Personalized cap body digital jet printing method based on three-dimensional curved surface model

Abstract

The invention relates to a personalized cap body digital jet printing method based on a three-dimensional curved surface model in the technical field of intelligent manufacturing, and the method comprises the steps: obtaining cap body three-dimensional scanning data, and processing the data through a curved surface reconstruction algorithm to obtain a complete three-dimensional curved surface model; wherein the model comprises geometric features of all curvature change areas for subsequent analysis; calculating a local curvature value of each area according to the three-dimensional curved surface model, determining a curvature change distribution diagram by adopting a Gaussian curvature calculation method, and marking a boundary line of a high-curvature area and a low-curvature area in the distribution diagram to guide pattern adjustment; and nozzle movement track data is extracted from the diffusion control parameter set, a three-dimensional printing path is generated through a path planning algorithm, and the path ensures that movement of a nozzle on a curved surface is synchronous with curvature change so as to avoid position deviation.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a method for digital inkjet printing of personalized hats based on a three-dimensional curved surface model. Background Technology

[0002] The decorative design of hats plays a vital role in the textile and fashion industry. It not only represents the core of a product's appearance but also directly influences consumer purchasing decisions and brand value. With the growth of personalized consumption demands, hat printing technology needs to meet requirements of diversity, high precision, and comfort to adapt to rapidly changing market trends.

[0003] Traditional decorative techniques, in addressing this demand, have gradually revealed significant shortcomings, limiting the industry's innovation and development. How to achieve high-quality pattern decoration on complex three-dimensional curved surfaces while maintaining fabric comfort has become a critical issue that the industry urgently needs to overcome. Traditional hat printing mainly relies on screen printing and heat transfer, but these methods have obvious limitations in adapting to modern needs. Screen printing involves a cumbersome plate-making process, struggles to achieve rich color gradients, and has low production efficiency, making it unsuitable for small-batch customization. While heat transfer is relatively simple to operate, the pattern often forms a hard coating on the fabric surface, reducing breathability and affecting the wearer's comfort. These methods struggle to ensure accurate pattern rendering on complex three-dimensional curved surfaces, often resulting in stretching or deformation, reducing the sophistication of the decorative effect. Accurate pattern mapping is a core technical challenge in three-dimensional curved surface printing. The curved structure of hats is complex, with significant curvature variations in different areas, making traditional planar printing techniques unable to effectively adapt to these geometric characteristics. If a flat pattern is directly printed onto a curved surface, the pattern is prone to distortion or stretching. For example, at the junction of the brim and the hat body, the pattern may become distorted due to changes in curvature, affecting the visual effect. This problem stems from a lack of precise capture and adaptation to the geometric features of three-dimensional curved surfaces, preventing printing equipment from dynamically adjusting the pattern mapping method according to the characteristics of the curved surface. Meanwhile, controlling the adhesion and diffusion of ink on curved surfaces is another key technical challenge. Due to the irregularity of three-dimensional curved surfaces, printing ink is prone to uneven penetration or lateral diffusion between fabric fibers. For example, in certain sloping areas of the hat, ink may flow due to gravity or fiber texture, resulting in blurred pattern edges and unnatural color transitions. This bleeding phenomenon not only reduces the clarity of the pattern but may also cause the fabric to stiffen due to excessive ink penetration, affecting the feel and wearing comfort. The difficulty of ink diffusion control is closely related to the problem of adapting to the geometry of three-dimensional curved surfaces, because only with precise mapping can the precise control of the ink jet position and amount be further achieved. Therefore, how to achieve precise pattern mapping on three-dimensional curved hat bodies and effectively control ink penetration and diffusion has become a key issue restricting the development of hat printing technology. Solving this problem requires breaking through the limitations of traditional printing techniques and developing innovative methods that can adapt to complex curved surfaces and achieve high-precision pattern printing to meet personalized design and comfort needs. This technical challenge is particularly prominent in actual production. For example, with customized baseball caps, consumers might request complex gradient patterns printed at the junction of the brim and the cap body, such as a streamlined design transitioning from dark blue to light blue.

[0004] However, due to the curvature of the brim and the spherical nature of the hat body, traditional inkjet printing equipment struggles to accurately calculate the printhead's trajectory across different curvature regions, resulting in noticeable stretching or misalignment of the pattern at the seams. Simultaneously, the ink may diffuse after printing due to the absorbency of the fabric fibers, blurring gradient boundaries and losing color depth. This not only reduces the product's visual appeal but also affects the lightweight feel of the garment due to the thick coating formed after ink curing. Faced with these challenges, the industry urgently needs a technology capable of high-precision pattern printing on three-dimensional curved surfaces while ensuring that the ink adhesion process does not compromise the fabric's softness and breathability. Only by solving these two core problems—curved surface geometry adaptation and ink diffusion control—can the market's demand for high-quality, personalized hats be truly met, providing manufacturers with greater design freedom and a competitive advantage.

