Printing pattern generation method and device based on Clariboard equation

Abstract

The invention discloses a printing pattern generation method and device based on a Clariboard equation. According to the method, the width and height of textile printing pattern cloth are set, a two-dimensional plane is obtained, a Dirac function is used for representing a point source of the two-dimensional plane, a square pattern size coefficient is set, a mathematical model of a Clariboard equation is constructed based on parameters of the Clariboard equation, and the size of the square pattern is calculated by adjusting boundary conditions of the mathematical model of the Clariboard equation and changing characteristic values. And solving a Clariboard equation after the boundary conditions are updated to obtain an analytical solution, and finally cutting the function by adopting a contour method and projecting the function to a two-dimensional plane for coloring to generate a digital pattern. Compared with a traditional method, the method has the advantages that the types of the generated digital patterns are richer, the patterns of different types can be flexibly generated according to the requirements of users on the patterns, and the finally generated patterns have certain controllability.

Description

Technical Field

[0001] The present invention relates to fields such as computer graphics, art design, and product (textile) design, and specifically to a method and device for generating printed patterns based on the Chladni plate equation. This invention is based on the mathematical model of the Chladni plate equation, applies different boundary conditions, solves it using the Fourier transform method, and finally uses the contour method to segment and color the pattern on a two-dimensional plane. The invention aims to generate aesthetically pleasing and controllable digital patterns, while providing users with a variety of pattern generation variations. Background Art

[0002] Digital pattern generation methods based on nonlinear theory have greatly improved design efficiency, enabling the creation of rich, varied, and endless patterns. This effectively addresses the challenges of limited design resources and low efficiency in traditional design. Currently, this field primarily encompasses a variety of digital patterns, including fractals, dynamical system graphics, and quasi-regular patterns. These digital patterns are not only complex and varied in appearance, but also possess an aesthetic that rivals traditional works of art, combining scientific value with artistic appeal. They provide a vast reservoir of inspiration for design in fields such as textiles, decoration, and architecture. However, the complexity of nonlinear theory and the inherent characteristics of its functions make the generated digital patterns lacking in controllability. Their compositions often appear monotonous, and the variations in patterns lack diversity, making them difficult to meet the diverse needs of designers.

[0003] In recent years, the rapid development of generative artificial intelligence (AIGC) has opened up new avenues for digital pattern generation. Designers can generate the desired digital patterns by training models, but this approach also comes with certain limitations. First, training AI models requires a large dataset, and sourcing and obtaining copyright for these materials are often costly. Second, the style of patterns generated by AI models is limited by the dataset used for training, making it difficult to transcend the inherent framework of the dataset. Finally, using AI models to generate patterns requires high computer equipment configuration, which makes the audience of this technology relatively limited.

[0004] To address the above-mentioned issues, the present invention introduces the mathematical model of the Chladni plate equation and provides a digital pattern generation method based on the Chladni plate equation. The mathematical model of the Chladni plate equation is based on a physical experiment conducted by German physicist Chladni, in which he struck the edge of a metal block, resulting in beautiful patterns appearing on a powder-coated metal block. Its advantages as a digital pattern generation method lie not only in its ability to produce beautiful patterns, but also in its ability to easily adjust the desired pattern, as the parameters involved have physical meaning. Based on the mathematical model of the Chladni plate equation, the present invention adjusts its boundary conditions and eigenvalues, further enriching the diversity of generated patterns, enhancing the controllability of the patterns, and satisfying the needs of most computers. The present invention can provide a large amount of pattern material for traditional design industries and artificial intelligence training, and has important practical significance for the textile and interior decoration industries, in particular.

[0005] To address these issues, the present invention introduces the mathematical model of the Chladni plate equation and proposes an innovative digital pattern generation method based on this equation. The Chladni plate equation originates from a classic physics experiment in which German physicist Chladni struck the edge of a metal block, causing a powdered substance coated on the block to produce beautiful patterns. Applying this model to digital pattern generation is advantageous not only because it can produce highly aesthetic patterns, but also because the parameters involved have clear physical meanings, allowing designers to easily adjust the desired pattern effect.

