A tiling fabric weave design method based on directed chain graph

Abstract

The application discloses a T-shaped paving fabric organization design method based on a directed chain graph. The method uses four T-shaped paving blocks to construct the spatial structure of the organization, and constructs a new fabric organization through editing a directed chain graph. Firstly, a directed chain graph representation method special for the T-shaped paving is used to design a directed chain graph on a checkerboard and edit the directed chain graph, and then the directed chain graph is converted into a T-shaped paving structure; then the designed basic organization is split and reorganized; finally, the T-shaped paving structure is converted into a paving fabric organization in combination with the split basic organization. The application overcomes problems of a traditional fractal and paving fabric organization design method, such as limited design space due to monotonous spatial structure. The method is convenient, intuitive and flexible, and can obtain more abundant and changeable paving structures and corresponding paving fabric organizations.

Description

Technical Field

[0001] This invention relates to the fields of textile design and fabric structure design, specifically to a method for designing T-shaped fabric structures based on directed chain graphs. Background Technology

[0002] Fabric structure refers to the pattern of interlacing or overlapping of warp and weft yarns within a fabric. Currently, fabric structures are typically designed digitally, with traditional methods including overall transformation and basic structure combination.

[0003] The holistic transformation method involves treating the tissue as a whole and performing various transformations. Examples include using symmetry principles and image transformation methods to transform the tissue as a whole, designing new tissues using rotational transformations, and designing tissues using iterative shift operations of the tissue matrix. These methods are intuitive and easy to implement, but they have limited degrees of freedom and can only create a limited number of new tissues.

[0004] The basic organization combination method involves spatially reorganizing one or more simple organizations according to certain rules. Typical examples include fractal-based and paving-based design methods. These methods utilize basic organizations to construct spatial fractal structures, and another organization fills the remaining space to balance floating-point numbers, generating novel organizations with self-similarity, nested structures, and multi-layered hierarchical structures. This method has spawned various variations, such as fractal organizations with distinct basic organizations in each layer, fractal organizations based on twill basic organizations, affine fractal organizations in the same layer, paving methods using chair-shaped organizations as basic units for spatial tiling, and paving methods using two different cycles of basic organizations. However, the spatial structures of these paving fabric organizations are relatively monotonous, and their variations mainly depend on the morphology of the basic organizations, offering limited user-controllable freedom and thus restricting the scope of organizational variation to some extent. Summary of the Invention

[0005] The purpose of this invention is to address some shortcomings of existing digital fabric structure design technologies by proposing a T-shaped lay-up fabric structure design method based on directed chain diagrams. The method involves editing the basic structure and its assembly form, selecting a splitting method to divide it into T-shaped lay-up blocks, editing the directed chain diagram and converting it into the corresponding lay-up structure, thereby generating an intuitive lay-up fabric structure design. The method utilizes the directionality of the directed chain diagram to establish a connection with the T-shaped lay-up method, ensuring that each set of directed chain diagrams corresponds to a unique and effective lay-up method. This avoids monotonous structure design and limited variation space. The method is versatile, convenient, and allows direct control of fabric structure design through editing the chain diagram. This invention primarily targets the design of woven fabrics.

[0006] The objective of this invention is achieved through the following technical solution: a method for designing T-shaped fabric structures based on directed chain graphs, the method comprising the following steps:

[0007] Step 1: Set the basic organizational structure, which is a basic structure consisting of 4 T-shaped paving blocks with a cycle number of 4S, where S is a positive integer;

[0008] Step 2: Select the assembly form of the T-shaped paving blocks in the basic structure, i.e., the splitting method;

[0009] Step 3: Determine the number of repeats n×m of the fabric weave structure, and limit the number of repeats n and m to be multiples of 4S, where n and m represent the number of repeats in the warp and weft directions;

[0010] Step 4: Calculate and construct the chessboard grid based on the cycle number. The number of square units in the lattice of the chessboard grid is: (n-2)*(m-2) / 4S;

[0011] Step 5: Construct or edit a valid directed chain graph on the chessboard grid, and automatically generate a T-shaped paving structure according to the paving rules represented by the directed chain graph.

