Interactive digital pattern generation method and device based on isohedron paving

Abstract

The invention discloses an interactive digital pattern generation method and device based on isohedron paving. The method comprises the following steps: firstly, selecting a polygon template based on a wallpaper group as an isohedron paving unit; interactively editing the shape of a paving unit through operations such as adding and deleting vertexes / moving the vertexes, performing triangular meshing on the paving unit, and defining a quasi-regular pattern function on the paving unit; constructing an energy equation according to constraints such as symmetry of the boundary of the paving unit and optimizing a quasi-regular pattern function; coloring based on the updated quasi-regular pattern function and generating a digital pattern; and finally, carrying out tetragonal periodic continuation on the digital patterns, so that the canvas is fully paved with the digital patterns. According to the method, flexible edition of the shape of the paving unit and seamless reconstruction of the texture are realized by utilizing an isohedral paving structure, symmetry of groups, gradient domain fusion and other technologies, the problem that control is not intuitive in a traditional digital pattern generation method is solved, and the paving units with curved-edge polygons in various forms can be generated; therefore, the change form of the digital pattern is enriched.

Description

Technical Field

[0001] The present invention relates to the fields of computer graphics, art design, product (textile) design, and more specifically to a method for interactively generating digital patterns using isohedra paving structures. The method introduces theories such as symmetry groups and wallpaper groups, and designs paving blocks in combination with mathematical properties such as the symmetry of isohedra paving, aiming to generate digital patterns with natural beauty and natural boundary transitions through interactive means, improve and realize the controllability of digital pattern generation, and enrich the variation forms and diversity of patterns. Background Art

[0002] The digital pattern generation method based on nonlinear theory can greatly improve the design efficiency and create endless and varied patterns, thus effectively solving the problems of design resources and design efficiency in traditional design. The digital patterns generated are also called "digital art graphics", such as fractal graphics, dynamic system graphics, quasi-regular patterns, etc. This type of graphics naturally has complex characteristics such as color, shape and texture. At the same time, it is abstract like traditional works of art, with dual value of science and art, and has become an important material for pattern design in the fields of architecture, decoration, textiles and clothing. However, due to the complexity of nonlinear theory, it has problems such as weak intuitiveness, difficult controllability, and monotonous spatial composition.

[0003] With the rapid development of artificial intelligence technology, generative artificial intelligence (AIGC) has emerged in various industries in recent years, and has also shined in the field of design, greatly improving design efficiency. However, it also has certain limitations: for example, training an AI model of a specific style requires a large amount of flower pattern materials, and the source and copyright issues of the materials limit the promotion of this technology; secondly, the theme style of the flower pattern generated by the AI ​​model is limited to a specific training data set, and it is impossible to break through the inherent theme style of the data set.

[0004] In view of the above problems, the present invention starts from the spatial composition of digital patterns and provides an interactive digital pattern generation method based on isohedral tiling. The so-called isohedral tiling means that the symmetry group of the tiling is transitive on the tiling blocks. Specifically, let T be the tiling. For two congruent tiling blocks T1 and T2 in T, there will be at least one planar rigid motion that maps T1 to T2. When the rigid motion is also a symmetry of the tiling, a special case will occur. In this case, when T1 and T2 correspond, the remaining tiling will also be mapped to itself, and the two tiling blocks are said to be transitively equivalent. Transitive equivalence is an equivalence relation that divides tiling blocks into transitive categories. When the tiling has only one transitive class, it is called isohedral tiling, also called monohedral tiling. More generally, k-isohedral tiling has k transitive categories. Isohedral tiling is a tiling that allows a single prototype to cover the entire plane by repeatedly applying rigid motions in the tiling symmetry group. Different from polygonal paving, isohedral paving units can be any curved polygons under local symmetry constraints, and have greater freedom of shape change, which can provide richer spatial composition forms for pattern design. The present invention introduces a quasi-regular pattern function model as a pattern texture generator to flexibly control the pattern style from multiple dimensions; and based on the mathematical theory of isohedral paving, paving units with complex shapes are flexibly constructed in an interactive manner to overcome the monotony problem of traditional composition. The present invention further expands the generation method of digital patterns, which not only has the advantages of traditional digital patterns, but also has richer and more complex and diverse composition forms, so that it has a certain anti-counterfeiting function, and can provide endless pattern materials for traditional design industries and artificial intelligence training, especially for industries such as textile design. It has important practical significance. Summary of the invention