[0006] Based on the Chladni plate equation, this invention further enriches the diversity of generated patterns and significantly enhances their controllability by adjusting key parameters such as boundary conditions and eigenvalues. Furthermore, this method has moderate computer requirements, meeting the needs of most users. This invention can provide a vast amount of pattern material for traditional design industries and artificial intelligence training, and has extremely important practical significance and application value, particularly in industries such as textiles and interior decoration. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention provides a method for generating printed patterns based on the Chladni plate equation. The present invention aims to increase the controllability and diversity of printed digital pattern generation. Based on a mathematical model based on the Chladni plate equation and utilizing its physical principles, the generated patterns exhibit a more natural and artistic regularity. This method avoids the limitations of traditional manual design methods, enabling designers to generate a variety of digital patterns, from simple to complex, and from symmetrical to irregular, based on different cultures, artistic styles, and customer needs by adjusting algorithm parameters. This improves designers' design efficiency and promotes the development and innovation of printed digital pattern generation technology.

[0008] The object of the present invention is achieved through the following technical solutions: In a first aspect, the present invention provides a method for generating a printing pattern based on a Chladni plate equation, comprising the following steps:

[0009] Step 1: Set the width and height of the textile print pattern fabric to obtain a two-dimensional plane, use the Dirac function to represent the two-dimensional plane point source, and set the square pattern size coefficient. Based on the parameters of the Chladni plate equation, a mathematical model of the Chladni plate equation is constructed;

[0010] Step 2: Adjust the boundary conditions of the Chladni plate equation according to the requirements of the textile printing pattern;

[0011] Step 3: Solve the equation to obtain its eigenvalue and eigenfunction according to its boundary conditions, and perturb the eigenfunction to change the symmetry of the solution;

[0012] Step 4: Using Fourier transform method to solve the Chladni plate equation to obtain an analytical solution;

[0013] Step 5, project the obtained function onto a two-dimensional plane using the contour cutting method;

[0014] Step six: color the two-dimensional plane graphics and generate textile printing digital patterns.

[0015] Furthermore, in step 1, the Chladni plate equation u is determined by selecting the source amplitude s0, the damping constant γ, the shear wave velocity v, the time t, the original frequency ω, the plane length L, and the plane width M, and a mathematical model of the Chladni plate equation u is constructed:

[0016]

[0017] where S is the sinusoidal impact force at the center of the Chladni plate:

[0018]

[0019] where δ represents the Dirac function, Represents a point on a two-dimensional plane There is a point source at , L = α, M = α, α is the square pattern size coefficient, sin(ωt) represents the excitation of the point source changing with time, which is a sine function with a frequency of ω.

[0020] Furthermore, in step 2, the Newman boundary conditions of the Chladni plate equation are adjusted to increase the symmetry types of the printed pattern finally generated; under these boundary conditions, patterns with various symmetry forms are generated: vertical / lateral symmetry, diagonal symmetry, mixed symmetry, and asymmetry; wherein the vertical / lateral symmetry boundary conditions are:

[0021] u′(0,y,t)=u′(L,y,t),u′(x,M,t)=u′(x,0,t)(2)

[0022] The diagonally symmetric boundary conditions are:

[0023] u′(0,y,t)=u′(x,0,t),u′(x,M,t)=u′(L,y,t)(3)

[0024] The mixed symmetry boundary conditions are:

[0025] u′(x,M,t)=u′(L,y,t)=u′(0,y,t)=u′(x,0,t),L=M(4)

[0026] The asymmetric boundary conditions are:

[0027] u′(x,M,t)≠u′(L,y,t)≠u′(0,y,t)≠u′(x,0,t)(5)

[0028] Furthermore, in step 3, in order to facilitate the solution of eigenvalues and characteristic functions, the Chladni plate equation (1) is first simplified to:

[0029]

[0030] Using the separation of variables method, the solution u(x, y, t) of the Chladni plate equation (6) is separated into the following form:

[0031] u(x,y,t)=X(x)Y(y)T(t)

[0032] Substituting the separated solution into equation (6) yields the ordinary differential equation:

[0033]

[0034] where μ 2 and λ 2 is a separation constant that affects the solution of the ordinary differential equation and is therefore called an eigenvalue; for X(x) and Y(y), the general solution of the equation is:

[0035] X(x)=Acos(μx)+Bsin(μx)

[0036] Y(y)=Ccos(λy)+Dsin(λy)

[0037] in

[0038] X′(0)=Bμ,X′(L)=-Aμsin(μL)+Bμcos(μL)

[0039] Y′(0)=Cλ,Y′(M)=-Cλsin(λM)+Dλcos(λM)

[0040] Among them, A, B, C, and D are coefficient parameters.

