Method for generating cup model capable of manufacturing three-dimensional Chinese characters based on energy driving

Abstract

The invention relates to the field of additive manufacturing, and particularly discloses a method for generating a cup model capable of manufacturing three-dimensional Chinese characters based on energy driving. According to the method, a smooth time sequence evolution path from a multi-contour initial region to a single target contour is constructed, a contour evolution process is described by adopting a level set function, and an energy functional including a curve length regularization item, an adaptive expansion item and a shape prior item is established; by introducing a dynamic coupling control mechanism based on a region area difference, a shape error and a boundary length, adaptive adjustment of an expansion coefficient is realized; a level set evolution equation is obtained through variational derivation, and after numerical discrete solution, a two-dimensional evolution sequence is subjected to additive superposition along a time axis to form a three-dimensional volume field; and finally, through contour surface extraction and shell thickness processing, a 3D printing three-dimensional Chinese character cup model which is complete in structure and uniform in wall thickness is generated.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of additive manufacturing, and in particular to a method for generating a manufacturable three-dimensional Chinese character cup model based on energy driving. BACKGROUND

[0002] In recent years, three-dimensional modeling technology has become the core driving force for the digital design and intelligent manufacturing of cultural and creative products. Especially in the development of cultural and creative products with Chinese characters as design elements (such as customized "Chinese character cups"), the technology not only needs to convert two-dimensional stroke outlines into three-dimensional geometric models, but also requires the model to faithfully restore the cultural charm and artistic beauty of Chinese characters in form, and to have sufficient mechanical rationality and additive manufacturing feasibility in structure. This process involves complex mapping from planar vector paths to three-dimensional solid models, and the technical key lies in how to realize the organic integration of multi-stroke outlines under complex structures (nesting, coupling and overlapping), and generate a manufacturable three-dimensional model with complete structure, smooth surface and uniform wall thickness.

[0003] Currently, one of the mainstream solutions is to adopt a technical path based on geometric optimization and variational modeling. This method defines a differentiable energy functional containing smoothness constraints and data fitting terms, and iteratively solves in the latent space or the output geometry through variational methods or numerical optimization techniques to find a solution that not only satisfies all constraint conditions, but also highly matches the model's learned data distribution. The iterative process is the process of driving the initial outline to evolve towards the target shape, and the evolution result meets the smoothness requirement. However, when dealing with complex structures such as Chinese characters that naturally contain nested, coupled or overlapping stroke outlines, this method has significant limitations. In addition, since its evolution process highly depends on the setting of the initial outline and parameter adjustment, and the energy function lacks coordinated control of the topological relationship between multiple outlines and global scale evolution, the model is prone to kinetic incoordination during the evolution process: the whole model rapidly expands in the early stage, the global scale converges too early, and only local details are slowly adjusted in the later stage. This "global saturation and local delay" feature leads to non-physical mutations in the spatiotemporal evolution trajectory, making the generated model's form discontinuous in the time dimension, resulting in loss of local details, unstable boundaries and insufficient smoothness, and further causing deviations from the overall form and the target design intent. This defect seriously restricts the application of such methods in the generation of high-fidelity, manufacturable three-dimensional models for cultural and creative products. SUMMARY

[0004] To solve the above technical problems, the present application provides a method for generating a manufacturable three-dimensional Chinese character cup model based on energy driving, to solve the topological structure distortion problem caused by unnatural fusion of complex stroke outlines in the prior art, as well as the non-physical mutations, detail loss and poor manufacturing adaptability caused by kinetic incoordination in the evolution process.

[0005] A kind of energy-driven manufacturable three-dimensional Chinese character cup model generation method based on, comprising the following steps:

[0006] S1: input definition and target establishment, receive multiple contour initial area and single target contour, construct smooth time evolution path, and fuse multiple contours into single target contour;

[0007] S2: define calculation domain, level set function, smooth approximation function and adaptive control factor;

[0008] S3: construct vector signed distance function, for representing the geometric information of contour;

[0009] S4: construct energy functional, model multiple contour fusion process as energy minimization problem;

[0010] S5: design adaptive inflation controller, dynamically and adaptively adjust inflation coefficient;

[0011] S6: obtain level set evolution equation by variational derivation;

[0012] S7: carry out numerical dispersion and stabilization processing;

[0013] S8: add two-dimensional evolution sequence along time axis to three-dimensional volume field, and carry out three-dimensional reconstruction;

[0014] S9: carry out thick shell processing to three-dimensional grid, generate thin shell structure suitable for 3D printing.

