Method for obtaining patterns of spatial three-dimensional configurations with genus 1

Abstract

The present invention provides a method for acquiring a pattern of a spatial solid configuration with a genus of 1, comprising triangulating the surface of the solid configuration to obtain a plurality of triangular mesh units; acquiring tunnel circles, handle circles, and four corresponding boundaries on the surface of the triangulated solid configuration; using a set of harmonic functions f and g corresponding to each edge as boundary constraints, acquiring the distribution of harmonic functions corresponding to each vertex of the triangular mesh unit within a square region according to the harmonic energy function; re-meshing the square region on a plane into a square mesh, wherein a grid point of each square mesh is located within a triangular mesh unit; and calculating the spatial coordinate values ​​of the grid points of the corresponding square mesh based on the spatial coordinate values ​​of the triangular mesh points. The method of the present invention significantly reduces the amount of computation and can ensure high robustness and strong adaptability with a low amount of computation.

Description

Technical Field

[0001] The present invention relates to the technical field of curved surface appearance design, and in particular to a method for obtaining a pattern of a spatial three-dimensional configuration with a genus of 1. Background Art

[0002] Texture, also known as grain, has a similar meaning to "texture" in design. It refers to the structure of an object's surface, such as crisscrossing, uneven, rough, and smooth finishes. As a fundamental form of visual art, texture, like color and line, has the ability to create form and express emotion. Texture design plays a crucial role in product design and is gaining increasing attention from businesses.

[0003] Surface texture / stripe design is an essential component of surface design. Surface modeling and surface stripe design have always been challenging in the industry. Previous design methods required the application of information from a background space, specifically three-dimensional Euclidean space, resulting in large computational data volumes. Furthermore, designing patterns on curved surfaces is challenging, primarily because the design of spatial curves has always been a challenge in geometric modeling. Furthermore, pattern design on curved surfaces involves the concept of conformal geometry, requiring that the local shape be consistent with the shape over the parametric domain. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art.

[0005] To this end, the present invention provides a method for acquiring a pattern of a spatial three-dimensional configuration with a genus of 1.

[0006] The technical solutions of the present invention are as follows:

[0007] According to one aspect, a method for acquiring a pattern of a spatial configuration with a genus of 1 is provided, the method comprising:

[0008] Import solid configurations with genus 1;

[0009] Dividing the surface of the solid configuration into triangles to obtain a closed surface composed of a plurality of triangular mesh units;

[0010] Obtaining tunnel circles and handle circles on the surface of the triangulated solid configuration;

[0011] Cutting the solid configuration surface along the tunnel ring and the handle ring to obtain two boundaries corresponding to the tunnel ring and two boundaries corresponding to the handle ring;

[0012] Set harmonic functions on the four obtained boundaries respectively, where each edge corresponds to a set of harmonic functions f and g;

[0013] Design harmonic energy functions;

[0014] Using a set of harmonic functions f and g corresponding to each edge as boundary constraints, the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area is obtained according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane;

[0015] Re-meshing the square area on the plane into a square grid, wherein a grid point of each square grid is located within a triangular grid unit;

[0016] Calculate the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid;

[0017] According to the coordinates of the grid points of the square grid, a square grid pattern of a three-dimensional configuration with a defect of 1 is obtained.

[0018] Furthermore, the harmonic energy functions E(f) and E(g) are designed according to the harmonic function by the following formula:

[0019]

[0020]

[0021] Among them, M represents the closed surface of the configuration, f, g represent harmonic functions, and any vertex of any triangle corresponds to a set of harmonic functions f, g, v i Represents a vertex of a triangle; j = i n ,n=1,2,3,4,......,v j Represents vertex v i The vertices of the surrounding triangles connected to this vertex; f(v i ) represents the vertex v i The harmonic function value of f(v j ) represents the vertex v j The harmonic function value of g(v i ) represents the vertex v i The harmonic function value of g(v j ) represents the vertex v j The harmonic function value of w ij is the weight factor of each triangle’s side length, Vertex v i With vertex v j The line connecting the two triangles corresponds to the vertex angles of the two triangles.

[0022] Furthermore, a set of harmonic functions f and g corresponding to each edge is used as a boundary constraint, and the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area is obtained according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane, including:

[0023] According to the harmonic energy function, by minimizing the harmonic energy value, the following equation is obtained:

[0024]

[0025] With each edge corresponding to a set of harmonic functions f and g as boundary constraints, the distribution of the harmonic functions inside the square area is obtained by iteratively solving the equation.

