machine, resulting in an initial fabric with a specific structure. This step employs double-needle bar warp-knitted technology to form a pile foundation within the fabric. Next, the pile splitting treatment is carried out, during which the fabric is split along the middle of the pile fibers, producing two single-sided pile fabrics [19,20]. This method ensures uniform pile distribution and structural stability. Finally, a series of finishing processes, such as sheering, heat setting, softening treatment, and anti-static treatment, are applied to further enhance the fabric’s physical properties and appearance, resulting in clustered pile fabrics with excellent hand feel and visual appeal [21]. As shown in Figure 1, the process flowchart for forming double-needle bar warp-knitted clustered pile fabrics is illustrated.

Figure 1

Process flowchart of the formation of double-needle bar warp-knitted clustered pile fabrics.

This study primarily focuses on the 3D simulation of solid color and jacquard double-needle bar knit pile fabrics. The fabrics are mainly produced using the Raschel double-needle bar with 6 guide bars, double plush loop machine, with the process parameters detailed in Tables 1 and 2. In the tables, A, B, C, and D represent the material specification numbers, and “” indicates an empty threading. For example, “6C, 4” indicates that material C is threaded six times, followed by four empty threads.

2.2 Chain notation model

In double-needle bar warp-knitted fabrics, the guide bars are alternately knitted on the front and back needle bars. Therefore, the actual unfolded height of the chain notation during knitting is represented as twice the pattern height of the fabric. This is represented by the matrix D _i :

In the equation, j ∈ {1, 2, 3,…, m}, where m is represented as the total number of courses, i.e., the height of the fabric pattern. The chain notation of double-needle bar warp-knitted fabric is composed of four digits: the first two digits are represented as the needle positions knitted on the front needle bar, while the last two digits are represented as the needle positions knitted on the back needle bar. The starting needle position is indicated by the first course of the matrix, and the ending needle position is indicated by the second course. Here, d _{2j−1,2k−1} and d _2j−1,2k are represented as the first two chain notations of the jth course and the kth wale, while d _2j,2k−1 and d _2j,2k are represented as the latter two chain notations of the jth course and the kth wale.

2.3 Threading model

Each guide bar in warp-knitted fabrics is followed by a specific threading pattern. To more clearly represent the corresponding threading method, a threading mathematical model is established [22] and is represented by the matrix C _ik :

In the formula, i ∈ {1, 2, 3, …, p}, where p is represented as the total number of guide bars, and k ∈ {1, 2, 3, …, n}, where n is represented as the total number of wales, i.e., the fabric’s pattern width. The type of yarn material is indicated by c _i,k .

2.4 Pile design pattern model

In the pile design pattern, a single design cell represents a pile loop. The height and width of the design pattern correspond to the pattern height and width of the pile fabric, respectively. When constructing the design pattern, the drawing is done from right to left and from bottom to top. The matrix is arranged in reverse order overall [23]. The matrix Q _i is described as follows:

In the equation, i ∈ {1, 2, 3,…,p}, where p is represented as the total number of guide bars; j ∈ {1, 2, 3,…,m}, where m is represented as the total number of courses; and k ∈ {1, 2, 3,…,n}, where n is represented as the total number of wales. q _j,k is defined as the status of the plush yarn loop at the jth course and kth wale. In this study, only two states are considered for the pile: one is a random state and the other is an aggregated clustered state. Therefore, the value of q _j,k can be either q _j,k = 1 or q _j,k = 4. When q _j,k = 1, the color of the design cell is represented as red, indicating that the current pile loop is classified as belonging to the clustered pile area and is in an aggregated state; when q _j,k = 4, the design cell is colored green, indicating that the current pile loop is classified as belonging to a non-clustered pile area, and the pile fibers are in a randomly deflected state.

3.1 Single pile geometric loop structure

The structure of a single pile loop in double-needle bar warp-knitted clustered pile fabrics is composed of ten control points, labeled P0–P9. Specifically, the main loop section is formed by six points, P2–P7, which create the basic skeleton structure of the pile fabric. The pile fibers are made up of two segments: P0-P1-P2 and P7-P8-P9. By connecting these control points, the appearance and shape of the pile fibers are created.