[0015] Preferably, in the step S1, the construction of the time evolution path includes:

[0016] evolve multiple contour initial area into single target contour;

[0017] Based on the path, construct three-dimensional space-time body model, and output printable three-dimensional Chinese character cup model by thick shell.

[0018] Preferably, the step S3 includes:

[0019] Map discrete grid coordinate system to continuous geometric space;

[0020] Split input closed region into line segment set, and calculate the minimum distance from pixel point to line segment in batch;

[0021] Use global even-odd rule to judge whether pixel point is located in the interior of polygon, to process complex contour containing hole or nested structure.

[0022] Preferably, in the step S4, the energy functional is:

[0023]

[0024] including a curve length regularization term , an inflation term and a shape prior term .

[0025] Preferably, in the step S5, the adaptive inflation coefficient is defined as:

[0026]

[0027] wherein, is an area difference, is a shape error, is a boundary length, , is a weight coefficient.

[0028] Preferably, in the step S6, the level set evolution equation is:

[0029]

[0030] wherein is a curvature.

[0031] Preferably, the step S9 comprises:

[0032] obtaining an outer surface mesh through an iso-surface extraction and a constrained inner offset technique, and performing self-intersection detection;

[0033] constructing a pair of rings at the opening and performing a stitching bridge;

[0034] performing mesh simplification using a thickness-constrained progressive error metric to control the tolerance within 5% of the wall thickness.

[0035] A system for implementing the above method, comprising:

[0036] an input module for receiving a multi-contour initial region and a target contour;

[0037] a processing module for performing level set evolution, energy functional optimization and three-dimensional reconstruction;

[0038] an output module for generating a 3D printable three-dimensional mesh file.

[0039] A non-transitory computer-readable storage medium storing a computer program, the program implementing the above method when executed by a processor.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] (1) Technological innovation: improving the accuracy and stability of three-dimensional reconstruction

[0042] By converting the multi-contour fusion problem into an energy functional extremum solution, and introducing a dynamic coupled adaptive inflation control mechanism, the model can balance the global shape coordination and local detail high fidelity during the evolution process. Further, it effectively overcomes the common dynamic incoordination problems such as contour misplacement, shape distortion, and "global saturation and local delay" in traditional methods, and the generated two-dimensional evolution path is continuous and stable in topological structure, laying a solid foundation for subsequent high-quality three-dimensional reconstruction;

[0043] (2) Cultural heritage: restore the charm of Chinese characters, help cultural landing

[0044] Through the precise controllable contour evolution and structure preservation ability, the unique shape beauty, stroke rhythm and frame structure of Chinese characters and other core cultural elements can be accurately converted into the modeling language of three-dimensional models; Further, it avoids the common semantic deviation and loss of artistic charm in the digital process, realizes the high-quality conversion of cultural symbols from two-dimensional plane to three-dimensional entity, and provides a reliable technical bridge for the modernization and embodiment expression of traditional cultural IP. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The method flowchart of the present application is shown in the figure;

[0046] Figure 2 The physical mutation (left) and expected effect (right) of the inflation item of the present application are shown in the figure;

[0047] Figure 3 The three-dimensional model output by the method of the present application and the 3D printing result are shown in the figure. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0049] Embodiment:

[0050] As shown in Figure 1 A manufacturable three-dimensional Chinese character cup model generation method based on energy driving includes the following steps:

[0051] S1. Input definition and target establishment:

[0052] The user gives a multi-outline initial region and a single target outline, and clearly defines the core target as constructing a smooth time evolution path to realize the "fusion" of the initial region into the single target outline during the evolution process. The result at each moment on the evolution path is called an intermediate region or a parallel region (a set of multiple outlines) and satisfies the continuity of the intermediate region in shape topology, scale ratio, and geometric characteristics with adjacent time steps, thereby realizing time smoothness. Based on the evolution path, a three-dimensional space-time body model is further constructed, and the two-dimensional intermediate region is added along the time axis to form a volume field, and finally a printable three-dimensional Chinese character cup model is output by using the thick shell algorithm. Further define the input and target levels as follows:

[0053] Input level: Clearly set "multi-outline initial region" and "single target outline" as the starting input data of the technical process, providing a basis for the construction of the subsequent evolution path.

[0054] Target level: Focus on the construction of a smooth time evolution path, which realizes the orderly transition from multiple initial outlines to a single target outline, rather than simple morphological superposition or replacement.

[0055] S2. Related parameter and function definition

[0056] S2.1. Calculation domain and level set function setting: define the calculation domain as , and the level set (LeveSet) function is used to describe the evolution curve, and the zero level set corresponds to the curve position at time ; the target outline (closed curve) is represented by the signed distance function , and its zero level set is the target outline.