[0005] The purpose of the present invention is to propose an interactive digital pattern generation method based on isohedra paving to improve the controllability and diversity of digital pattern generation. By introducing symmetry group, wallpaper group constraint information and gradient domain fusion ideas, natural and beautiful digital patterns with smooth boundaries are generated, thereby meeting the needs of contemporary design and daily life for aesthetics and personalized pursuits, and promoting the development and innovation of digital pattern generation technology.

[0006] The object of the present invention is achieved through the following technical solutions: In a first aspect, the present invention provides an interactive digital pattern generation method based on isohedral paving, comprising the following steps:

[0007] Step 1: Select a polygonal template based on wallpaper group as an isohedral paving unit and as the basic shape of the digital pattern space composition;

[0008] Step 2: interactively edit the paving unit shape by adding and deleting vertices / moving vertices and triangulate it;

[0009] Step 3, defining a quasi-regular pattern function on the paving unit;

[0010] Step 4: construct the energy equation and optimize the quasi-regular pattern function according to the symmetry constraints and smoothness conditions of the paving unit boundary;

[0011] Step 5, coloring and generating digital patterns based on the updated quasi-regular pattern function;

[0012] Step six: Extend the digital pattern in a four-way periodic manner to fill the entire canvas.

[0013] Furthermore, in step 1, a polygonal template based on a wallpaper group is selected as the isohedral paving unit Ω: the wallpaper group type i is input, and the shape and boundary symmetry conditions of the isohedral paving unit are determined according to its associated symbol and paving edge type.

[0014] Furthermore, in step 2, by interactively adding points {p i}(different from polygon vertices), where Increase the freedom of boundary shape deformation and add new point sets by interactively moving {p i} to edit the curve shape; after determining the shape of the paving unit, the updated paving unit boundary is subjected to Delaunay triangulation to obtain the triangulated mesh M; since the paving boundary has symmetry, when {p i} moves, its symmetrical point will move synchronously; let p i The symmetric point p i The position of ′ is expressed as:

[0015] p′ i = beg(e′)+p i -beg(e),

[0016] Where e′ is the symmetric edge of e, beg(e) refers to the position of the starting vertex of edge e; therefore, when the user moves vertex p i When p i and p i The coordinates of ′ are described as:

[0017] p i =p i +v,p i ′=p i ′+Rv,

[0018] Where R is p i and p i ′ is the rotational symmetric matrix of the two symmetric edges to which it belongs, and the vector v represents the direction and distance of the movement.

[0019] Furthermore, in step 2, the paving unit boundary is subdivided according to the step size step, and the subdivided boundary curve is further locally edited according to user needs to generate a discrete curve interpolated at the original paving unit vertices and user-set conditions under symmetry constraints.

[0020] Furthermore, in step 3, a quasi-regular pattern function is defined inside the paving unit; based on the basic function model of the quasi-regular pattern, it is transformed and expanded by superposition, compounding, multiplication, and taking absolute value or square root method to enrich the types and quantity of function changes. The specific methods are:

[0021] a. Function superposition: Superposition and transformation of basic function models with elementary functions such as trigonometric functions, polynomials, logarithmic functions or power functions:

[0022]

[0023] b. Function combination: The basic function model is superimposed and transformed with the absolute value function, trigonometric function, power function, logarithmic function or exponential function. The result of the composite transformation with the trigonometric function is:

[0024]

[0025] c. Function multiplication: The basic function model is superimposed and transformed with trigonometric functions, logarithmic functions or exponential functions. The result of the multiplication with trigonometric functions is:

[0026]

[0027] By combining the above extension methods, a large number of function models can be obtained. At the same time, by changing the parameter q in the function model, more abundant function variation forms can be obtained. q The contour lines of (x, y) give a family of closed invariant curves of various shapes and sizes. By visualizing these families of invariant curves, we can obtain the digital patterns generated by the quasi-regular spot figures.