In the geometric modeling process of pile fibers, the control points P0, P1, P8, and P9 are randomly deflected along the y-axis and z-axis to simulate the natural state and randomness of the pile fibers. This random deflection not only reflects the complex structure and appearance characteristics of the pile fabric more accurately but also enhances the realism and diversity of the simulation model. The number of pile fibers can be adjusted as needed. As shown in Figure 2, a total of eight pile fibers are present in the pile loop, and the deflection angle of each individual pile fiber within the loop is varied randomly. Through the reasonable configuration and adjustment of these control points, high-precision modeling of the pile fabric structure is achieved, providing a detailed geometric description and capturing randomness features, thus laying a solid foundation for subsequent 3D simulation.

Figure 2

Geometric structure of a single pile loop: (a) front view and (b) side view.

3.2 Principle of pile cluster geometric structure

The surface pile structure of double-needle bar warp-knitted clustered pile fabrics is composed of clusters of pile fibers. Therefore, it is formed by the aggregation of multiple adjacent pile loop structures. To simulate a realistic clustered pile state, it is necessary for the model to ensure that the ends of the pile fibers converge toward a single point. However, since the pile fibers have been trimmed, their lengths are fixed. Consequently, as they converge toward a point, the edges of the pile cluster do not reach the height of the convergence point, but their ends still point in the direction of the convergence point.

Since the fabric is knitted in both longitudinal and transverse directions, the state of the fabric appears rectangular; however, the final clustered area may not be rectangular and must be determined based on the values of q _j,k in Section 2.4. The positions where q _j,k = 1 are identified as clustered areas, indicated by the light-colored region at the bottom of Figure 3. Regardless of whether the arrangement of the selected loop positions is regular, the final appearance of the clustering effect resembles the circular appearance shown in Figure 3. To better understand the effect of the clustered structure, the clustered positions on the fabric are depicted as circular areas. Thus, the position of each pile fiber shown in Figure 3 can be viewed as the pile fibers at different loop positions within the current clustered area. A single pile loop position can have multiple pile fibers, but ultimately, whether from different loop positions or multiple pile fibers from one pile loop position, all are directed toward the center of the clustering area. The position range for the central cluster is randomly selected from the pile loop positions of the current clustered area. The clustering effect shown in Figure 3 is represented as one such clustered effect within the fabric and can be applied throughout the fabric. Each clustered pile has only one central pile; therefore, the position of the central pile in the fabric is determined by the selected clustered pile area.

Figure 3

Principle of clustered pile aggregation.

The light-colored clustered structure area at the bottom of Figure 3 also indicates the direction of the main loop fibers, arranged along the XY direction. R1 and R2 represent the positions of the clustered structure on the XOY plane; R1 indicates the X direction relative to the current center coordinate of a cluster; and R2 indicates the Y direction. R3 represents the length of the pile fibers, where each point at the tail end of the pile fiber in Figure 3, directed toward point P, corresponds to the P0 (P9) control point of each pile loop. α is the deflection angle of the pile with respect to the Z-axis, representing the rotation range around the Y-axis, while β is the deflection angle with respect to the X-axis, indicating the rotation range around the Z-axis. Therefore, the principle for constructing the clustered structure model involves randomly selecting a central pile fiber as the aggregation coordinate, with its direction coinciding with the Z-axis and R3 being its length. The coordinates of the remaining pile fibers are translated to the position of the central fiber, rotated around the Y-axis, and the angle α is calculated using geometric principles. Similarly, the rotation around the Z-axis is calculated for β. The calculated angles are applied to the rotation matrices EY and EZ, resulting in A′B′, which represents the direction of the pile after rotation. Finally, these fibers are translated back to their original positions, denoted as AB, and the same process is applied to the other pile fibers, yielding the corresponding clustered geometric model.