[0057] S2.2. Smooth approximation function and curvature calculation: adopt the smooth Heaviside function and Dirac function to ensure numerical stability and differentiability, and calculate the curvature by difference approximation method.

[0058] S2.3. Adaptive control factor: the invention introduces a time-dependent adaptive inflation control factor , which dynamically adjusts the driving force strength. On the basis of the smoothness of the curve constrained by the geometric regularization term, it balances the area residual and shape error in the evolution process, and ensures the convergence stability and physical reasonableness of the curve approximation to the target outline.

[0059] S3. Vector signed distance function (SDF)

[0060] S3.1. Construction of Core and Mathematical Form: Focusing on multiple smooth contour curves represented by vectors, the calculation is simplified using Discrete SDF while preserving geometric accuracy. Its mathematical form is as follows: ;in, Let Euclidean distance be the distance from the point to the nearest boundary. This is an indicator function for determining the sign of a point.

[0061] S3.2. Key Process: First, the discrete grid coordinate system is mapped to a continuous geometric space to ensure that the distance calculation is consistent with the original contour; then, the input closed region is split into a set of line segments, and the minimum distance from the pixel to the line segment is calculated in batches in a matrix manner, and the memory overflow is avoided by using a block evaluation strategy; finally, following the global even-odd rule, the parity of the intersection of the ray and the line segment is statistically analyzed to determine whether the pixel is located inside the polygon, so as to accurately handle complex contours with holes or nested structures.

[0062] S4. Constructing Energy Functionals

[0063] Multi-contour profiles are gradually merged into a single target profile. The process is modeled as a problem coupled with energy minimization and level set evolution. Evolutionary partial differential equations are obtained through energy functional construction and variational derivation, achieving continuous contour deformation and smooth transition. Based on curve evolution theory, the energy functional is defined as shown in Equation 1 below:

[0064]

[0065] The above energy functional It includes three core constraints:

[0066] (1) Curve length regularization term Adjusting the curvature ensures a smooth curve and suppresses distortions such as sharp points and burrs;

[0067] (2) Expansion / Area Item :pass Adjust the expansion or contraction behavior of the contour curve (see Adaptive Expansion Controller).

[0068] (3) Shape prior / target constraint : Drives the current curve to gradually approach the target contour No additional external force is required.

[0069] S5. Adaptive Expansion Controller

[0070] Existing methods often suffer from dynamic inconsistencies in controlling scale expansion. Figure 2 (Left), therefore, this invention designs an expansion coefficient that adaptively adjusts over time. Introducing regional area differences Three types of quantities—area difference, shape error, and boundary length—form a dynamically coupled control mechanism. The calculation is shown in Formula 2.

[0071]

[0072] in Indicates the area of ​​the target region. Indicates the first The current area of ​​the region at any given moment. (Through...) Controlling the expansion or contraction of the contour curve, if If the area is large, expansion is required; otherwise, contraction is necessary. In this invention, the target region is significantly larger than the current region, so only expansion needs to be considered. The area can be represented by the following integral:

[0073]

[0074] The above formula is based on the convention that level set functions are "negative inside and positive outside": Represents the outline boundary. Corresponding to the outer region of the boundary, This represents the internal region (i.e., the region where the "area information" is located). Definition symbol. For a unit step function, when Its value is 1 at this time, a setting that facilitates subsequent description of the area increment during the contour expansion process. Shape error Defined as the area of ​​the symmetric difference between the target and the current region:

[0075]

[0076] The profile length L(t) can be expressed by the following integral:

[0077]

[0078] Therefore, the adaptive expansion coefficient can be defined as:

[0079]

[0080] in, and These are the weighting coefficients for area-driven and shape-driven approaches, respectively. A regularization parameter is introduced to avoid numerical instability. Compared to the two-stage dynamics exhibited by the traditional balloon term, the first term ensures the area difference... The first term is a radial linear expansion term that converges exponentially to the uniform scaling factor of the second stage. The second term is a shape error term that maintains a certain driving force when the area difference is close to zero but the shape error still exists, so that the inflation term does not disappear too early, thus avoiding the model stopping the scaling too early. In addition, to avoid numerical oscillation and improve the stability of evolution, this paper performs exponential weighted smoothing on the time:

[0081]

[0082] where is the smoothing factor, represents the new parameter value or observation value calculated at time . This strategy can eliminate the violent fluctuations of the inflation term in the iteration process without affecting the overall convergence speed, ensuring the continuity of the spacetime surface and the stable evolution of the geometric curvature. Finally, in the evolution equation, replaces the constant coefficient of the original area term, as shown in equation 8.