[0012] Step six involves filling the paving structure with the disassembled basic structure blocks according to their spatial shape, ultimately forming a "T-shaped fabric structure". Specifically, after the basic structure is disassembled into four independent paving blocks, while maintaining their spatial shape, the T-shaped paving structure generated in step five is disassembled into paving blocks according to the basic structure assembly shape in step two, and its warp and weft points are filled to form the final T-shaped paving fabric structure.

[0013] Furthermore, in step five, the effective directed chain graph for forming the T-shaped paving structure is defined as follows:

[0014] In vertex set V t Construct a directed graph D = <V t ,E>, where the edge set E is V t A directed graph is a set of directed edges connecting two adjacent vertices. If the directed graph satisfies the following chain graph condition, then the directed graph uniquely corresponds to a T-shaped paving:

[0015] a) Each directed edge lies on the sub-boundary of a cell;

[0016] b) The in-degree and out-degree of any vertex in the graph are both 1;

[0017] c) The cell colors are set to two, arranged in a checkerboard pattern, and one of the color cells must have two non-adjacent directed edges.

[0018] Furthermore, in step two, the four T-shaped paving blocks are combined into a fabric structure, and the structure points are drawn on it to define the basic structure. The basic structure is then disassembled to obtain the T-shaped paving blocks, which are then recombined using the directed chain graph method to form the paving fabric structure.

[0019] Furthermore, in step five, the directed chain graph is divided into several links, and these links are rearranged and combined to form more new directed chain graphs, thereby generating a brand new T-shaped paving.

[0020] Furthermore, in step five, the overall structure of the paving can be changed by editing the shape of the directed chain graph. The editing methods are mainly as follows:

[0021] a) Reversing the direction of the sub-link graph: Let the sub-link graph... And Di is formed by directed links v1v2, v2v3, ..., v n v1 is composed of, then D is reverse edited. i By determining the direction of the edges, we obtain a new sub-chain graph D. i Its directed link is: v1v n v n v n-1 , ..., v2v1;

[0022] b) Subgraph merging: Let subgraph D i , Their directed links are v1v2, v2v3, ..., v n v1 and u1u2, u2u3, ..., u m u1, if parallel links v exist in both sub-graphs p v p+1 …v p+k with u q u q+1 …u q+k If the two links are in opposite directions and there are no other links in between, then the two subgraphs can be merged; delete the two parallel links and add directed edges to connect the two subgraphs to form a new directed chain graph;

[0023] c) Sub-graph splitting: Splitting is considered the reverse operation of merging; let the sub-graph... If D i There are 2 parallel links v p v p+1 …v p+k With v q v q+1 …v q+k If the two links are in opposite directions and there are no other links between them, then the subgraph is split: delete the two parallel links, split the subgraph into two connected subgraphs, add directed edges, and form a new directed chain graph from the resulting connected subgraphs.

[0024] The beneficial effects of this invention are:

[0025] This invention utilizes the directionality of directed chain diagrams to establish a connection with the T-shaped paving method, enabling each set of directed chain diagrams to correspond to a unique and effective paving method, avoiding monotonous organizational design and limited variation space; at the same time, this method is diverse and convenient, and can directly control the fabric organizational design method by editing the chain diagram, bringing paving effects with different styles. Attached Figure Description

[0026] Figure 1 This is a flowchart of a T-shaped pavement fabric structure design method based on a directed chain graph in one embodiment of the present invention;

[0027] Figure 2 This is the basic organizational form in one embodiment of the present invention;

[0028] Figure 3 These are two optional basic organizational structures of the present invention;

[0029] Figure 4 This is a directed chain graph in one embodiment of the present invention;

[0030] Figure 5 This is a T-shaped paving structure generated from a directed chain graph in one embodiment of the present invention;

[0031] Figure 6 This refers to the "T-shaped fabric structure" ultimately generated in one embodiment of the present invention;

[0032] Figure 7 These are three optional directed chain graphs of the present invention, or variations thereof;

[0033] Figure 8 This invention provides a basic directed chain graph capable of undergoing transformations such as reversal, local merging, and local splitting.