[0026] Furthermore, the step of calculating the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid includes:

[0027] According to the harmonic function values ​​corresponding to the three vertices of the triangle, a set of harmonic function values ​​corresponding to the grid points of the square grid is obtained through the barycentric coordinate relationship;

[0028] According to the three-dimensional coordinates (x, y, z) corresponding to the three vertices of the triangle, the three-dimensional coordinate values ​​of the grid points corresponding to the square grid are obtained through the barycentric coordinate relationship;

[0029] According to a set of harmonic function values ​​and three-dimensional coordinate values ​​of the grid points of the square grid, a square grid pattern with a configuration of genus 1 is obtained.

[0030] Furthermore, a set of harmonic function values ​​corresponding to the three vertices of the triangle is obtained through the following formula using the barycentric coordinate relationship to obtain the corresponding grid points of the square grid:

[0031] p=αp1+βp2+γp3

[0032] Where p represents the harmonic functions f and g corresponding to the square grid point, α, β, and γ are the coordinates of the center of gravity of the grid point of the square grid, satisfying α+β+γ=1, and p1, p2, and p3 are the harmonic function values ​​f and g corresponding to the three vertices of the triangle where a grid point of the square grid is located.

[0033] Furthermore, the three-dimensional coordinates (x, y, z) corresponding to the three vertices of the triangle are obtained by the following formula and the barycentric coordinate relationship to obtain the three-dimensional coordinate values ​​of the grid points of the corresponding square grid:

[0034] p′=αp1′+βp′2+γp3′

[0035] Where p′ represents the three-dimensional spatial coordinate (x, y, z) corresponding to the square grid point, α, β, γ are the centroid coordinates of the grid point of the square grid, satisfying α+β+γ=1, and p1′, p′2, p3′ are the three-dimensional spatial coordinates corresponding to the three vertices of the triangle where a grid point of the square grid is located.

[0036] Furthermore, the method further includes: coloring the square grid pattern to obtain a checkerboard pattern of a spatial three-dimensional configuration with a genus of 1.

[0037] According to another aspect, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned pattern acquisition method when executing the computer program.

[0038] By applying the above technical solution, tunnel rings and handle rings and four corresponding boundaries cut along them are obtained on the surface of the solid configuration that has been triangulated, and harmonic functions are set on the boundaries. A harmonic energy function is designed and the harmonic energy function is solved based on the designed boundaries to map the triangulated diagram on the surface of the solid configuration to a two-dimensional plane; finally, the square area on the plane is re-divided into a square grid, and the spatial coordinate values ​​of the grid points of the square grid are calculated; thereby, a high degree of automation of the generation of high-quality curve families and stripe patterns can be achieved. By using the method of the present invention, the amount of calculation is greatly reduced, and it can be ensured that the method has high robustness and strong adaptability with a small amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings are included to provide a further understanding of the embodiments of the present invention, constitute a part of the specification, illustrate the embodiments of the present invention, and together with the description, explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0040] Figure 1 A triangular mesh distribution diagram of a solid configuration surface provided by an embodiment of the present invention;

[0041] Figure 2 A schematic diagram of the positional relationship between the tunnel ring and the shank ring in a configuration with a genus of 1 provided by an embodiment of the present invention;

[0042] Figure 3 A schematic diagram of a process for cutting along a tunnel ring and a ring handle ring provided in an embodiment of the present invention;

[0043] Figure 4A schematic diagram of a topological quadrilateral obtained by cutting a closed surface with genus 1 along the tunnel loop and the handle loop, provided in an embodiment of the present invention;

[0044] Figure 5-8 The distribution law of the harmonic functions f and g of the four boundaries provided in the embodiment of the present invention;

[0045] Figure 9 The embodiment of the present invention provides Angle diagram;

[0046] Figure 10 A partial schematic diagram of a triangular mesh of a solid configuration surface provided by an embodiment of the present invention;

[0047] Figure 11 A distribution diagram of triangular meshes within a square on a plane obtained by applying a harmonic mapping method to triangular meshes on a solid configuration surface provided by an embodiment of the present invention;

[0048] Figure 12 A distribution diagram of small squares within a square on a plane provided by an embodiment of the present invention;

[0049] Figure 13 The embodiment of the present invention provides a checkerboard stripe pattern on the surface of a solid obtained based on a small square distribution pattern on a plane. DETAILED DESCRIPTION