[0005] Therefore, how to achieve precise printing of patterns on complex three-dimensional curved surfaces while maintaining the original properties of the fabric has become a key issue driving the innovation of hat printing technology. Summary of the Invention

[0006] This invention provides a personalized digital printing method for hats based on a three-dimensional curved surface model, comprising the following steps:

[0007] A 3D scan of the cap body is acquired, and the data is processed using a surface reconstruction algorithm to obtain a complete 3D surface model. This model includes the geometric features of all curvature variation regions for subsequent analysis. Local curvature values ​​for each region are calculated based on the 3D surface model, and a Gaussian curvature calculation method is used to determine a curvature variation distribution map. This distribution map indicates the boundary lines between high and low curvature regions to guide pattern adjustment. A surface mapping algorithm is used to project the planar pattern onto the curvature variation distribution map. If the projected pattern exhibits distortion in high curvature regions, the mapping parameters are dynamically adjusted to obtain a distortion-free, adaptable surface pattern. This adapted pattern retains the original gradient effect's color transition. For the adapted surface pattern, an ink adhesion process is simulated. A diffusion simulation algorithm is used to predict the ink penetration path in different curvature regions. If the predicted path shows lateral diffusion exceeding the predicted value, the ink is further processed. A threshold is set to optimize the ink jet volume, resulting in a diffusion control parameter set, which includes the ink volume and velocity values ​​at each jet point. Printhead motion trajectory data is extracted from this parameter set, and a 3D printing path is generated using a path planning algorithm. This path ensures that the printhead's movement on the curved surface is synchronized with curvature changes to avoid positional deviations. If a potential misalignment is detected at the connection between the brim and the body of the hat, a correction algorithm is applied to adjust the trajectory coordinates, resulting in a final optimized printing path. This path integrates all requirements for accurate pattern mapping and ink diffusion control. The final optimized printing path drives a digital inkjet printer to perform pattern printing operations, acquiring real-time feedback data to determine the uniformity of ink adhesion during printing, resulting in a complete, high-precision 3D curved surface printing result that satisfies personalized gradient effects and fabric comfort.

[0008] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0009] This invention discloses a personalized digital printing method and system for hats based on a 3D curved surface model, solving the business scenario problems of accurate pattern mapping, uniform ink adhesion, and preservation of gradient effects on complex curved hat surfaces. Addressing the challenges of complex hat surfaces, curvature variations leading to pattern distortion, and uneven ink diffusion, this invention acquires hat data through 3D scanning, uses a surface reconstruction algorithm to generate a model containing curvature features, and calculates a Gaussian curvature distribution map to identify high and low curvature regions. A surface mapping algorithm projects a planar pattern, dynamically adjusting mapping parameters to eliminate distortion in high curvature regions while preserving gradient color effects. Furthermore, a diffusion simulation algorithm predicts the ink penetration path, optimizes the jet volume to generate a diffusion control parameter set, and combines a path planning algorithm to generate a printing path synchronized with curvature. A correction algorithm is applied at the connection between the brim and the hat body to eliminate misalignment, ultimately driving the printing equipment to achieve uniformly adhered personalized printing. This invention achieves high-precision pattern printing on complex curved surfaces, meeting personalized customization needs and fabric comfort. Attached Figure Description

[0010] Figure 1 This is a flowchart of a personalized digital printing method for hats based on a three-dimensional curved surface model according to the present invention.

[0011] Figure 2 This is a schematic diagram of a personalized hat digital printing method based on a three-dimensional curved surface model according to the present invention.

[0012] Figure 3 This is another schematic diagram of a personalized digital printing method for hats based on a three-dimensional curved surface model according to the present invention. Detailed Implementation

[0013] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0014] like Figure 1-3 This embodiment of a personalized hat digital printing method based on a three-dimensional curved surface model may specifically include:

[0015] S101. Obtain the three-dimensional scanning data of the hat body, and process the data through a surface reconstruction algorithm to obtain a complete three-dimensional surface model, wherein the model contains the geometric features of all curvature variation regions for subsequent analysis.

[0016] Acquire 3D scan data of the hat body and extract a point cloud set from the data. Preprocess the point cloud set by using a filtering algorithm to remove noise, obtaining a first point cloud set. Apply a surface reconstruction algorithm to the first point cloud set to generate a preliminary 3D surface model. For the preliminary 3D surface model, calculate the curvature gradient, identify regions of curvature variation, and obtain a set of geometric features for these regions. Integrate the geometric feature sets and use a mesh optimization algorithm to process the preliminary 3D surface model, generating a complete 3D surface model containing all regions of curvature variation. Smooth the complete 3D surface model to obtain the final 3D surface model.

[0017] Specifically, in one implementation, three-dimensional scan data of the hat body is first acquired.

[0018] Specifically, a laser scanner or structured light scanning device is used to scan the cap, for example, a sports cap, capturing surface point cloud data from multiple angles. This data includes the coordinates of points on the outer contour of the cap, ensuring coverage of areas such as the top, brim, and sides. In this way, the obtained high-density point cloud data reflects the overall geometry of the cap, providing a foundation for subsequent processing. Further, the data is processed using a surface reconstruction algorithm to obtain a complete 3D surface model. A surface reconstruction algorithm is a surface fitting method based on point cloud data, such as parametric surface fitting technology, to convert discrete point clouds into a continuous surface representation. During processing, the scanned data is first preprocessed, including removing noise and outliers, for example, by using statistical filtering to remove isolated points to improve data quality. Then, a meshing algorithm is applied to generate a triangular mesh model, and NURBS surface fitting is further used to smooth the surface. This algorithm ensures the integrity of the model, covering all parts of the cap without losing detail.