[0034] Figure 9 for Figure 8 A new directed graph is formed after the inverse transformation of a directed graph;

[0035] Figure 10 for Figure 8 A new directed chain graph is formed after a local merging transformation of a directed chain graph;

[0036] Figure 11 for Figure 8 A new directed chain graph is formed after a local split transformation of a directed chain graph;

[0037] Figure 12 These are four T-shaped paving blocks that constitute the same basic structure in this invention;

[0038] Figure 13This corresponds to the directed edges of the directed chain graph in this invention and the arrangement of T-shaped paving blocks. Detailed Implementation

[0039] To address the shortcomings of the prior art, the present invention aims to provide a T-shaped fabric weave design method based on a directed chain diagram. This method utilizes the directionality of the directed chain diagram to establish its connection with the T-shaped weave method, enabling the directed chain diagram to serve as a determination method for the weave structure. This method is versatile, convenient, and can provide a large number of design solutions.

[0040] The present invention will be further illustrated below with specific implementation examples. It should be understood that these implementation examples are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0041] It should be noted that in the claims and specification of this patent, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0042] All documents mentioned in this invention are incorporated herein by reference as if each document were individually incorporated by reference. Furthermore, it should be understood that after reading the foregoing teachings of this invention, those skilled in the art can make various alterations or modifications to this invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0043] The specific embodiments of this invention relate to a T-shaped plywood weave design method based on directed chain graph editing. This method offers great flexibility and a wide range of effects. Compared to traditional fractal and plywood weave design methods, this method enriches the variations in fabric weave in terms of spatial structure, thereby expanding the design space of plywood weave to a greater extent and providing new methods and ideas for the digital design of woven fabrics.

[0044] like Figure 1 As shown, the specific process of the method of the present invention is as follows:

[0045] Step 101: Set the basic weave structure of the woven fabric, that is, a basic weave structure of woven fabric consisting of 4 T-shaped building blocks with a repeat number of 4S. The value of S is set to 1, so the basic weave structure of the woven fabric consists of 4 T-shaped building blocks with a repeat number of 4; For example... Figure 2 As shown, this is the basic organizational form of woven fabric in one embodiment of the present invention. The black and white checkered pattern represents the warp and weft weft points, and it can be disassembled and reassembled using different splicing forms.

[0046] Step 102: Select the T-shaped paving block arrangement in the basic weave of the woven fabric, i.e., the disassembly method, see [link / reference]. Figure 3 There are two types of fabric construction patterns, with each T-shaped pavement block consisting of 4 weaving points. In this embodiment, the first construction pattern is selected. The 4 T-shaped pavement blocks are combined into one structure, and weaving points are drawn on it to define the "basic structure" of the woven fabric. The T-shaped pavement blocks obtained by disassembling the basic structure of the woven fabric can be recombined using the directed chain graph method in subsequent steps to form the pavement fabric structure. The basic structure of the woven fabric consists of 16 weaving points and is also composed of 4 T-shaped pavement blocks. The 4 T-shaped pavement blocks constituting the basic structure of the same woven fabric are as follows: Figure 12 As shown, each paving block maintains the same orientation as its placement in the basic structure before disassembly, to more intuitively represent the combination relationship between the paving blocks; the T-shaped paving block in the basic structure of the woven fabric has two types of splicing forms. An xy coordinate system is established with the planar positions of 16 weaving points, with the lower left weaving point being (1,1). The four T-shaped paving blocks are named T1, T2, T3, and T4 respectively. T1 is composed of four weaving points (1,4), (2,4), (3,4), and (2,3), T2 is composed of four weaving points (1,1), (1,2), (1,3), and (2,2), T3 is composed of four weaving points (2,1), (3,1), (4,1), and (2,2), and T4 is composed of the remaining four weaving points. The second splicing form is obtained by horizontally flipping the first splicing form; each T-shaped paving block is composed of 4 weaving points. The same basic structure of the woven fabric will form different T-shaped paving blocks under different splicing forms.

[0047] Step 103: Determine the number of repeats n×m of the woven fabric structure, and limit the number of repeats n and m to be multiples of 4S; n and m represent the number of repeats in the warp and weft directions; in this embodiment, n=12, m=12, that is, the number of repeats of the woven fabric structure is 12×12.