4.1 Recognition of pile design pattern

In the design pattern, each design block is represented by a two-dimensional (2D) array q _j,k . The 2D array q _j,k is traversed using DFS, with the values of all connected regions updated, ensuring that each node is correctly accessed and processed while identifying all red design cells belonging to the current aggregated region. As shown in Figure 4, the coordinates of the red design cells are (0,0), (0,1), (1,0), and (1,1). The traversal process identifies all design cells, where q _j,k = 1 in the 2D array, as illustrated in Figure 5. The DFS function is called for each unvisited cell that meets the criteria, with all connected regions being detected and marked, while the entire 2D array is traversed. Each detected region is added to the “region” list, which represents all adjacent red area blocks, in other words, a clustered pile region. The number of these regions corresponds to the number of clustered pile areas.

Figure 4

Conversion diagram from matrix to design pattern.

Figure 5

Diagram of specific region in 2D array using DFS.

4.2 Region segmentation of pile design pattern

After the clustered pile design block regions are identified, they need to be divided into multiple areas, with different red design cell regions representing different pile clusters. As shown in Figure 6, two clustered pile areas are present.

Figure 6

Region index mapping.

The “region” list is traversed, and each area is processed. In the design blocks of Figure 6, two clustered regions are identified. By traversing the “region” list, the corresponding coordinates identified are (0,0), (0,1), (1,0), (1,1), (3,4), (3,5), (4,5), and (4,4). From Section 2.4, it is known that adjacent red design cell coordinates form a single pile cluster. Therefore, using the “block ToRegionMap” dictionary, the coordinates are mapped to their respective index areas: (0,0), (0,1), (1,0), and (1,1) are mapped to region index 0, while (3,4), (3,5), (4,5), and (4,4) are mapped to region index 1. This segments the red design cells in the clustered state into different aggregation area blocks.

4.3 Rapid identification of aggregation coordinates

After the aggregated regions are identified and segmented, as noted in Section 3.2, the coordinates of the central pile need to be found to achieve the clustered state. Therefore, in each different pile cluster region, the corresponding central pile aggregation coordinates must be identified to achieve the pile clustering effect. Consequently, the central pile coordinates need to be queried. From the segmented region list “region,” a red design cell coordinate is randomly selected from each area as the central pile coordinate. The “selectedBlocks” list is created to store the coordinates of the randomly chosen aggregation points in each region. The “blockToRegionMap” dictionary provides an efficient way to map the location of the red blocks to their respective regions. During the traversal process, once a region index is found, the corresponding random block can be obtained from the “selectedBlocks” list to update the central pile coordinates (Figure 7).

Figure 7

Schematic diagram of central coordinate selection.

5.1 Lighting model

In the 3D simulation of pile fabrics, the Phong lighting model [24] is employed to simulate lighting effects. Variations in light and shadow on the surface of objects are effectively reproduced by the Phong lighting model through the consideration of ambient light, diffuse light, and specular reflection. As illustrated in Figure 8, the superposition of these three lighting conditions is rendered, clearly demonstrating the influence of each type of reflected light on the model. Specifically, ambient light is used to simulate the base brightness uniformly distributed across the scene, diffuse light is applied to describe the isotropic scattering of light on the fabric surface, and specular reflection is responsible for simulating the gloss in highlight areas. By applying the Phong lighting model to the geometric model of the pile fabric, the lighting characteristics of the fabric are successfully recreated, enhancing the light and shadow effects from different directions, thereby improving the realism of the 3D simulation.

Figure 8

Performance of material under different lighting conditions and the superposition of light effects.

To further explain the application of the Phong lighting model in pile fabric simulation, a diagram in Figure 9 is presented, showing the decomposition of lighting angles and providing a detailed analysis of the relationships between the vectors. In the figure, vector L is used to represent the direction of reflected light toward the light source, vector N denotes the normal direction of the surface, and vector R indicates the direction of reflected light relative to L . The angle δ is used to represent the angle of incidence, i.e., the angle between the incident light L and the normal N , while the angle θ is used to represent the angle between the reflected light R and the normal N . This decomposition of lighting angles further clarifies how each angle influences light intensity and direction, thereby determining the brightness and shadow effects in the final simulation image. The final total lighting intensity I _z is calculated by the following formula:

Figure 9

Illustration of lighting angle decomposition.

where k _a , k _d , and k _s are defined as the ambient light reflection coefficient, diffuse reflection coefficient, and specular reflection coefficient, respectively. i _a , i _d (g), and i _s (g) are represented as the ambient light intensity, diffuse light intensity, and specular light intensity, respectively. n indicates the number of light sources, and λ represents the material’s specular exponent. According to the lighting calculation formula in equation 8, the Phong lighting model comprehensively considers these angle-related factors, with the visual effects of real lighting on fabric surfaces simulated through the superposition of ambient light, diffuse light, and specular reflection.