[0019] The model incorporates the geometric features of all curvature variation regions for subsequent analysis. Curvature variation regions refer to areas on the hat surface where the curvature changes significantly, such as the curved edge of the brim or the rounded transition of the crown. These geometric features are extracted through a curvature calculation module in the algorithm, for example, calculating the Gaussian curvature and average curvature value for each point and embedding these values ​​into the model. Specifically, this process involves performing local neighborhood analysis on the point cloud, estimating the curvature tensor, and then labeling high-curvature regions while preserving their accurate geometric description. In this way, the model is not only complete but also highlights these features for subsequent applications such as strength analysis or manufacturing optimization.

[0020] For example, in one implementation scenario in the field of helmet design, for a safety helmet, after the scanning data is acquired, the surface reconstruction algorithm can adjust the parameters to emphasize the curvature variation area of ​​the helmet shell.

[0021] For example, increasing the mesh resolution to capture sharp bends in the hat brim ensures the model supports finite element analysis for assessing impact resistance. In this way, the technical solution demonstrates its versatility in the hat digitization process.

[0022] Preferably, in another embodiment, a multi-resolution algorithm can be introduced to process the data for the surface reconstruction of fashion hats.

[0023] Specifically, a coarse reconstruction is first performed to generate a basic model, and then fine subdivision is applied to areas of curvature variation, such as using the Loop subdivision method to enhance local details. This approach maintains the overall integrity of the model while highlighting geometric features for subsequent texture mapping or 3D printing preparation.

[0024] Understandably, the innovation of surface reconstruction algorithms lies in their mechanism for preserving regions of curvature variation.

[0025] For example, when processing cap scan data, the algorithm minimizes surface errors through iterative optimization steps, ensuring the accuracy of geometric features. The specific process includes initial surface fitting, followed by error checking and adjustment, such as comparing the distance deviation between the reconstructed surface and the original point cloud, and adding control points for high curvature areas. This mechanism makes the model applicable to various cap types, such as baseball caps or fedoras, providing a reliable analytical basis. Further, in this embodiment, for scanning a winter beanie, data acquisition uses a portable scanner to capture a flexible surface. The surface reconstruction algorithm then needs to handle deformation factors, such as incorporating an elastic deformation model to correct scanning deviations, ensuring that the geometric features of curvature variation areas, such as brim folds, are fully preserved for subsequent dimensional adjustment analysis.

[0026] In one possible implementation, the technical solution can be extended to cap quality inspection scenarios.

[0027] For example, curvature analysis can be performed on a 3D model of an industrial cap to identify potential defect areas. This extension demonstrates the flexibility of the algorithm without altering the core processing flow.

[0028] Specifically, the above implementation method ensures the full realization of technical features through a logical flow from data acquisition to model generation. Preserving the geometric features of the model helps improve the accuracy of the hat design, for example, by analyzing the impact of curvature on comfort during simulated wearing.

[0029] For example, in the field of hat manufacturing, the generated model can be directly imported into CAD software to further optimize production parameters. This application emphasizes the practical value of the technical solution.

[0030] S102. Calculate the local curvature value of each region based on the three-dimensional surface model, and determine the curvature variation distribution map using the Gaussian curvature calculation method. The distribution map indicates the boundary line between the high curvature region and the low curvature region to guide the pattern adjustment.

[0031] A set of surface point coordinates for each region is obtained from a 3D surface model. This set contains the 3D coordinates of multiple surface points. Using a Gaussian curvature calculation method, the local curvature value of each surface point is obtained by calculating the principal curvature product of the surface point coordinates. A curvature variation distribution map is generated based on these local curvature values, marking the boundary lines between high and low curvature regions. A curvature gradient vector is calculated for each boundary line by calculating the difference between the local curvature values ​​on both sides of the boundary line. The curvature gradient vector is used to determine the smoothness of the region transition. If the smoothness of the region transition is lower than a preset threshold, the boundary line position is adjusted to obtain an adjusted boundary line. A pattern optimization path is generated from the adjusted boundary line, and this path guides the pattern adjustment.

[0032] Specifically, in one implementation, the three-dimensional surface model is first divided into regions to calculate the local curvature value of each region.

[0033] Specifically, a 3D surface model can be understood as a surface structure represented by a mesh, such as the surface modeling used for product shells in industrial design. The process of region partitioning involves dividing the surface into multiple small blocks, each corresponding to a computational unit. This partitioning allows for analysis of local surface features, ensuring the accuracy of curvature calculations.

[0034] For example, in a surface model, it is divided into triangular mesh cells, and the vertex coordinates of each cell are used for subsequent calculations. This method helps identify the degree of curvature on the surface, providing basic data for pattern adjustment. In practical applications, this division can adjust the mesh density according to the complexity of the surface, thus adapting to different design requirements. Furthermore, a Gaussian curvature calculation method is used to determine the local curvature value of each region. Gaussian curvature is a fundamental concept in surface differential geometry; it describes the degree of curvature of a surface at a point and is represented by the product of principal curvatures. In the specific implementation, the normal and tangent vectors of the surface in that region are first obtained, and then the principal curvatures are calculated, i.e., the maximum and minimum curvatures of the surface along two orthogonal directions. The value of the Gaussian curvature is equal to the product of these two principal curvatures; a positive value indicates an ellipsoidal surface, a negative value indicates a saddle-shaped surface, and a zero value indicates a planar or cylindrical surface. This calculation method can quantify the intrinsic geometric properties of the surface without relying on an external coordinate system.