[0083]

[0084] Through the above design, the area difference and the shape error are dynamically coupled and controlled during the evolution process: when is large, the inflation term is mainly driven by the area difference; when is small but still exists, the shape term continues to provide additional contraction or expansion force, so that the size and shape converge synchronously on the time axis. This method effectively eliminates the physical mutation phenomenon of the original model in the transition stage, making the overall geometric change process smoother, and the reconstruction result presents a natural transition as Figure 2 right.

[0085] The traditional sign function is not differentiable at zero, which easily leads to numerical instability. Therefore, a smoothed version is introduced, such as

[0086]

[0087] which remains consistent with when far away from zero, and provides a continuous and differentiable transition within the neighborhood. In addition, to ensure the stability of numerical calculation, the upper and lower bound constraints are imposed on the inflation speed parameter :

[0088] ​

[0089] This constraint can effectively suppress the phenomenon of too fast expansion due to too rough contour region in the initial stage. Fast expansion may cause numerical divergence or instability, thus affecting the convergence of the entire evolution process.

[0090] S6. Variational derivation and level set evolution equation

[0091] In the level set method based on energy functional, the evolution process of the contour region can be formalized as an energy minimization problem. To obtain the optimal solution, the idea of gradient descent is usually adopted, that is, by controlling the time evolution of the level set function ϕ, it is constantly approximated to the stable state along the direction of energy descent. Specifically, the evolution equation can be expressed as

[0092]

[0093] where represents the energy functional of the variational derivative of the level set function . By expanding each term in the energy and taking the variation, the following form can be obtained:

[0094] (1) Curve length term:

[0095] (2) Expansion term:

[0096] (3) Shape prior term:

[0097] In the above terms, the curve length term realizes the constraint of geometric smoothness by introducing the curvature operator, which is defined as

[0098]

[0099] Its essence is the average curvature of the level set surface, which can suppress the high-frequency oscillation of the local boundary and ensure the smoothness of the curve or surface. The expansion term controls the speed of interface expansion or contraction through the adjustment of the factor , thus determining the overall scale evolution trend. The shape prior term realizes the difference between the current interface and the target shape , so that the evolution process is not only constrained by geometry, but also guided by global shape information. Combining the above variational results, the complete level set evolution equation can be obtained:

[0100]

[0101] where is the weight coefficient of curvature smoothing term, which is used to regulate the smoothness of local geometry; is the dilation term control factor, which controls the expansion or contraction of the overall scale; is the strength coefficient of shape prior constraint, which is used to balance the consistency of geometric smoothness and target shape. Formula 16 simultaneously considers the local geometric smoothness, dilation constraint term and global target constraint, so as to smoothly fuse multiple initial contours into a single target curve during the evolution process.

[0102] S7. Numerical Discretization and Stabilization Strategy

[0103] To ensure numerical stability and differentiability, the smooth function and function approximation are used, respectively, and , are represented. In numerical calculation, the continuous domain is discretized into a two-dimensional pixel grid, and the spatial step size is taken . The gradient adopts finite difference approximation, and the curvature term can be calculated by the second-order difference formula. The time discretization adopts explicit iteration:

[0104]

[0105] where The value needs to meet the stability condition, and usually , is the iteration result of formula 16. To ensure that the level set function satisfies the properties of signed distance function (i.e. ), the Sussman algorithm is usually used to perform reinitialization regularly.

[0106] S8. Additive Superposition and Three-dimensional Reconstruction

[0107] In the process of three-dimensional reconstruction, the two-dimensional level set function sequence is stacked along the time axis into a three-dimensional volume field , where is the sampling time. Then, the frame sequence is converted into a tensor, and optional Gaussian filtering (standard deviation ) is used to smooth the noise and improve the smoothness. Subsequently, the Marching Cubes algorithm is used to generate the vertex and face index of the space-time surface, realizing the output of the three-dimensional model.

[0108] S9. Three-dimensional Grid Thick Shell Processing Step

[0109] To realize intelligent manufacturing, the obtained three-dimensional mesh also needs to be "thickened inward" for 3D printing (such as Figure 3 ). The present application adopts mesh domain thickening, first extracts the outer surface mesh from the isosurface, and performs constrained inner offset based on the consistent normal on the millimeter scale; self-intersection or collision detection is performed and local rollback reconstruction is implemented. In order to maintain the open shape, a pair of rings is constructed at the cup mouth and a suture bridge is implemented, so that the outer wall and the inner wall are continuously connected at the mouth edge, thereby forming a thin shell suitable for 3D printing. The difficulty lies in the normal direction, thin wall simplification and topological robustness.