[0028] Furthermore, in step 4, in order to solve the joint problem of the quasi-regular pattern at the paving boundary and realize the symmetry of the digital pattern, the gradient domain fusion idea is used to solve the approximate quasi-regular pattern function under the boundary constraint condition; the quasi-regular pattern function on the paving unit before updating is assumed to be: f * =H q (x, y), the updated function is f. In order to make the reconstructed function close to the original quasi-regular pattern function, the energy functional is constructed to fit the value range and gradient domain v of the original function; on the other hand, the symmetry constraints and smoothness conditions under different boundaries must be guaranteed. Thus, the following energy functional can be established:

[0029]

[0030] Where α and β are given parameters greater than zero.

[0031] Furthermore, in step four, in order to solve the energy functional, the differential operator is discretized on the discrete domain where the paving unit is located, converted into a convex quadratic programming problem under equality constraints, and then converted into a system of linear equations for efficient solution, to obtain a continuous reconstructed quasi-regular pattern function on the boundary of the paving unit for generating digital patterns.

[0032] Furthermore, the quasi-regular pattern function model in the paving unit is q The height field is divided into n non-intersecting intervals Then, the connected area corresponding to each interval is assigned the same predefined color to generate a digital pattern within the paving unit; the paving unit is periodically extended to the canvas in a four-way continuous manner so that it covers the entire canvas, thereby generating the final digital pattern.

[0033] In a second aspect, the present invention also provides an interactive digital pattern generation device based on isohedral paving, 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 interactive digital pattern generation method based on isohedral paving.

[0034] In a third aspect, the present invention further provides a computer-readable storage medium having a program stored thereon, and when the program is executed by a processor, the method for generating an interactive digital pattern based on isohedral paving is implemented.

[0035] The beneficial effects of the present invention are:

[0036] (a) Improve controllability and creativity: By designing paving blocks with curved polygons that can express complex shapes, digital art graphics can be made more creative and personalized.

[0037] (b) Enriching graphic diversity: By introducing a quasi-regular pattern model to generate texture details with seamless boundaries, the diversity and expressiveness of digital art graphics are enhanced, making digital patterns more colorful.

[0038] (c) Solving the texture continuity problem: By optimizing the quasi-regular pattern function defined on the paving blocks, the continuity problem of the paving boundaries is solved, making the transition of digital patterns smoother and more natural.

[0039] (d) High quality and high efficiency: The generated paving blocks are of high quality, enriching the generation form. At the same time, the algorithm has high execution efficiency and provides parameters suitable for real-time interaction, providing users with a smooth and fast operation experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 The present invention is a flowchart of an interactive digital pattern generation method based on isohedral paving in one embodiment of the present invention.

[0042] Figure 2 The figure is a schematic diagram of the interior point neighborhood and boundary point neighborhood of an interactive digital pattern generation method based on isohedral paving in one embodiment of the present invention.

[0043] Figure 3 This is a result diagram for visualizing various steps of an interactive digital pattern generation method based on isohedral paving in one embodiment of the present invention.

[0044] Figure 4 This is a computer program user-side visualization result in one embodiment of the present invention.

[0045] Figure 5 This is an example effect of the digital pattern design for the textile field according to the present invention.

[0046] Figure 6 This is an example effect of the present invention for architectural interior mapping design.

[0047] Figure 7 It is a structural diagram of an interactive digital pattern generating device based on isohedral paving according to the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with specific examples. It should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0049] It should be noted that, in the claims and description of the present invention, relational terms such as first and second, etc., are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including 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, the elements defined by the sentence "comprise one" do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0050] Example

[0051] All documents mentioned in the present invention are cited as references in this application, just as each document is cited as reference individually. In addition, it should be understood that after reading the above teachings of the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the claims attached to this application.

[0052] Quasi-regular patterns have many application scenarios, such as the creation of digital artworks, textile pattern design, game map generation, texture design, and product pattern design, etc., which provide designers with rich and diverse textures and patterns, and enhance the visual appeal and uniqueness of the works. The present invention takes the generation of textile patterns in the textile design process as an example, and introduces the implementation process of an interactive textile pattern generation method based on isohedra paving. The method specifically includes: the user inputs the width and height Wx, Wy of the fabric in the textile pattern production, and selects the wallpaper group i of the isohedra paving block; the shape of the isohedra paving block is interactively edited by adding and deleting vertices on the paving block and moving the vertex position; the user inputs the number of iterations q of the quasi-regular model and the paving body meshing step step, and defines a quasi-regular function on the isohedra paving block; inputs the boundary symmetry constraint parameters α, β, and adjusts the constraint parameters according to user needs to eliminate the boundary break of the digital pattern in the image space; the quasi-regular pattern in the polygon is colored according to the divided area of ​​the height field of the quasi-regular pattern function; the quasi-regular pattern period is extended so that the newly generated quasi-regular pattern is covered with textiles.