[0035] In one possible implementation, the Gaussian curvature is calculated point-by-point for each grid point within a region, and the average value across all points in the region is taken as the local curvature value for that region. This averaging process helps smooth noise and ensures the reliability of the curvature value. In industrial design scenarios, such as designing the curved surfaces of a car body, this calculation can reveal complex areas of the surface, thereby guiding the placement of patterns to avoid deformation.

[0036] The specific process of calculating Gaussian curvature involves several key steps. First, based on the parametric representation of the surface model, the first and second partial derivatives are calculated. These derivatives are used to construct the basic forms, namely the first and second basic forms. The first basic form describes the metric properties of the surface, and the second basic form describes the curvature properties. Then, the specific numerical value of the Gaussian curvature is calculated using these basic forms.

[0037] For example, in a parametric surface, Gaussian curvature can be derived from its derivative using a specific formula. While this doesn't involve numerical details, it ensures the accurate acquisition of curvature values. In practice, if the surface model is generated from point cloud data, surface fitting is performed first, followed by the above calculations. This method is particularly useful in design because it can handle complex surfaces, such as the irregular shapes of electronic product casings, helping designers understand the surface's geometric properties and laying the foundation for pattern adjustments. This detailed calculation generates a comprehensive curvature distribution, providing data support for subsequent steps.

[0038] Preferably, after calculating the local curvature value of each region, a curvature variation distribution map is determined.

[0039] Specifically, a curvature variation distribution map maps the curvature values ​​of all regions onto a two-dimensional or three-dimensional visualization, using color gradients to represent the degree of curvature.

[0040] For example, areas with high curvature are marked in red, and areas with low curvature are marked in blue. The generation of this distribution map involves interpolation techniques that smoothly connect discrete curvature values ​​into a continuous distribution, thus visually displaying the bending changes of the surface.

[0041] In one embodiment, for a curved surface model, the distribution map can be overlaid on the original model to facilitate observation of the curvature gradient. This visualization helps identify regions of abrupt curvature changes, providing guidance for pattern adjustments.

[0042] For example, in industrial design, curvature variation distribution maps can be used to analyze the surface of a phone case. When the distribution map shows that certain areas have high curvature, designers can adjust the position of patterns accordingly, avoiding placing fine details in areas of high curvature to prevent distortion. Determining such a distribution map also includes threshold setting, that is, defining the boundary between high and low curvature. For example, the threshold can be set by statistically analyzing the mean and standard deviation of all curvature values, thereby automatically classifying areas. In one implementation, the distribution map indicates the boundary line between high and low curvature regions.

[0043] Specifically, boundary lines are drawn by detecting gradient changes in curvature values. When the curvature difference between adjacent regions exceeds a preset threshold, these points are connected to form a boundary line. This marking method clearly delineates different curved areas on a surface, for example, highlighting boundaries with black lines on a distribution map. The generation of these boundary lines enhances the usability of the distribution map, allowing users to quickly identify key areas. In design scenarios, such as designing patterns for furniture surfaces, these boundary lines guide the segmentation of the pattern, ensuring a smooth transition in low-curvature areas and simplifying the design in high-curvature areas. Furthermore, these boundary lines guide pattern adjustments.

[0044] Specifically, the pattern adjustment process is based on information from the distribution map and boundary lines. For example, the pattern scale is reduced in areas of high curvature, or the pattern details are expanded in areas of low curvature to fit the geometry of the curved surface. This guidance enables a better match between the pattern and the curved surface, avoiding visual distortion.

[0045] In one possible implementation, the system automatically generates adjustment suggestions, such as deformation compensation when moving pattern elements across boundary lines. This method is applicable to multiple scenarios within the same design domain, such as adjusting printed patterns on curved fabrics in clothing design or optimizing label placement in packaging design. Through this adjustment, the optimized configuration of the pattern is achieved, enhancing the overall design effect.

[0046] Understandably, in another embodiment, for more complex surface models, such as the exterior wall surfaces of architectural models, Gaussian curvature calculation can be combined with finite element analysis to further refine the region division. This combined approach first generates a surface representation using a finite element mesh, then calculates the curvature value of each element to generate a distribution map. Boundary line marking uses an edge detection algorithm to highlight the junctions of high and low curvature. This embodiment demonstrates the versatility of the technical solution and can be applied to handle surfaces of different scales in the design field.

[0047] For example, in practice, if the surface model originates from scanned data, noise filtering is performed before calculating the curvature values. This preprocessing ensures the accuracy of the distribution map, while boundary lines are automatically generated through curvature gradient calculations to guide pattern adjustments, such as optimizing texture mapping in product prototyping. This approach emphasizes a complete workflow from data to adjustment.

[0048] In one embodiment, the curvature variation distribution map may also include interactive functionality, allowing users to view specific curvature values ​​by clicking on boundary lines, thus enabling more precise pattern adjustments. This extension, implemented in design software, enhances the user experience and covers a variety of scenarios within the same domain, ranging from simple to complex surfaces.