[0050] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0051] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0052] Unless otherwise specifically stated, the relative arrangement of the parts and steps, the numerical expressions and the numerical values ​​set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The techniques, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the techniques, methods and equipment should be considered as part of the authorization specification. In all examples shown and discussed here, any specific values ​​should be interpreted as being merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following figures, and therefore, once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0053] like Figure 1-13 As shown, in one embodiment of the present invention, a method for acquiring a pattern of a spatial three-dimensional configuration with a genus of 1 is provided, the method comprising:

[0054] S101, importing a solid configuration with a genus of 1;

[0055] S102, triangulating the solid configuration surface (i.e., the closed curved surface) to obtain a closed curved surface composed of a plurality of triangular mesh units;

[0056] S103, obtaining a tunnel ring and a handle ring on the surface of the solid configuration after triangulation;

[0057] S104, cutting the solid configuration surface along the tunnel ring and the handle ring to obtain two boundaries corresponding to the tunnel ring and two boundaries corresponding to the handle ring;

[0058] S105, setting harmonic functions on the four obtained boundaries respectively, wherein each edge corresponds to a set of harmonic functions f and g;

[0059] S106. Design a harmonic energy function;

[0060] S107, using a set of harmonic functions f and g corresponding to each edge as boundary constraints, obtaining the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane;

[0061] S108, re-dividing the square area on the plane into square grids, wherein a grid point of each square grid will (must) be located in a triangular grid unit;

[0062] S100, calculating the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid;

[0063] S110 , obtaining a square grid pattern of a three-dimensional configuration with a defect of 1 according to the coordinates of the grid points of the square grid.

[0064] In the embodiment of the present invention, the triangular distribution of the surface of the solid configuration is constructed (such as Figure 1 This is a conventional technical means in this field and will not be described in detail here.

[0065] In the embodiment of the present invention, the schematic diagram of the tunnel ring and the ring handle ring is shown in FIG. Figure 2 ,in, Figure 2 In the figure, a is the positive boundary obtained by cutting along the tunnel ring, and b is the positive boundary obtained by cutting along the ring handle ring. Figure 3 In the figure, a is the positive boundary obtained by cutting along the tunnel circle, and a -1 is the reverse boundary obtained by cutting along the tunnel ring, b is the forward boundary obtained by cutting along the ring handle ring, and b -1 is the reverse boundary obtained by cutting along the handle circle, and A is the intersection of the tunnel circle and the handle circle. For example, after cutting the topological tire into a quadrilateral, point A will become four points, such as Figure 4 shown.

[0066] In the embodiment of the present invention, the distribution rules of the harmonic functions can be set on the four boundaries according to actual needs. Figure 5-8 The harmonic function values ​​of the four boundaries set in this embodiment are shown.

[0067] It can be seen that the embodiment of the present invention obtains the tunnel ring and the ring handle ring and the four corresponding boundaries cut along them on the surface of the solid configuration after triangulation, sets a harmonic function on the boundary, designs a harmonic energy function and solves the harmonic energy function based on the designed boundary to map the triangulation diagram on the surface of the solid configuration to a two-dimensional plane; finally, the square area on the plane is re-divided into a square grid, and the spatial coordinate values ​​of the grid points of the square grid are calculated; thereby, a high degree of automation of the generation of high-quality curve families and stripe patterns can be achieved. By adopting the method of the present invention, the amount of calculation is greatly reduced, and it can be guaranteed that it has high robustness and strong adaptability with a small amount of calculation.

[0068] In the above embodiment, if Figure 9-10 As shown, the harmonic energy function E(f), E(g) can be designed according to the harmonic function by the following formula:

[0069]

[0070]

[0071] Among them, M represents the closed surface of the configuration, f and g represent harmonic functions (two harmonic functions), and any vertex of any triangle corresponds to a set of harmonic functions f and g (that is, two harmonic functions), v i Represents a vertex of a triangle; j = i n ,n=1,2,3,4,......,v j Represents vertex v i The vertices of the surrounding triangles connected to this vertex; f(v i ) represents the vertex v i The harmonic function value of f(v j ) represents the vertex v j The harmonic function value of g(v i ) represents the vertex v i The harmonic function value of g(v j ) represents the vertex v j The harmonic function value of w ij is the weight factor of each triangle’s side length, Vertex v i With vertex v j The vertex angles of the two triangles corresponding to the line connecting them are as follows: Figure 9 As shown, when j=i1, then Vertex v i With vertex The vertex angles of the two triangles corresponding to the line connecting them are the same when j = other values.