[0041] Furthermore, in step three, an interference coefficient is added according to the boundary conditions to destroy the symmetry of the digital pattern and enrich the visual perception of the graphic;

[0042] The expression of the eigenvalue corresponding to equation (2) is:

[0043]

[0044] where μ i is the eigenvalue in the X-axis direction, λ j is the eigenvalue in the Y-axis direction, i, j are serial numbers, ε1, ε2 are perturbation terms used to destroy the symmetry of the digital pattern; p1, p2 are eigenvalue coefficients used to enrich the pattern types, p1≠p2;

[0045] The expression of the eigenvalue corresponding to equation (3) is:

[0046]

[0047] The expression of the eigenvalue corresponding to equation (4) is:

[0048]

[0049] That is μ i and λ j Each term is equivalent and formally conforms to the solution of equation (2), where c is a fixed constant; equation (5) does not require any perturbation because it is an asymmetric graph.

[0050] Furthermore, in step 4, the Fourier transform method is used to solve the Chladni plate equation to obtain an analytical solution. First, the Chladni plate equation is converted from the spatial domain to the frequency domain by the Fourier transform method. Then, the frequency domain solution of the Chladni plate equation is solved in the frequency domain. Finally, the frequency domain solution is converted back to the spatial domain by the inverse Fourier transform, and the following analytical solution is obtained:

[0051]

[0052] Where n,m are the number of summation terms specified by the user, and:

[0053]

[0054] Furthermore, in steps 5 and 6, the function is cut and colored using the contour method to generate digital patterns for textile printing; the height field of the analytical solution is divided into several non-intersecting intervals. Then the connected areas corresponding to each interval are assigned the same predefined color to generate a digital pattern for textile printing.

[0055] Furthermore, in step six, the connected areas corresponding to the intervals on the two-dimensional plane are colored. The present invention uses a set of color cards to perform detailed color mapping on the area, and locates the colors at equal intervals in the color card according to the function values corresponding to the points in the area for gradient coloring to obtain the colored pattern. The present invention calculates the state of each pixel on the GPU through the compute shader of OpenGL. The shader is written in GLSL and efficiently processes large-scale grid data. To optimize performance, the present invention first draws the pattern into the frame buffer object, and then reads the pattern information from the frame buffer object and draws it to the display window to ensure that the rendering process is smooth. Ultimately, the GPU acceleration capability of OpenGL significantly improves the efficiency of pattern generation and rendering.

[0056] In a second aspect, the present invention also provides a printing pattern generation device based on the Chladni plate equation, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it implements the printing pattern generation method based on the Chladni plate equation.

[0057] In a third aspect, the present invention further provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the method for generating a printing pattern based on the Chladni plate equation.

[0058] The main advantages of the present invention include:

[0059] (a) Improving the controllability of nonlinear theoretical functions: Utilizing the physical meaning of the parameters corresponding to the mathematical model of the Chladni plate equation, we can strengthen the control over the shape of the generated printing pattern. For example, by varying the frequency and intensity of the vibration source, we can control the complexity of the printing pattern.

[0060] (b) Enriching the diversity of printed patterns: By modifying the boundary conditions of the Chladni plate equation, we can create a variety of beautiful printed digital patterns. The changes in boundary conditions can form different styles of printed patterns, making the visual effect of the final printed pattern both regular and varied.

[0061] (c) High quality and high efficiency: The generated digital printed patterns are of high quality, enriching the generation forms. At the same time, the algorithm has high execution efficiency, providing users with a smooth and fast operation experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The present invention is a flowchart of a method for generating a printing pattern based on the Chladni plate equation in one embodiment of the present invention.

[0063] Figure 2 This is a specific process of an embodiment of a printing pattern generation method based on the Chladni plate equation in one embodiment of the present invention.