[0110] Finally, in the simplification stage, a progressive error metric with thickness constraint is adopted, the boundary vertices are locked, cross-wall welding is prohibited, and the quantitative tolerance is controlled within 5% of the wall thickness; combined with connected component retention and non-manifold detection, the model not only meets the manufacturing requirements in terms of millimeter-level dimensional accuracy and structural integrity, but also significantly reduces storage and transmission costs.

[0111] The embodiments of the present application are given for example and description, although the embodiments of the present application have been shown and described above, it can be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application, and the changes, modifications, replacements and modifications of the above-mentioned embodiments made by those skilled in the art within the scope of the present application shall be included in the protection scope of the present application.

Claims

1. A method for generating a manufacturable three-dimensional Chinese character cup model based on energy-driven processes, characterized in that, Includes the following steps: S1: Input definition and target establishment, receiving multiple initial contour regions and a single target contour, constructing a smooth temporal evolution path, and merging multiple contours into a single target contour; S2: Define the computational domain, level set function, smooth approximation function, and adaptive control factor; S3: Construct a vector symbolic distance function to represent the geometric information of the contour; S4: Construct an energy functional to model the multi-contour fusion process as an energy minimization problem; S5: Design an adaptive expansion controller to dynamically and adaptively adjust the expansion coefficient; S6: The evolution equation of the level set is derived through variational derivation; S7: Perform numerical discretization and stabilization processing; S8: Additively stack the two-dimensional evolution sequence along the time axis into a three-dimensional volume field and perform three-dimensional reconstruction; S9: Thicken the 3D mesh to generate a thin-shell structure suitable for 3D printing; The adaptive control factor refers to the time-dependent adaptive expansion control factor. Its dynamic adaptive adjustment of driving force intensity, based on the curve smoothness constrained by geometric regularization, balances the area surplus and shape error in the evolution process, ensuring the convergence stability and physical rationality of the curve approximating the target contour. The adaptive expansion controller is an expansion coefficient that adaptively adjusts over time. Introducing regional area differences The three types of quantities—shape error, boundary length, and shape error—form a dynamically coupled control mechanism. The mathematical expression for the expansion coefficient is: in, The difference between the target area and the current area. For the difference in area due to shape symmetry, The current boundary length, , These are the weighting coefficients. For regularization parameters, This is a function for smoothing the sign.

2. The method according to claim 1, characterized in that, In step S1, the construction of the temporal evolution path includes: The initial region with multiple contours is gradually evolved into a single target contour; Based on this path, a three-dimensional spatiotemporal volume model is constructed, and a printable three-dimensional Chinese character cup model is output through thickening.

3. The method according to claim 1, characterized in that, Step S3 includes: Mapping a discrete grid coordinate system to a continuous geometric space; The input closed region is split into a set of line segments, and the minimum distance from each pixel to the line segment is calculated in batches. Use global even-odd rules to determine whether a pixel is inside a polygon in order to handle complex contours with holes or nested structures.

4. The method according to claim 1, characterized in that, In step S4, the energy functional is: Including curve length regularization term Expansion term and shape priors ; These are smoothing weighting coefficients used to control the curvature smoothing intensity of the contour boundaries; An adaptive expansion coefficient that varies with time, used to dynamically control the expansion or contraction behavior of the profile; The target shape constraint weight coefficient is used to control the intensity of the current contour's approximation of the target contour.

5. The method according to claim 1, characterized in that, In step S6, the evolution equation of the level set is: in, It represents the local curvature of the contour described by the level set function and is used to control the smoothness of the boundary; It is a differentiable approximation of the standard Dirac function, used to stably handle boundary evolution in numerical computation; It is a differentiable approximation of the unit step function, used to distinguish between the interior and exterior regions of a contour; Geometric information used to describe the shape of the target.

6. The method according to claim 1, characterized in that, Step S9 includes: The outer surface mesh is obtained through isosurface extraction and constrained inner offset techniques, and self-intersection detection is performed. Construct a pairing ring at the opening and then stitch the bridging ring together. Mesh simplification is achieved using a progressive error metric with thickness constraints, controlling the tolerance to within 5% of the wall thickness.

7. A system for generating manufacturable three-dimensional Chinese character cup models, characterized in that, The system is used to implement the method according to any one of claims 1-6, comprising: The input module is used to receive the initial region and target contour of the multi-contour system. The processing module is used to perform level set evolution, energy functional optimization, and 3D reconstruction. The output module is used to generate 3D printable mesh files.

8. A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements the method as described in any one of claims 1-6.

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