[0049] S103. The planar pattern is projected onto the curvature change distribution map using a surface mapping algorithm. If the pattern is distorted in the high curvature region after projection, the mapping parameters are dynamically adjusted to obtain a non-deformed surface-fitting pattern, wherein the fitted pattern retains the color transition of the original gradient effect.

[0050] Obtain surface geometry data, including a curvature variation distribution map. Extract high-curvature regions from the curvature variation distribution map; these high-curvature regions are those where the curvature value exceeds a preset threshold. If the projected pattern within the high-curvature region exhibits distortion, adjust the mapping parameters using the least squares method. This method fits the surface points by minimizing the sum of squared errors to obtain a preliminary adaptation pattern. Extract color gradient vectors from the preliminary adaptation pattern; these vectors represent the direction and intensity of color changes within the pattern. Perform dynamic interpolation on the color gradient vectors at uneven transitions within the high-curvature regions. This dynamic interpolation calculates intermediate color values ​​using linear interpolation to obtain a uniform color transition pattern. Calculate the texture density distribution based on the uniform color transition pattern; this texture density distribution represents the distribution density of texture elements within the pattern. If the texture density distribution exceeds a preset threshold, merge neighboring pixel values. This merging of neighboring pixel values ​​involves weighted averaging of adjacent point colors to obtain a texture-balanced pattern. Obtain the boundary contour of the texture equalization pattern, smooth the boundary contour using a Bezier curve, which generates a smooth path based on control points to obtain the final surface adaptation pattern.

[0051] Specifically, in one implementation, the planar pattern is projected onto the curvature variation distribution map using a surface mapping algorithm. First, the curvature variation distribution map needs to be generated.

[0052] Specifically, the curvature variation distribution map is obtained by analyzing the geometric properties of the target surface.

[0053] For example, by meshing a surface and calculating the local curvature value at each mesh point, such as Gaussian curvature or mean curvature, a two-dimensional or three-dimensional map representing the curvature distribution can be formed. This distribution map can highlight high-curvature regions, such as bends or peaks in the surface, providing basic data for subsequent projection. In graphic design, such as in product surface texture design, this map helps identify potential deformation risk areas, ensuring the accuracy of pattern projection. Furthermore, the surface mapping algorithm can be implemented using parametric methods, such as using UV mapping technology to map the coordinates of the planar pattern to the parameter space of the surface.

[0054] For example.

[0055] In one possible implementation, the planar pattern is first represented as a pixel grid. Then, a projection transformation matrix is ​​calculated using a least-squares conformal mapping algorithm to project the pattern points onto the surface points corresponding to the curvature distribution map. This method can initially achieve pattern fitting, but potential distortion needs to be considered in high-curvature regions.

[0056] If the projected pattern is distorted in the high curvature region, the mapping parameters are dynamically adjusted.

[0057] Specifically, distortion detection is achieved by comparing the geometric features of the pattern before and after projection, such as calculating the change in length or area ratio of the pattern edges. If the change exceeds a preset threshold, such as a length change rate greater than 10%, it is considered distorted. After distortion is detected, dynamic adjustment involves iteratively optimizing mapping parameters, such as modifying the scaling factor or rotation parameters in the mapping function, and gradually minimizing the distortion through gradient descent. This adjustment process can be executed in real time in graphics processing software, ensuring the natural extension of the pattern on the curved surface. In industrial design scenarios, such as designing patterns for car bodies, this dynamic adjustment can avoid pattern stretching and deformation in high-curvature areas, such as the curves of car doors, thus maintaining the aesthetics and consistency of the design. This step is the core innovation because it introduces an adaptive mechanism, which can better handle complex curved surfaces and improve the fidelity of projection compared to traditional static mapping. Through multiple iterations, typically within 5 to 10 loops, the distortion can be reduced to an acceptable level, achieving a distortion-free adapted pattern.

[0058] Preferably, a curvature compensation factor can be introduced during the dynamic adjustment process.

[0059] Specifically, the curvature compensation factor is a weighted value calculated based on the curvature distribution map. For example, higher compensation weights are assigned to areas with high curvature, and the deformation is balanced by multiplying by the mapping parameter. This compensation helps preserve the original proportions of the pattern and avoids overstretching or compression.

[0060] In one embodiment, for the projection of a spherical surface, the compensation factor can be set according to the inverse ratio of the radius of curvature, so that the pattern is appropriately locally adjusted at the high curvature of the sphere top.

[0061] For example, in another implementation, for irregular curved surfaces such as the surface pattern projection of a human body model, the surface can be first divided into multiple sub-regions. Each sub-region is independently mapped using a mapping algorithm, and then smoothly connected at the boundaries to reduce overall distortion. During dynamic adjustment, if deformation is detected in a certain sub-region, parameters are optimized only for that region without affecting the global model. This block-based processing enhances the flexibility of the technology and is suitable for pattern adaptation of human body curved surfaces in the field of clothing design.

[0062] Understandably, the resulting non-deformable surface-fitting pattern needs to retain the color transition of the original gradient effect.

[0063] Specifically, a gradient effect refers to the visual characteristic of a pattern where colors smoothly transition from one hue to another, such as a linear transition from blue to green. During projection and adjustment, color values ​​are processed using a bilinear interpolation method to ensure that the color value at each projection point is calculated based on the neighborhood average of the original pattern, thus avoiding color breaks or blurring. This preservation mechanism is particularly useful in digital art creation, such as in the design of surface patterns for 3D printed models, where it can maintain the artistic expression of gradients.