[0072] In the above embodiment, a set of harmonic functions f and g corresponding to each edge is used as a boundary constraint, and the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area is obtained according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane, including:

[0073] According to the harmonic energy function, by minimizing the harmonic energy value, the following equation is obtained:

[0074]

[0075] With each edge corresponding to a set of harmonic functions f and g as boundary constraints, the distribution of the harmonic functions inside the square area is obtained by iteratively solving the equation.

[0076] That is, the principle of the iterative method of harmonic mapping in real time of the present invention is: given the harmonic function value at the boundary, the harmonic function of a point in the internal area is jointly determined by the harmonic functions of multiple points surrounding the point. Figures 5 to 8To set the harmonic function values ​​of each point on the four boundaries, for the harmonic function values ​​of each point in the internal area, the initial values ​​of the harmonic functions f and g are given, and through iterative calculation, the final result after convergence can be given, and then the distribution of the harmonic function inside the square area can be obtained, thus obtaining Figure 11 , so that we can map the triangulation diagram on the surface of the solid configuration to the two-dimensional plane.

[0077] In the above embodiment, the step of calculating the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid includes:

[0078] According to the harmonic function values ​​corresponding to the three vertices of the triangle, a set of harmonic function values ​​corresponding to the grid points of the square grid is obtained through the barycentric coordinate relationship;

[0079] According to the three-dimensional coordinates corresponding to the three vertices of the triangle, the three-dimensional coordinate values ​​of the grid points corresponding to the square grid are obtained through the barycentric coordinate relationship;

[0080] According to a set of harmonic function values ​​and three-dimensional coordinate values ​​of the grid points of the square grid, a square grid pattern with a configuration of genus 1 is obtained.

[0081] In the embodiment of the present invention, a set of harmonic function values ​​corresponding to the grid points of the square grid is obtained by using the following formula based on the harmonic function values ​​corresponding to the three vertices of the triangle and the barycentric coordinate relationship:

[0082] p=αp1+βp2+γp3

[0083] Where p represents the harmonic functions f and g corresponding to the square grid point, α, β, and γ are the coordinates of the center of gravity of the grid point of the square grid, satisfying α+β+γ=1, and p1, p2, and p3 are the harmonic function values ​​f and g corresponding to the three vertices of the triangle where a grid point of the square grid is located.

[0084] The following formula is used to obtain the spatial three-dimensional coordinates (x, y, z) of the three vertices of the triangle and the barycentric coordinate relationship of the grid points of the corresponding square grid:

[0085] p′=αp1′+βp′2+γp3′

[0086] Where p′ represents the three-dimensional spatial coordinate (x, y, z) corresponding to the square grid point, α, β, γ are the centroid coordinates of the grid point of the square grid, satisfying α+β+γ=1, and p1′, p′2, p3′ are the three-dimensional spatial coordinates corresponding to the three vertices of the triangle where a grid point of the square grid is located.

[0087] According to one embodiment of the present invention, Figure 12-13 As shown, the method further includes: coloring the square grid pattern to obtain a checkerboard pattern with a genus of 1.

[0088] In addition, the present invention also provides an application of the pattern obtained in the above embodiment in the physical modeling decoration and gaming industries.

[0089] According to another embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned pattern acquisition method when executing the computer program.

[0090] It can be seen that the present invention provides a method for obtaining a pattern on a configuration with a defect of 1. By reasonably selecting parameters, a checkerboard pattern on a solid configuration can be obtained. By changing the parameter distribution law on the parameter domain, a series of checkerboard or other style schemes on the closed surface of the solid configuration can be obtained. In this way, the direction constraint of the tangent vector at the endpoint of the curve and the shape change constraint of the curve can be met, thereby introducing the idea of ​​computational conformal geometry into the process of surface generation. This method can better complete the design of adaptive and compatible stripes or patterns on closed surfaces under general circumstances. The pattern completed by this method can ensure the consistency and matching of the pattern everywhere. Pattern generation under complex configurations is achieved, and the feasibility of the design method is preliminarily demonstrated, laying the foundation for the parametric research of this design method.

[0091] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship of a device or feature to other devices or features as shown in the figures. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figures. For example, if the device in the drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0092] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0093] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for obtaining a pattern of a spatial three-dimensional configuration with a genus of 1, characterized in that: The method comprises: Import solid configurations with genus 1; Dividing the surface of the solid configuration into triangles to obtain a closed surface composed of a plurality of triangular mesh units; Obtaining tunnel circles and handle circles on the surface of the triangulated solid configuration; Cutting the solid configuration surface along the tunnel ring and the handle ring to obtain two boundaries corresponding to the tunnel ring and two boundaries corresponding to the handle ring; Set harmonic functions on the four obtained boundaries respectively, where each edge corresponds to a set of harmonic functions f and g; Design harmonic energy functions; Using a set of harmonic functions f and g corresponding to each edge as boundary constraints, the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area is obtained according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane; Re-meshing the square area on the plane into a square grid, wherein a grid point of each square grid is located within a triangular grid unit; Calculate the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid; According to the coordinates of the grid points of the square grid, a square grid pattern of a three-dimensional configuration with a defect of 1 is obtained.