[0064] Figure 3 This is a comparison diagram of error addition results of a printing pattern generation method based on the Chladni plate equation in one embodiment of the present invention.

[0065] Figure 4 Result diagram of different element types of a printing pattern generation method based on the Chladni plate equation in one embodiment of the present invention.

[0066] Figure 5 This is a visualization result of a computer program user terminal in one embodiment of the present invention.

[0067] Figure 6 This is a diagram showing the effect of applying a printing pattern generation method based on the Chladni plate equation to clothing materials in one embodiment of the present invention.

[0068] Figure 7 This is a rendering of the effect of applying a printing pattern generation method based on the Chladni plate equation in interior decoration in one embodiment of the present invention.

[0069] Figure 8 The present invention is a structural diagram of a printing pattern generation device based on the Chladni plate equation in one embodiment of the present invention. DETAILED DESCRIPTION

[0070] The present invention will be further described below with reference to specific examples. It should be understood that these examples are only intended to illustrate the present invention and are not intended to limit the scope of the present invention.

[0071] It should be noted that, in the claims and description of the present invention, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises", "includes" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the phrase "comprising a" does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0072] Example

[0073] All documents mentioned in this application are incorporated herein by reference, just as if each document were incorporated herein by reference individually. It should also be understood that after reading the above teachings of the present invention, those skilled in the art may make various changes or modifications to the present invention, and that such equivalents also fall within the scope of the claims appended hereto.

[0074] Digital patterns have many application scenarios, such as the creation of digital artworks, textile pattern design, game map generation, texture design, and product pattern design, providing designers with a rich variety of textures and patterns, enhancing the visual appeal and uniqueness of their works. This invention takes the design of textile print patterns in the textile design process as an example, and introduces the implementation process of a print pattern generation method based on the Chladni plate equation. The invention specifically includes: the user inputs the width W of the fabric in the production of the textile print pattern x and height W y , select the source amplitude s0, damping constant γ, shear wave velocity ν, time t, original frequency ω, and square pattern length L and width M, and construct a mathematical model of the Chladni plate equation; adjust the boundary conditions of the Chladni plate equation according to user needs, and select the pattern symmetry form required by the user; input the interference coefficient ε according to user needs to change the symmetry of the solution and enhance its visual perception; use the Fourier transform method to solve the Chladni plate equation to obtain an analytical solution; use the contour method to divide the analytical solution into height fields, and project each height field onto a two-dimensional plane for graphic coloring; periodically extend the generated pattern on the textile so that the newly generated pattern covers the entire textile.

[0075] Figure 1 This is a flow chart of a method for generating a digital pattern based on the Chladni plate equation in one embodiment of the present invention. The method includes the following steps: Step 101, a user inputs the parameters of the Chladni plate equation to construct a mathematical model of the Chladni plate equation; Step 102, adjusting the boundary conditions of the Chladni plate equation according to user requirements; Step 103, solving the equation based on the boundary conditions to obtain its eigenvalues and characteristic functions, and perturbing the characteristic functions to change the symmetry of the solution; Step 104, solving the Chladni plate equation using the Fourier transform method to obtain an analytical solution; Step 105, cutting the function using the contour line method and projecting it onto a two-dimensional plane; Step 106, coloring the two-dimensional plane figure and generating a digital pattern;

[0076] Specifically, the present invention provides a digital pattern generation method based on the Chladni plate equation. Figure 2 The present invention shows a specific real-time process of an embodiment of a digital pattern generation method based on the Chladni plate equation. The embodiment includes the following steps:

[0077] Step 1: The user inputs the parameters of the Chladni plate equation: source amplitude s0, damping constant γ, shear wave velocity ν, time t, and original frequency ω; at the same time, inputs the pattern length L and width M, and the fabric width W. x and height W y . Construct the mathematical model of the Chladni plate equation u:

[0078]

[0079] where S is the sinusoidal impact force at the center of the Chladni plate:

[0080]

[0081] where δ represents the Dirac function, Represents a point on a two-dimensional plane There is a point source at , L = α, M = α, α is the square pattern size coefficient, sin(ωt) represents the excitation of the point source changing with time, which is a sine function with a frequency of ω.