[0053] Figure 1It is a flowchart of an interactive digital pattern generation method based on isohedra paving in one embodiment of the present invention. The method includes the following steps: step 101, selecting a polygonal template based on a wallpaper group as an isohedra paving unit, as a composition unit of a digital pattern; step 102, interactively editing the paving unit shape and triangulating it by adding and deleting vertices / moving vertices, etc.; step 103, defining a quasi-regular pattern function on the paving unit; step 104, constructing an energy equation and optimizing the quasi-regular pattern function according to constraints such as the symmetry of the paving unit boundary; step 105, coloring and generating a digital pattern based on the updated quasi-regular pattern function; step 106, extending the digital pattern in a four-way periodic manner to cover the entire canvas.

[0054] Specifically, in a Figure 3 In an embodiment, the present invention provides an interactive digital pattern generation method based on isohedral paving, comprising the following steps:

[0055] Step 1, select the wallpaper polygon template to determine the roughly isohedra paving unit: input wallpaper group type i, there are 17 wallpaper groups with different structures, recorded as: p1, p2, pm, pg, cm, pmm, pmg, pgg, c2mm, p4, p4m, p4g, p3, p3m1, p31m, p6, p6m, in the present invention, the user selects wallpaper group type p2 as the basic shape of the textile digital pattern space composition. According to its associated symbol and the type of paving edge, determine the isohedra paving unit shape and boundary symmetry conditions of the pattern.

[0056] Step 2: The user interactively edits the tiling unit by adding, deleting, moving vertices, etc. to achieve a "rough edit" of the shape. Specifically, by interactively adding points {p i},in Ω represents the internal area of ​​the paving block, which increases the degree of freedom of boundary shape deformation and adds a new point set {p i} to edit the curve shape. Since the paving boundary is symmetrical, when {p i When the} moves, its symmetrical point will move synchronously.

[0057] p i '=beg(e′)+p i -beg(e),

[0058] Where e′ is the symmetric side of e, beg(e) refers to the position of the starting vertex of side e, and beg(e′) refers to the position of the starting vertex of the corresponding side e′. i When p i and p′ i The coordinates can be described as:

[0059] p i =p i +v,p i '=p i '+Rv,

[0060] Where R is p i and p′ i The rotational symmetric matrix of the two symmetric edges belongs to it, and the vector v represents the direction and distance of movement of the vertex.

[0061] Subdivide the textile pattern paving unit boundary according to the step size step, and further perform local "fine editing" (optional) on the subdivided boundary curve according to user needs, such as generating a discrete curve interpolated at the original paving unit vertices and user-set conditions under symmetry constraints to meet the needs of curve shape refinement. After determining the shape of the paving unit, perform Delaunay triangulation on the updated paving unit boundary to obtain a triangulated mesh M=<T,V> , where T is the triangle face set of the mesh and V is the vertex set of the mesh.

[0062] Step 3: First, each pixel point (n x , n y ) is converted to the normalized space [x t ,y t ]×[x t +sπ,y t +sπ]:

[0063]

[0064] Where Wx and Wy represent the width and height of the canvas in the textile pattern production, 500×500, (x t ,y t ) is the translation amount, x t =0,y t = 0, s is the scale parameter used to control the normalized space. The user inputs the resonance number q = 4 and maps it to the Hamiltonian H q The determined q-order quasi-symmetric random network is smoothed and the Hamiltonian obtained is H q (0) . Noh Mask H q (0) The contour lines of give the closed invariant curve families of various shapes and sizes of the system. By visualizing these invariant curve families, a quasi-regular pattern can be obtained. The basic model of the quasi-regular pattern is as follows:

[0065]

[0066] Where q represents the resonance number, (x,y)∈R2 is the normalized coordinate value.