2. The method for obtaining a pattern of a spatial three-dimensional configuration with a genus of 1 according to claim 1, characterized in that: The harmonic energy functions E(f) and E(g) are designed according to the harmonic function by the following formula: Among them, M represents the closed surface of the configuration, f, g represent harmonic functions, and any vertex of any triangle corresponds to a set of harmonic functions f, g, v i Represents a vertex of a triangle; j = i n ,n=1,2,3,4,......,v j Represents vertex v i The vertices of the surrounding triangles connected to this vertex; f(v i ) represents the vertex v i The harmonic function value of f(v j ) represents the vertex v j The harmonic function value of g(v i ) represents the vertex v i The harmonic function value of g(v j ) represents the vertex v j The harmonic function value of w ij is the weight factor of each triangle’s side length, Vertex v i With vertex v j The line connecting the two triangles corresponds to the vertex angles of the two triangles.

3. The method for obtaining a pattern of a spatial three-dimensional configuration with a genus of 1 according to claim 2, characterized in that: A set of harmonic functions f and g corresponding to each edge is used as a boundary constraint, and the distribution of the harmonic functions corresponding to each vertex of the triangular mesh unit within the square area is obtained according to the harmonic energy function to map the triangulation graph on the surface of the solid configuration onto a two-dimensional plane, including: According to the harmonic energy function, by minimizing the harmonic energy value, the following equation is obtained: With each edge corresponding to a set of harmonic functions f and g as boundary constraints, the distribution of the harmonic functions inside the square area is obtained by iteratively solving the equation.

4. The method for acquiring a pattern of a spatial three-dimensional configuration with a genus of 1 according to any one of claims 1 to 3, characterized in that: The step of calculating the spatial coordinate values ​​of the grid points of the square grid surrounded by the triangle according to the spatial coordinate values ​​of the three vertices of the triangle surrounding a grid point of the square grid comprises: According to the harmonic function values ​​corresponding to the three vertices of the triangle, a set of harmonic function values ​​corresponding to the grid points of the square grid is obtained through the barycentric coordinate relationship; According to the three-dimensional coordinates (x, y, z) corresponding to the three vertices of the triangle, the three-dimensional coordinate values ​​of the grid points corresponding to the square grid are obtained through the barycentric coordinate relationship; According to a set of harmonic function values ​​and three-dimensional spatial coordinate values ​​of the grid points of the square grid, a square grid pattern of a spatial solid configuration with a defect of 1 is obtained.

5. The method for obtaining a pattern of a three-dimensional configuration with a genus of 1 according to claim 4, characterized in that: The following formula is used to obtain a set of harmonic function values ​​corresponding to the three vertices of the triangle and the barycentric coordinate relationship of the grid points of the corresponding square grid: p=αp1+βp2+γp3 Where p represents the harmonic functions f and g corresponding to the square grid point, α, β, and γ are the coordinates of the center of gravity of the grid point of the square grid, satisfying α+β+γ=1, and p1, p2, and p3 are the harmonic function values ​​f and g corresponding to the three vertices of the triangle where a grid point of the square grid is located.

6. The method for obtaining a pattern of a spatial configuration with a genus of 1 according to claim 4, characterized in that: The following formula is used to obtain the spatial three-dimensional coordinates (x, y, z) of the three vertices of the triangle and the barycentric coordinate relationship of the grid points of the corresponding square grid: p′=αp1′+βp′2+γp3′ Where p′ represents the three-dimensional spatial coordinate (x, y, z) corresponding to the square grid point, α, β, γ are the centroid coordinates of the grid point of the square grid, satisfying α+β+γ=1, and p1′, p′2, p3′ are the three-dimensional spatial coordinates corresponding to the three vertices of the triangle where a grid point of the square grid is located.

7. The method for obtaining a pattern of a spatial three-dimensional configuration with a genus of 1 according to claim 1, characterized in that: The method further includes: coloring the square grid pattern to obtain a checkerboard pattern with a spatial three-dimensional configuration of genus 1.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the pattern acquisition method according to any one of claims 1 to 7 when executing the computer program.

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