[0064] In one embodiment, for a pattern projection onto a wavy surface, a curvature variation distribution map is first generated, highlighting the high curvature areas at the peaks and troughs. Then, a surface mapping algorithm is applied for initial projection. If the pattern becomes distorted at the peaks, such as curved texture lines, the mapping parameters are dynamically adjusted. For example, a local curvature smoothing filter is added, and the parameters are modified by averaging the neighborhood curvature. This process iterates until the distortion is eliminated. The final adapted pattern retains the original radial gradient colors, grading from red at the center to yellow at the edges, ensuring a smooth transition without jumps. This implementation demonstrates the application of the technology in decorative design scenarios, enabling efficient adaptation of curved surface patterns. Furthermore, to enhance versatility, in one implementation in the field of graphics animation, this method can be integrated into a rendering engine.

[0065] For example, when projecting textures onto the skin of a virtual character, the curvature distribution map is generated based on the skeletal animation of the character model. Parameters are dynamically adjusted to account for curvature changes between animation frames, thus maintaining pattern integrity during motion and preserving gradient effects such as natural transitions in skin tones. This not only improves rendering quality but also reduces the workload of manual correction.

[0066] Specifically, algorithms for dynamically adjusting mapping parameters can employ a feedback loop mechanism. For example, after initial projection, a deformation metric function, such as a torsion index based on the Jacobian matrix, is calculated. If the index exceeds a threshold, the parameter vector is updated, and the optimization problem is solved using Newton's method. This mechanism ensures the accuracy of the adjustment and is particularly effective in high curvature regions. In product packaging design, such as when designing label patterns for curved bottle surfaces, this method can generate a deformation-free, adapted version, preserving the gradient background color transition on the label and enhancing visual appeal.

[0067] In one embodiment, the projection process for an elliptical surface includes: generating a curvature map, projecting a planar pattern, detecting distortion in the high curvature region of the major axis, eliminating deformation by adjusting affine transformation parameters, and finally obtaining an adapted pattern that retains the original radial gradient colors. This diverse range of embodiments supports broad protection under the claims and demonstrates the flexible application of the technology within the same graphics processing domain.

[0068] S104. For the surface adaptation pattern, simulate the ink adhesion process and use a diffusion simulation algorithm to predict the ink penetration path in different curvature regions. If the predicted path shows that the lateral diffusion exceeds a preset threshold, optimize the ink injection amount to obtain a diffusion control parameter set, wherein the parameter set includes the ink volume and velocity value of each injection point.

[0069] A surface mesh, comprising multiple element meshes, is obtained from the surface geometry data. The element meshes are processed using the finite element method to calculate the Gaussian curvature value of each element mesh, resulting in a regional curvature distribution. Based on this regional curvature distribution, a diffusion simulation algorithm is used to simulate the ink flow path, obtaining ink penetration prediction data. If the lateral diffusion value of the ink penetration prediction data exceeds a preset threshold, the injection volume is adjusted based on this lateral diffusion value, determining the volume adjustment and velocity setting. Based on the volume adjustment and velocity setting, adhesion process control parameters and pattern adaptation verification parameters are generated, resulting in a diffusion control parameter set. The ink adhesion effect is verified against this diffusion control parameter set, and the diffusion control parameter set is adjusted to obtain an optimized diffusion control parameter set.

[0070] Specifically, in one implementation, for the ink adhesion process of a curved surface adapting to a pattern, the curved surface is first digitally modeled to simulate the ink adhesion environment.

[0071] Specifically, geometric data of the curved surface, including curvature distribution information, is acquired using a 3D scanning device. For example, when printing decorative patterns on the curved surface of ceramic products, the surface model can be represented as a mesh structure, where each mesh point is labeled with a local curvature value. This modeling ensures the accuracy of subsequent simulations and provides the basic data for the diffusion algorithm. In this way, various surface types, such as spherical or cylindrical surfaces, can be handled, ensuring the universality of pattern adaptation. Furthermore, a diffusion simulation algorithm is used to predict the penetration path of ink in different curvature regions. This algorithm is based on the principle of physical diffusion, simulating the trajectory of ink molecules on the curved surface.

[0072] Specifically, the algorithm treats ink as a collection of particles. In areas of high curvature, the particles are slowed down by surface tension, while in flat areas they diffuse more rapidly. By iteratively calculating particle positions, the algorithm predicts the penetration path, such as a sequence of vectors extending from the injection point outwards. This prediction takes into account the constraints of surface curvature on ink flow, enabling the reproduction of the actual adhesion process in a simulated environment.

[0073] The diffusion simulation algorithm can be implemented by path calculation using the finite element method.

[0074] In one possible implementation, the surface is divided into multiple regions, which are classified into high curvature regions and low curvature regions based on curvature thresholds.

[0075] For example, in high curvature regions, the algorithm introduces a curvature correction factor to adjust the diffusion rate, simulating the phenomenon that ink flows more easily along the tangential direction. This method ensures the accuracy of path prediction and avoids the errors of traditional uniform simulation. If the predicted path shows lateral diffusion exceeding a preset threshold, the ink ejection volume is optimized.