[0067] In order to obtain more models, the present invention expands the basic model of the quasi-regular pattern and expands and transforms the basic model of the quasi-regular pattern by superposition, compounding, multiplication, taking absolute value or square root based on the existing functions, enriching the types and quantity of functions, wherein the specific methods are:

[0068] a. Function superposition: The basic model can be superimposed and transformed with elementary functions such as trigonometric functions, polynomials, logarithmic functions or power functions:

[0069]

[0070] b. Function compounding: the basic model can be superimposed and transformed with absolute value function, trigonometric function, power function, logarithmic function or exponential function. The result of compound transformation with trigonometric function is:

[0071]

[0072] c. Function multiplication: The basic model can be transformed by superimposing trigonometric functions, logarithmic functions or exponential functions. The result of multiplication with trigonometric functions is:

[0073]

[0074] Step 4: For the generated isohedral paving block, Ω represents the internal area of ​​the paving block. After partial paving, its boundary area can be obtained. f * is a known quasi-regular pattern function defined in the Ω region, v is f * The vector field f is defined in Unknown scalar function of the region. First, the seams between the paved boundaries of the quasi-regular pattern need to be eliminated, which means that (1) the function value of any point p on the S edge needs to be the same as the function value of the corresponding point p′ after rotating half a circle around its center; (2) the function value of a point p on the J edge needs to be the same as the function value of the corresponding point p′ on another J edge, which can be obtained as follows:

[0075]

[0076] Then, the idea of ​​gradient domain fusion is used to solve the seam problem of the quasi-regular pattern at the paving boundary, and the gradient of the function f at any point on the edge of the figure is equal to the original height field f * The gradient v of is as consistent as possible, which can be achieved by minimizing the following objective function:

[0077]

[0078] In order to make the function value change smoothly at the joints of paving blocks, the constraint function f is The gradient at is as small as possible, which can be achieved by minimizing the following objective function:

[0079]

[0080] Finally, considering that the desired f should be consistent with the original quasi-regular pattern function f * As similar as possible to maintain the texture structure of the original pattern of the quasi-regular pattern:

[0081] ∫ Ω ||ff * || 2 dΩ.

[0082] Combining the above formulas, the following energy functional can be established:

[0083]

[0084] α and β are user parameters used to balance the weights of various energies and are both set to 1 by default.

[0085] Furthermore, in step 4, the variational problem is discretized, and arbitrary polygonal paving units are considered to triangulate their coverage area; since the internal triangles T of the mesh M cover the definition domain Ω, that is, Then the variational problem can be discretized:

[0086]

[0087] Where A is the total area of ​​the paved unit, L is the total length of the paved unit boundary, and L i is the Voronoi line segment of the boundary vertex i on the boundary line, f * is a discrete quasi-regular pattern function defined on the grid, that is, a piecewise linear function f * Approximate the original quasi-regular pattern function, where and v are constants. Since the last part of the formula involves numerical integration, the calculation is relatively complicated. In order to simplify the calculation, the present invention adopts the following method to approximate:

[0088]

[0089] Among them, V i is the area of ​​the Voronoi region at vertex i. Therefore, the total energy function formula can be discretized as:

[0090]

[0091] Among them, A t is the area of ​​the tth triangle, L tis the length of the Voronoi line segment of the boundary vertex i on the boundary line; f i and f i * The vertex p i The above function f and function f * The function value of the boundary vertex i can be obtained by interpolating the gradient of the two semi-neighborhood triangles of the vertex (one is the internal triangle of the paving unit, and the other is the triangle set outside the paving unit obtained by local paving compensation). That is, the neighborhood triangle j of vertex i consists of two parts, that is, j∈N + (i) or j∈N - (i) , where j∈N + (i) is the vertex index adjacent to vertex i, N - (i) is the vertex index adjacent to the vertex i symmetric point i′, such as Figure 2 As shown;

[0092] Furthermore, in step 4, the differential operator of the energy formula is further discretized and its minimum value is sought, that is, its gradient is set to 0, and the following is obtained about f = [f1, f2, ... f n ] is the linear equation system:

[0093]