[0082] Step 2: Adjust the boundary conditions of the Chladni plate equation according to user needs. Adjust the Newman boundary conditions of the Chladni plate equation to increase the symmetry of the final printed pattern; generate patterns with various symmetry forms under these boundary conditions: vertical / lateral symmetry, diagonal symmetry, mixed symmetry, and asymmetry; the vertical / lateral symmetry boundary conditions are:

[0083] u′(0,y,t)=u′(L,y,t),u′(x,M,t)=u′(x,0,t)(2)

[0084] The diagonally symmetric boundary conditions are:

[0085] u′(0,y,t)=u′(x,0,t),u′(x,M,t)=u′(L,y,t)(3)

[0086] The mixed symmetry boundary conditions are:

[0087] u′(x,M,t)=u′(L,y,t)=u′(0,y,t)=u′(x,0,t),L=M(4)

[0088] The asymmetric boundary conditions are:

[0089] u′(x,M,t)≠u′(L,y,t)≠u′(0,y,t)≠u′(x,0,t)(5)

[0090] For example, in the present invention, when the user requires a pattern with a relatively high degree of symmetry, the user selects the mixed symmetry mode, and the corresponding boundary conditions are:

[0091] u′(x,M,t)=u′(L,y,t)=u′(0,y,t)=u′(x,0,t)

[0092] Step 3: Solve the Chladni plate equation eigenvalue and eigenfunction according to the boundary conditions, and perturb the eigenfunction according to the user's needs. The user specifies the interference coefficient ε to destroy the symmetry of the pattern ( Figure 3 The specific process is as follows: To facilitate the solution of eigenvalues and characteristic functions, first simplify the Chladni plate equation (1):

[0093]

[0094] Using the separation of variables method, the solution u(x, y, t) of the Chladni plate equation (6) is separated into the following form:

[0095] u(x,y,t)=X(x)Y(y)T(t)

[0096] Substituting the separated solution into equation (6) yields the ordinary differential equation:

[0097]

[0098] where μ 2 and λ 2 is a separation constant that affects the solution of the ordinary differential equation and is therefore called an eigenvalue; for X(x) and Y(y), the general solution of the equation is:

[0099] X(x)=Acos(μx)+Bsin(μx)

[0100] Y(y)=Ccos(λy)+Dsin(λy)

[0101] in

[0102] X′(0)=Bμ,X′(L)=-Aμsin(μL)+Bμcos(μL)

[0103] Y′(0)=Cλ,Y′(M)=-Cλsin(λM)+Dλcos(λM)

[0104] Among them, A, B, C, and D are coefficient parameters, but they have little effect on the pattern shape. Therefore, unless there is a special case, the present invention sets A=B=C=D=1. The boundary condition (2) is solved to obtain the eigenvalue:

[0105]

[0106] The present invention obtains a series of bases for the solution of the equation, μ i is the eigenvalue in the X-axis direction, λ jis the eigenvalue in the Y-axis direction, where i, j are the base numbers, p1, p2 are the eigenvalue coefficients, and p1≠p2;

[0107] Solve the boundary condition (3) to get the eigenvalue:

[0108]

[0109] Solving the boundary condition (4) yields the eigenvalue:

[0110]

[0111] Add interference coefficients according to boundary conditions to destroy the symmetry of digital patterns and enrich the visual perception of graphics;

[0112] The expression of the eigenvalue corresponding to equation (2) is:

[0113]

[0114] where μ i is the eigenvalue in the X-axis direction, λ j is the eigenvalue in the Y-axis direction, i, j are serial numbers, ε1, ε2 are perturbation terms used to destroy the symmetry of the digital pattern; p1, p2 are eigenvalue coefficients used to enrich the pattern types, p1≠p2;

[0115] The expression of the eigenvalue corresponding to equation (3) is:

[0116] and i≤20, k=1,2

[0117] The expression of the eigenvalue corresponding to equation (4) is:

[0118]

[0119] That is μ i and λ j Each term is equivalent and formally conforms to the solution of equation (2), where c is a fixed constant; equation (5) does not require any perturbation because it is an asymmetric graph.