[0076] Specifically, a preset threshold can be set to trigger optimization when the path width exceeds 2 mm. The optimization process adjusts the jetting parameters through a feedback loop, such as reducing ink volume to limit the diffusion range. This optimization is based on path simulation results, iteratively calculating until the lateral diffusion is controlled within the threshold, thereby achieving a stable adhesion effect.

[0077] For example, in a scenario where a curved pattern is printed on a mobile phone case, if the simulated ink shows lateral diffusion exceeding a threshold in the edge curvature area, the system can reduce the jetting speed in that area to prevent ink overflow. Through multiple iterations, the optimization process can generate adaptive parameters to ensure a clear pattern.

[0078] Preferably, a diffusion control parameter set is obtained, wherein the parameter set includes the ink volume and velocity value for each ejection point.

[0079] Specifically, the parameter set is stored in array form. For example, for 100 ejection points on a curved surface, each point corresponds to a volume value such as 0.1 microliters and a velocity value such as 5 meters per second. This parameter set, output through an optimized algorithm, can be directly imported into the inkjet equipment for precise control.

[0080] In one embodiment, for printing on curved glass bottles, a diffusion simulation algorithm first predicts the ink path in the high-curvature region of the bottle neck. If diffusion exceeds a threshold, the injection volume is optimized to a minimum, while the speed is adjusted to match the curvature variation. This implementation demonstrates the applicability of the technology in container printing, reducing ink waste and improving pattern quality. Furthermore, the process can be extended to adapting to curved textile surfaces, such as printing patterns on curved fabrics. The simulation algorithm considers the fabric's permeability, predicts the path, and optimizes parameters to ensure uniform ink adhesion without smudging. Through this extension, the technology demonstrates versatility in the field of flexible curved surfaces.

[0081] It is understandable that the diffusion control parameter set obtained through the above steps can guide inkjet operations in actual production, such as in the coating of curved surfaces of automotive parts. The parameter set helps control ink distribution and achieve uniform coverage. This implementation method supports the technical features of the claims and provides specific support in various scenarios.

[0082] S105. Extract nozzle motion trajectory data from the diffusion control parameter set, and generate a 3D printing path through a path planning algorithm, wherein the path ensures that the movement of the nozzle on the curved surface is synchronized with the curvature change to avoid positional deviation.

[0083] Nozzle motion trajectory data is obtained from the diffusion control parameter set. A path planning algorithm is used to process the trajectory data to obtain a preliminary 3D printing path. Based on the preliminary 3D printing path, surface curvature changes are analyzed to obtain curvature synchronization adjustment parameters, determining the synchronous mapping relationship between nozzle movement and surface curvature changes. For this synchronous mapping relationship, position deviation risk points are extracted. If the deviation risk points exceed a preset threshold, the path parameters are adjusted to obtain a deviation-corrected printing path. Based on the deviation-corrected printing path, material deposition rate control is integrated, and the rate value is adjusted using a preset deposition model to generate an interlayer fusion enhancement path. The integrity of the interlayer fusion enhancement path is assessed by comparing the consistency between continuous path segments and curvature change points to obtain the final 3D printing path.

[0084] Specifically, in one implementation, extracting nozzle motion trajectory data from a diffusion control parameter set first requires understanding the concept of a diffusion control parameter set. This parameter set includes key variables in the printing process, such as nozzle speed, material diffusion rate, and temperature control values, which directly affect the stability of the printing path. By extracting this data, the initial motion trajectory information of the nozzle can be obtained.

[0085] Specifically, the extraction process involves filtering motion-related subsets from the parameter set, such as velocity vectors and position coordinates, and then using data parsing algorithms to convert this information into a processable trajectory sequence. This extraction ensures the accuracy of the underlying data for subsequent path planning, providing reliable input for generating the 3D printing path. Further, the 3D printing path is generated using a path planning algorithm. This algorithm is based on the extracted trajectory data and incorporates a surface geometry model for calculation. The path planning algorithm can employ a spline curve-based interpolation method to connect the initial trajectory points into a continuous path.

[0086] For example, when dealing with spherical surfaces, the algorithm first calculates a parametric representation of the surface and then adjusts the path points to match the curvature variations. This generation process ensures the smoothness and continuity of the path, avoiding abrupt changes in printing.

[0087] Preferably, the path ensures that the movement of the nozzle on the curved surface is synchronized with the curvature change to avoid positional deviation. This synchronization mechanism is the core innovation, involving real-time monitoring of curvature and adjustment of the nozzle attitude. Specifically, the local curvature of the surface is first calculated, for example, by evaluating the degree of curvature using a Gaussian curvature formula, and then the nozzle speed and direction are dynamically modified based on the curvature value.

[0088] For example, when printing a freeform surface with varying curvature, if the curvature increases, the algorithm slows down the nozzle speed and adjusts the tilt angle to maintain uniform material deposition. This synchronization is achieved through a feedback loop: at fixed time intervals, the system compares the deviation of the current position from the expected path and applies a correction vector to make adjustments, thereby preventing the accumulation of positional deviations.

[0089] One possible implementation approach considers different implementation scenarios for different surface types.

[0090] For example, when printing a cylindrical curved surface, the trajectory data extracted from the diffusion control parameter set includes axial velocity and radial offset values. The path planning algorithm then generates a helical path to ensure that the nozzle movement is synchronized with the curvature of the cylinder. In this way, the printing process maintains a uniform material distribution and avoids interlayer deviations caused by curvature mismatch.