[0094] Among them, A3 is the identity matrix, α' and β' are the first term A1 T The weights recalculated after A1 normalization,

[0095]

[0096] The element values ​​in A1 and A2 are cosθ ij +cosθ ji is the cotangent Laplace weight obtained by discretizing the differential operator, θ ij With θ ji Corresponding to half of the grid<i,j> With half<j,i> The angle of the diagonal. At the same time, the following linear constraints can be obtained from the constraints:

[0097]

[0098] Where i′ is the index of the symmetric point of vertex i, and B represents the symmetric point constraint matrix. The Lagrange multiplier method can be used to solve the above linear equations with linear constraints and obtain a discrete quasi-regular pattern function f with boundary symmetry properties defined on the grid.

[0099] Step 5: Color the quasi-regular pattern in the polygon according to the divided area of ​​the height field of the quasi-regular pattern function f, as shown in Figure 3 As shown, first, according to the pixel point (n x ,n y ) calculates the triangle to which it belongs and its barycentric coordinates (u, v, w), and according to the barycentric coordinates (u, v, w) and the scalar value (f u ,f v ,f w ) interpolation to get pixel point (h x ,n y ) at f n , H in the quasi-regular pattern model q The height field f n Divide into several non-intersecting intervals The connected regions corresponding to each interval are then assigned the same predefined color, thereby generating a color image of the textile pattern tiling unit.

[0100] Step six, periodically extending the paving unit onto the textile pattern canvas in a four-way continuous manner so that it covers the entire canvas, thereby generating the final textile digital pattern.

[0101] The present invention also provides a computer program product, including a computer program, such as Figure 4 As shown, when the computer program is executed by a processor, the interactive digital pattern generation method based on isohedral paving is implemented.

[0102] The present invention can generate a large number of digital patterns after the user adjusts some parameters, which can not only be applied to pattern design in the textile field, such as Figure 5 As shown, it can also be applied to material paving for interior architectural effects and material paving for game modeling, such as Figure 6 shown.

[0103] Corresponding to the aforementioned embodiment of an interactive digital pattern generation method based on isohedral paving, the present invention also provides an embodiment of an interactive digital pattern generation device based on isohedral paving.

[0104] See also Figure 7 An embodiment of the present invention provides an interactive digital pattern generation device based on isohedral paving, including a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it is used to implement an interactive digital pattern generation method based on isohedral paving in the above embodiment.

[0105] An embodiment of an interactive digital pattern generation device based on isohedral paving 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 internal memory for execution. From the hardware level, if Figure 7 As shown, it is a hardware structure diagram of any device with data processing capability for an interactive digital pattern generation device based on isohedra paving provided by the present invention, except Figure 7 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 embodiments 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.

[0106] 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.

[0107] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

[0108] 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, an interactive digital pattern generation method based on isohedral paving in the above embodiment is implemented.

[0109] The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, 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 capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0110] The present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the interactive digital pattern generation method based on isohedral paving.

[0111] It should be noted that in the claims and description of this patent, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including 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 sentence "comprises one" does not exclude the presence of other identical elements in the process, method, article or device including the element. Although the present invention has been illustrated and described with reference to certain preferred embodiments of the present invention, it should be understood by those skilled in the art that various changes can be made to it in form and detail without departing from the spirit and scope of the present invention.

Claims

1. An interactive digital pattern generation method based on isohedral paving, characterized in that: The following steps are involved: Step 1: Select a polygonal template based on wallpaper group as an isohedral paving unit and as the basic shape of the digital pattern space composition; Step 2: interactively edit the paving unit shape by adding and deleting vertices / moving vertices and triangulate it; Step 3, defining a quasi-regular pattern function on the paving unit; Step 4: construct the energy equation and optimize the quasi-regular pattern function according to the symmetry constraints and smoothness conditions of the paving unit boundary; Step 5, coloring and generating digital patterns based on the updated quasi-regular pattern function; Step six: Extend the digital pattern in a four-way periodic manner to fill the entire canvas.

2. The interactive digital pattern generation method based on isohedral paving according to claim 1, characterized in that: In step 1, a polygonal template based on a wallpaper group is selected as the isohedral paving unit Ω: the wallpaper group type i is input, and the shape and boundary symmetry conditions of the isohedral paving unit are determined according to its associated symbol and paving edge type.