[0048] Step 104: Calculate and construct the chessboard grid based on the cycle number. The number of lattice (square units) of the chessboard grid is: (n-2)*(m-2) / 4S=25;

[0049] Step 105: Construct or edit a valid directed chain graph on the chessboard grid, such as... Figure 4As shown, and following the paving rules represented by the directed chain graph, a T-shaped paving structure is automatically generated. The corresponding paving structure is as follows: Figure 5 As shown;

[0050] The directed chain diagram consists of several closed directed chain links. The arrows in the directed chain diagram correspond one-to-one with the paving direction of the T-shaped paving blocks; that is, the arrows in the directed chain diagram determine the placement of the T-shaped paving blocks. Figure 7 The diagram shows three optional directed chain graphs of the present invention, or variations thereof. A T-shaped paving block has 10 vertices, encoded as A to J from left to right and top to bottom, forming a directed chain. Figure 1 The starting point of each directed edge corresponds to point D, and the ending point corresponds to point F. This allows for a one-to-one correspondence between directed edges and T-shaped paving blocks, and consequently, a one-to-one correspondence between the directed chain graph and the paving structure. Replacing the edges of the directed chain graph with T-shaped paving structures according to this correspondence creates non-overlapping T-shaped paving structures. The correspondence between the paving block vertex encoding and its directed edges is as follows: Figure 13 As shown;

[0051] The specific correspondence between directed chain graphs and T-shaped paving is as follows:

[0052] For a T-shaped paving that covers a rectangular area, establish a Cartesian coordinate system on it. Let the side length of the square unit constituting the paving block be 1, and the internal corner point of the lower left corner of the paving diagram be the origin coordinate. Then, according to the coordinate position, all the internal corner points of the paving are divided into two categories: if the corner point coordinate is (0,0) or (2,2) when modulo 4, it is a corner point of category A; if the coordinate is (0,2) or (2,0) when modulo 4, it is a corner point of category B.

[0053] Define a gray and white checkerboard pattern, where each cell is 2×2 in size, and let V be the set of all the corner vertices of the checkerboard. t And each vertex is assigned an integer coordinate value, then the two types of corner points and vertex set V are paved. t There is a one-to-one correspondence in spatial location;

[0054] The effective directed chain graph that can form a T-shaped paving structure is defined as follows:

[0055] In vertex set V t A directed graph D can be constructed on top of this. <V t ,E>, where the edge set E is V t A directed graph is a set of directed edges connecting two adjacent vertices. If this directed graph satisfies the following chain graph condition, then this directed graph uniquely corresponds to a T-shaped paving:

[0056] a) Each directed edge lies on the sub-boundary of a cell;

[0057] b) The in-degree and out-degree of any vertex in the graph are both 1;

[0058] c) Each white or gray cell must have two non-adjacent directed edges;

[0059] The overall structure of a paved graph can be altered by editing its shape. The main editing methods are as follows:

[0060] a) Reversing the direction of the sub-link graph: Let the sub-link graph... And D i Given directed links v1v2, v2v3, ..., v n v1 is composed of, then D is reverse edited. i By determining the direction of the edges, we obtain a new sub-chain graph D. i Its directed link is: v1v n v n v n-1 , ..., v2v1;

[0061] b) Subgraph merging: Let subgraph D i , Their directed links are v1v2, v2v3, ..., v n v1 and u1u2, u2u3, ..., u m u1, if parallel links v exist in both sub-graphs p v p+1 …v p+k with u q u q+1 …u q+k If the two links are in opposite directions and there are no other links in between, then the two subgraphs can be merged; delete the two parallel links and add directed edges to connect the two subgraphs to form a new directed chain graph;

[0062] c) Sub-graph splitting: Splitting is considered the reverse operation of merging; let the sub-graph... If D i There are 2 parallel links v p v p+1 …v p+k With v q v q+1 …v q+k If the two links are in opposite directions and there are no other links between them, then the subgraph is split: delete the two parallel links, split the subgraph into two connected subgraphs, add directed edges, and form a new directed chain graph from the resulting connected subgraphs.

[0063] Figure 8 This invention provides a basic directed chain graph capable of undergoing transformations such as reversal, local merging, and local splitting. Figure 9 , Figure 10 , Figure 11 They are respectively for Figure 8 The new directed chain graph is formed by performing reverse transformation (each local directed chain link is reversed to form a new directed chain graph), local merging (merging the two chain links at the top of the image to form a long directed chain link), and local splitting transformation (splitting the chain link at the top left of the image into two short directed chain links). This invention represents the diversity of transformations of the directed chain graph, and can form a variety of paving patterns and plant tissue morphologies.