[0120] Step 4: Use the Fourier transform method to solve the Chladni plate equation and obtain an analytical solution. First, the Chladni plate equation is converted from the spatial domain to the frequency domain using the Fourier transform method. Then, the frequency domain solution of the Chladni plate equation is solved in the frequency domain. Finally, the frequency domain solution is converted back to the spatial domain using the inverse Fourier transform to obtain the analytical solution. The analytical solution obtained is

[0121]

[0122] Where n,m are the number of summation items specified by the user, and

[0123]

[0124] Step 5: Use the contour method to cut the function and project it onto a two-dimensional plane, and color the two-dimensional plane graph. After obtaining a satisfactory shape, divide the region according to the height field of the analytical solution, and divide the height field of the analytical solution u into several non-intersecting intervals. Project it onto a two-dimensional plane to obtain the connected area corresponding to each interval on the two-dimensional plane.

[0125] Furthermore, in step 6, the connected area corresponding to the interval on the two-dimensional plane is colored. The user selects a color card from the color card library, and locates the color at equal intervals in the color card according to the function value corresponding to the point in the area for gradient coloring, and the colored pattern is obtained ( Figure 4 ). The present invention calculates the state of each pixel on the GPU through the OpenGL compute shader. The shader is written in GLSL and efficiently processes large-scale grid data. To optimize performance, the present invention first draws the pattern into the frame buffer object, then reads the pattern information from the frame buffer object and draws it into the display window to ensure that the rendering process is smooth. Ultimately, the GPU acceleration capability of Open GL significantly improves the efficiency of pattern generation and rendering. Figure 6 and Figure 7 The figures shown are effect diagrams of the present invention applied to clothing materials and interior decoration respectively.

[0126] Corresponding to the aforementioned embodiment of a printing pattern generation method based on the Chladni plate equation, the present invention also provides an embodiment of a printing pattern generation device based on the Chladni plate equation.

[0127] See also Figure 8 An embodiment of the present invention provides a printing pattern generation device based on the Chladni plate equation, including a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement a printing pattern generation method based on the Chladni plate equation in the above embodiment.

[0128] The embodiment of the printing pattern generation device based on the Chladni plate equation provided by the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Figure 8As shown in FIG. 1 , a hardware structure diagram of a printing pattern generating device based on the Chladni plate equation provided by the present invention is provided in any device with data processing capability, except Figure 8 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0129] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0130] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present invention. A person of ordinary skill in the art can understand and implement the present invention without inventive work.

[0131] An embodiment of the present invention further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, a printing pattern generation method based on the Chladni plate equation in the above embodiment is implemented.

[0132] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the aforementioned embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0133] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the method for generating a printing pattern based on the Chladni plate equation ( Figure 5 ).

[0134] It should be noted that in the claims and specification of this patent, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "includes," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. Without further limitation, an element defined by the phrase "comprising a" does not exclude the presence of other identical elements in the process, method, article, or device comprising the element. Although the present invention has been illustrated and described with reference to certain preferred embodiments thereof, it should be understood by those skilled in the art that various changes may be made thereto in form and detail without departing from the spirit and scope of the invention.

Claims

1. A printing pattern generation method based on the Chladni plate equation, characterized in that: The following steps are involved: Step 1: Set the width and height of the textile print pattern fabric to obtain a two-dimensional plane, use the Dirac function to represent the two-dimensional plane point source, and set the square pattern size coefficient. Based on the parameters of the Chladni plate equation, a mathematical model of the Chladni plate equation is constructed; Step 2: Adjust the boundary conditions of the Chladni plate equation according to the requirements of the textile printing pattern; Step 3: Solve the equation to obtain its eigenvalue and eigenfunction according to its boundary conditions, and perturb the eigenfunction to change the symmetry of the solution; Step 4: Using Fourier transform method to solve the Chladni plate equation to obtain an analytical solution; Step 5, project the obtained function onto a two-dimensional plane using the contour cutting method; Step six: color the two-dimensional plane graphics and generate textile printing digital patterns.

2. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In step 1, the Chladni plate equation u is determined by selecting the source amplitude s0, damping constant γ, shear wave velocity v, time t, original frequency ω, plane length L, and plane width M, and a mathematical model of the Chladni plate equation u is constructed: where S is the sinusoidal impact force at the center of the Chladni plate: where δ represents the Dirac function, Represents a point on a two-dimensional plane There is a point source at , L = α, M = α, α is the square pattern size coefficient, sin(ωt) represents the excitation of the point source changing with time, which is a sine function with a frequency of ω.

3. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In step 2, the Newman boundary conditions of the Chladni plate equation are adjusted to increase the symmetry of the final printed pattern. Various symmetric patterns are generated under these boundary conditions: vertical / lateral symmetry, diagonal symmetry, mixed symmetry, and asymmetry. The vertical / lateral symmetry boundary conditions are: u′(0,y,t)=u′(L,y,t),u′(x,M,t)=u′(x,0,t)(2) The diagonally symmetric boundary conditions are: u′(0,y,t)=u′(x,0,t),u′(x,M,t)=u′(L,y,t)(3) The mixed symmetry boundary conditions are: u′(x,M,t)=u′(L,y,t)=u′(0,y,t)=u′(x,0,t),L=M(4) The asymmetric boundary conditions are: u′(x,M,t)≠u′(L,y,t)≠u′(0,y,t)≠u′(x,0,t)(5).

4. The method for generating a printing pattern based on the Chladni plate equation according to claim 2, wherein: In step 3, in order to facilitate the solution of eigenvalues and characteristic functions, the Chladni plate equation (1) is first simplified to the form: Using the separation of variables method, the solution u(x, y, t) of the Chladni plate equation (6) is separated into the following form: u(x,y,t)=X(x)Y(y)T(t) Substituting the separated solution into equation (6) yields the ordinary differential equation: where μ 2 and 2 is a separation constant that affects the solution of the ordinary differential equation and is therefore called an eigenvalue; for X(x) and Y(y), the general solution of the equation is: X(x)=Acos(μx)+Bsin(μx) Y(y)=Ccos(λy)+Dsin(λy) in X′(0)=Bμ,X′(L)=-Aμsin(μL)+Bμcos(μL) Y′(0)=Cλ,Y′(M)=-Cλsin(λM)+Dλcos(λM) Among them, A, B, C, and D are coefficient parameters.

5. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In step 3, interference coefficients are added according to boundary conditions to destroy the symmetry of the digital pattern and enrich the visual perception of the graphic; The expression of the eigenvalue corresponding to equation (2) is: where μ i is the eigenvalue in the X-axis direction, λ j is the eigenvalue in the Y-axis direction, i, j are serial numbers, ε1, ε2 are perturbation terms used to destroy the symmetry of the digital pattern; p1, p2 are eigenvalue coefficients used to enrich the pattern types, p1≠p2; The expression of the eigenvalue corresponding to equation (3) is: The expression of the eigenvalue corresponding to equation (4) is: That is μ i and λ j Each term is equivalent and formally conforms to the solution of equation (2), where c is a fixed constant; equation (5) does not require any perturbation because it is an asymmetric graph.

6. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In step 4, the Fourier transform method is used to solve the Chladni plate equation to obtain an analytical solution. First, the Fourier transform method is used to convert the Chladni plate equation from the spatial domain to the frequency domain. Then, the frequency domain solution of the Chladni plate equation is solved in the frequency domain. Finally, the inverse Fourier transform is used to convert the frequency domain solution back to the spatial domain, obtaining the following analytical solution: Where n,m are the number of summation terms specified by the user, and:

7. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In steps 5 and 6, the function is cut and colored using the contour method to generate digital patterns for textile printing; the height field of the analytical solution is divided into several non-intersecting intervals. Then the connected areas corresponding to each interval are assigned the same predefined color to generate a digital pattern for textile printing.

8. The method for generating a printing pattern based on the Chladni plate equation according to claim 1, wherein: In step six, C++ language and the OpenGL graphics rendering engine are used to generate digital patterns for textile prints using GPU rendering. The state of each pixel is calculated on the GPU through OpenGL's compute shader, which is written in GLSL. The pattern is first drawn into a frame buffer object, and then the pattern information is read from the frame buffer object and drawn into the display window.

9. A printing pattern generation device based on the Chladni plate equation, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, a printing pattern generation method based on the Chladni plate equation as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, a printing pattern generation method based on the Chladni plate equation as described in any one of claims 1 to 8 is implemented.

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