3. The interactive digital pattern generation method based on isohedral paving according to claim 1, characterized in that: In step 2, we interactively add points {p i }(different from polygon vertices), where Increase the freedom of boundary shape deformation and add new point sets by interactively moving {p i } to edit the curve shape; after determining the shape of the paving unit, the updated paving unit boundary is subjected to Delaunay triangulation to obtain the triangulated mesh M; since the paving boundary has symmetry, when {p i } moves, its symmetrical point will move synchronously; let p i The position of the symmetric point p′i is expressed as: p′ i =beg(e′)+p i -beg(e), Where e′ is the symmetric edge of e, beg(e) refers to the position of the starting vertex of edge e; therefore, when the user moves vertex p i When p i and p′ i The coordinates are described as: p i =p i +v,p i ′=p i ′+Rv, Where R is p i and p′ i The rotational symmetric matrix of the two symmetric edges belongs to it, and the vector v represents the direction and distance of movement of the vertex.

4. The interactive digital pattern generation method based on isohedral paving according to claim 3, characterized in that: In step 2, the paving unit boundary is subdivided according to the step size step, and the subdivided boundary curve is further locally edited according to user needs to generate a discrete curve interpolated at the original paving unit vertices and user-set conditions under symmetry constraints.

5. The interactive digital pattern generation method based on isohedral paving according to claim 1, characterized in that: In step 3, a quasi-regular pattern function is defined inside the paving unit; based on the basic function model of the quasi-regular pattern, it is transformed and expanded by superposition, compounding, multiplication, and taking absolute value or square root method to enrich the types and quantity of function changes. The specific methods are: a. Function superposition: Superposition and transformation of basic function models with elementary functions such as trigonometric functions, polynomials, logarithmic functions or power functions: b. Function combination: The basic function model is superimposed and transformed with the absolute value function, trigonometric function, power function, logarithmic function or exponential function. The result of the composite transformation with the trigonometric function is: c. Function multiplication: The basic function model is superimposed and transformed with trigonometric functions, logarithmic functions or exponential functions. The result of the multiplication with trigonometric functions is: By combining the above extension methods, a large number of function models can be obtained. At the same time, by changing the parameter q in the function model, more abundant function variation forms can be obtained. q The contour lines of (x,y) give a family of closed invariant curves of various shapes and sizes. By visualizing these families of invariant curves, we can obtain the digital patterns generated by the quasi-regular spot figures.

6. The interactive digital pattern generation method based on isohedral paving according to claim 1, characterized in that: In step 4, in order to solve the joint problem of the quasi-regular pattern at the paving boundary and realize the symmetry of the digital pattern, the gradient domain fusion idea is used to solve the approximate quasi-regular pattern function under the boundary constraint condition; the quasi-regular pattern function on the paving unit before updating is assumed to be: f * =H q (x, y), the updated function is f. In order to make the reconstructed function close to the original quasi-regular pattern function, the energy functional is constructed to fit the value range and gradient domain v of the original function; on the other hand, the symmetry constraints and smoothness conditions under different boundaries must be guaranteed. Thus, the following energy functional can be established: Where α and β are given parameters greater than zero.

7. The interactive digital pattern generation method based on isohedral paving according to claim 6, characterized in that: In step 4, in order to solve the energy functional, the differential operator is discretized on the discrete domain where the paving unit is located, and it is converted into a convex quadratic programming problem under equality constraints, and then converted into a system of linear equations for efficient solution to obtain a new quasi-regular pattern function with continuous paving unit boundaries for generating digital patterns.

8. The interactive digital pattern generation method based on isohedral paving according to claim 1, characterized in that: The H in the quasi-regular pattern function model within the paving unit q The height field is divided into n non-intersecting intervals Then, the connected area corresponding to each interval is assigned the same predefined color to generate a digital pattern within the paving unit; the paving unit is periodically extended to the canvas in a four-way continuous manner so that it covers the entire canvas, thereby generating the final digital pattern.

9. An interactive digital pattern generation device based on isohedral paving, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, an interactive digital pattern generation method based on isohedral paving 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, an interactive digital pattern generation method based on isohedral paving as described in any one of claims 1 to 8 is implemented.

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