[0064] Step 106: Fill the paving structure with the basic structural blocks of the disassembled woven fabric according to their spatial shape, ultimately forming a "T-shaped fabric structure" of the woven fabric, such as... Figure 6 As shown, the black and white squares only represent warp and weft weft points. After the basic structure of the woven fabric is disassembled, it becomes four independent laying blocks. While maintaining its spatial shape, the laying structure formed in the previous step is disassembled into laying blocks according to the basic structure assembly shape, and its warp and weft weft points are filled in to form the final T-shaped laying fabric structure of the woven fabric.

[0065] It should be noted that in the claims and specification of this patent, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0066] The above description is merely a preferred embodiment of the present invention. The present invention has been illustrated and described, but those skilled in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the present invention.

Claims

1. A T-paving fabric weave design method based on a directed chain graph, characterized by, The method comprises the following steps: Step one, setting the basic tissue form, i.e. the basic tissue with a cycle number of 4S composed of four T-shaped paving blocks, wherein S is a positive integer; Step two, selecting the assembly form of the T-shaped paving block in the basic tissue, i.e. the splitting mode; Step three, determining the cycle number n x m of the paving fabric tissue, and limiting the cycle numbers n and m to be multiples of 4S, wherein n and m represent the cycle numbers in the warp and weft directions; Step four, calculating and constructing the checkerboard according to the cycle number, wherein the lattice, i.e. the number of square cells, of the checkerboard is (n-2)*(m-2) / 4S; Step five, constructing or editing the effective directed chain graph on the checkerboard, and automatically generating the T-shaped paving structure according to the paving rules represented by the directed chain graph; the directed chain graph is divided into a plurality of chain links, and the chain links are rearranged and combined to form more new directed chain graphs, thereby generating a new T-shaped paving; the overall structure of the paving can be changed by editing the form of the directed chain graph, and the editing modes mainly include the following modes: a) Sub-chain graph direction reversal: Let sub-chain graph D and Di be composed of directed links v1v2, v2v3, …, v n 1, then a new sub-chain graph D i ' is obtained by reversing the direction of the edges of D i , which has directed links: v1v n , v n v n-1 , …, v2v1; b) Subgraph merging: Let subgraph D i , Their directed links are v1v2, v2v3, ..., v n v1 and u1u2, u2u3, ..., u m u1, if parallel links v exist in both sub-graphs p v p+1 …v p+k with u q u q+1 …u q+k If the two links are in opposite directions and there are no other links in between, then the two subgraphs can be merged; delete the two parallel links and add directed edges to connect the two subgraphs to form a new directed chain graph; c) Sub-graph splitting: Splitting is considered the reverse operation of merging; let the sub-graph... If D i There are 2 parallel links v p v p+1 …v p+k With v q v q+1 …v q+k If the two links are in opposite directions and there are no other links between them, then the subgraph is split: delete the two parallel links, split the subgraph into two connected subgraphs, add directed edges, and form a new directed chain graph from the resulting connected subgraphs. Step six, filling the paving structure according to the spatial form of the disassembled basic tissue block, and finally forming the "T-shaped fabric tissue", specifically: after the basic tissue is disassembled into four independent paving blocks, the T-shaped paving structure generated in step five is disassembled into paving blocks according to the basic tissue assembly form in step two, and the warp and weft tissue points are filled to form the final T-shaped paving fabric tissue.

2. The method of designing a T-paving fabric organization based on a directed chain graph according to claim 1, wherein, In step five, the effective directed chain graph for forming the T-shaped paving structure is defined as follows: A directed graph D = <V t ,E> is constructed on the vertex set V t , where the edge set E is the set of directed edges connecting adjacent two vertices in V t ; if the directed graph satisfies the chain graph condition described below, the directed graph uniquely corresponds to a T-shaped paving. a) Each directed edge is located on the boundary of the cell lattice; b) The in-degree and out-degree of any vertex in the graph are both 1; c) The color of the cell lattice is set to two, arranged in the form of a checkerboard, and there are two non-adjacent directed edges on the cell lattice of one color.

3. The method of claim 1, wherein, In step two, four T-shaped paving blocks are combined into a fabric tissue, and tissue points are drawn on the fabric tissue to define the basic tissue. The T-shaped paving blocks are obtained by disassembling the basic tissue, and the paving fabric tissue is formed by recombining the T-shaped paving blocks using the directed chain graph method.

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