To verify the effect of the Phong lighting model in pile fabric simulation, the simulation results under different lighting conditions are displayed in Figure 8. It has been shown through experiments that more delicate and realistic effects are produced when simulating the highlight and shadow areas of pile fabrics using the Phong lighting model.

On this basis, multiple directional light sources were introduced to further optimize the uniformity and realism of the lighting. The lighting coordinates of these directional lights were precisely set at different angles to ensure that the fabric surface could be evenly illuminated from multiple directions, thereby reducing the phenomenon of overly concentrated shadows. In this study, when directional light sources were utilized, the randomness of pile fiber orientation was considered, and light sources primarily illuminating from the front of the fabric were employed, including the directions (−1,1,1), (1,1,1), (−1,−1,1), (1,−1,1), and (0,0,1). These directional lights ensured that the pile fibers at various angles on the fabric’s front surface were evenly illuminated, creating natural shadow effects. By combining these directional lights, the model was able to more accurately reproduce the fabric’s appearance under natural lighting. The final experimental results showed that the simulation images produced using the Phong lighting model and multiple directional lights more closely resembled the gloss and texture details of real pile fabrics, demonstrating the superiority of this method in simulating complex fabric structures.

5.2 Blurring process

In the process of 3D simulation, blurring techniques are employed to better replicate the visual effect and realism of clustered pile fabrics. Blurring is used to smooth the pixels of the rendered image, effectively reducing sharp edges and noise, thereby enhancing the soft texture of the fabric. During front-end rendering, post-processing effects provided by Three.js are utilized, specifically implementing horizontal and vertical blurring steps. This approach allows for the maintenance of model details while making the appearance more closely resemble real pile fabrics.

To achieve the aforementioned blurring effect, the 3D scene is rendered to an intermediate texture object, effectively saving the initial render result onto a texture. Subsequently, horizontal and vertical blur shaders are applied to process the texture on a per-pixel basis. This texture-based blurring method allows for flexible adjustment of blur intensity to accommodate different display needs and visual effects. As shown in Figure 10, the 3D simulation image after blurring significantly enhances the visual realism and softness of the pile fabric compared to the unprocessed image, demonstrating the effectiveness and practicality of this method.

Figure 10

Comparison of blurring process for clustered pile fabric: (a) before blurring and (b) after blurring.

5.3 Experimental results

In the simulation implementation presented in this study, the geometric model of the pile fabric was constructed based on the aggregation-state information identified by the DFS algorithm. The specific implementation process is illustrated in Figure 11, which outlines the detailed steps and logical relationships involved in the simulation.

Figure 11

Flowchart of the 3D simulation implementation for clustered pile fabrics.

To validate the effectiveness of the proposed method, the generated 3D simulation was compared with the actual pile fabric. The experimental results indicate that the proposed method not only visually replicates the true appearance of the pile fabric but also achieves a high level of precision and detailed representation. In this study, the pile height of the solid colored clustered pile fabric was recorded as 3 mm, while the pile height of the jacquard clustered pile fabric was recorded as 5 mm. According to the geometric principles of clustered pile structures discussed in Section 3.2, an increase in height results in corresponding changes in the aggregation angle, leading to variations in the appearance height of the clustered pile. This effect can be observed in Figures 12(b) and 13(b). Furthermore, a comparison with the actual fabric images, as shown in Figures 12 and 13, clearly demonstrates the high degree of similarity in height between the two. This result confirms the practicality and reliability of the proposed method, highlighting its promising application potential.

Figure 12

Simulation of solid color clustered pile fabrics: (a) physical picture and (b) fabric simulation.

Figure 13

Simulation of jacquard clustered pile fabrics: (a) physical picture and (b) fabric simulation.