[0091] The extraction of diffusion control parameter sets can be extended to multi-material printing scenarios. In such scenarios, the parameter set also includes material switching parameters, and the extraction process accordingly separates the trajectory data of different materials. The path planning algorithm then generates layered paths, with each layer independently and synchronously changing its curvature. This extension demonstrates the versatility of the technology in the field of 3D printing, capable of adapting to printing needs ranging from simple geometry to complex structures.

[0092] Specifically, the detailed process of synchronizing curvature changes can be further broken down into several sub-steps. First, a surface model is constructed, and the surface topology is represented using a meshing method. Then, based on the extracted trajectory data, the algorithm iteratively calculates the tangent and normal vectors at path points to ensure that the nozzle attitude is aligned with the local curvature. If the curvature changes drastically, the system introduces a buffer path to smoothly transition and minimize deviation. This mechanism is particularly effective when printing curved surfaces for aerospace parts, enabling high-precision forming while controlling positional deviations within the micrometer level.

[0093] For example, when printing a wavy surface, the path ensures synchronous passage through a pre-calculated curvature gradient map. The algorithm incorporates gradient information when generating the path, adjusting the nozzle trajectory to follow the changes in peaks and troughs, thereby avoiding material buildup or gaps. Furthermore, in another implementation, the path planning algorithm can integrate sensor feedback. Extracted trajectory data is fused with real-time sensor data to generate an adaptive path. This method ensures more precise synchronization when handling irregular surfaces.

[0094] Understandably, this technical solution achieves precise control of the nozzle movement through the above steps, thereby improving the quality and efficiency of curved surface printing in 3D printing.

[0095] S106. If a potential misalignment is detected at the connection between the brim and the body of the hat in the three-dimensional printing path, a correction algorithm is applied to adjust the trajectory coordinates to obtain the final optimized printing path, wherein the path integrates all the requirements of accurate pattern mapping and ink diffusion control.

[0096] Coordinate data at connection points are obtained from path misalignment detection. A preset threshold is used to determine the potential degree of misalignment, resulting in misalignment adjustment requirements. For these requirements, a coordinate transformation algorithm is applied to adjust the trajectory coordinates. This algorithm takes the trajectory coordinates and the adjustment requirements as input to obtain the adjusted coordinates. Pattern precision mapping parameters are then integrated to determine the adjusted coordinate sequence. Based on this sequence, ink diffusion control requirements are integrated to generate optimized printing path data. Using this optimized path data, the operating parameters of the printing equipment are adjusted to obtain the final printing path. If the deviation of the final printing path exceeds a preset threshold, the coordinate transformation is recalculated based on the deviation value, and the adjusted coordinate sequence is updated.

[0097] Specifically, in one implementation, if a potential misalignment is detected at the connection between the brim and the body of the hat in the 3D printing path, it is first detected by a geometric comparison method.

[0098] Specifically, the detection process involves comparing a pre-defined connection model with the actually generated path data, such as calculating the coordinate offset at the connection point. If the offset exceeds a threshold, it is identified as a potential misalignment. This detection ensures the accuracy of the printed path in complex curved surface transition areas, providing basic data for subsequent correction. This method is particularly suitable for identifying misalignment problems caused by abrupt curvature changes when printing hat-shaped curved surfaces. Further, a correction algorithm is applied to adjust the trajectory coordinates. This algorithm calculates a correction vector based on the offset, first extracting local curvature information at the connection point, and then modifying the position of the trajectory points through an iterative optimization method.

[0099] For example, if a misalignment is detected at the junction of the brim and the hat body, the algorithm generates a correction matrix, transforming the original coordinates into an adjusted coordinate sequence. This adjustment process involves multiple steps: initial coordinate input, offset vector calculation, transformation application, and a verification loop. Through these steps, the trajectory coordinates are accurately corrected, avoiding layer discontinuities in printing.

[0100] Preferably, a final optimized printing path is obtained, wherein the path integrates all requirements for accurate pattern mapping and ink diffusion control. Specifically, accurate pattern mapping involves projecting the design pattern onto the adjusted path, ensuring that pattern elements are aligned with the surface contours. Simultaneously, ink diffusion control is achieved through parameter adjustment, such as adjusting the ink flow rate according to the path speed, to maintain uniform distribution. This integration ensures that the final path comprehensively meets printing requirements.

[0101] For example, when printing a curved surface of a hat with a decorative pattern, the correction algorithm first detects misalignment at the brim edge, then adjusts the trajectory to ensure the pattern mapping accurately covers the connecting areas. Ink diffusion control synchronizes the path speed to prevent excessive ink diffusion at points of curvature change. This scenario demonstrates the application of this technology in curved surface printing, ensuring the integrity of the overall structure.

[0102] This correction algorithm can be extended to multi-layer printing scenarios. In such scenarios, inter-layer cumulative errors are considered when detecting misalignments, and the algorithm accordingly applies a cumulative correction vector to adjust all relevant trajectory coordinates. Finally, color gradient control is included when integrating the pattern mapping into the path to accommodate dynamic changes in ink diffusion. This extension enhances the flexibility of the technical solution, making it suitable for printing hats of varying thicknesses.

[0103] Specifically, the detailed process of ink diffusion control first defines diffusion parameters, such as diffusivity and viscosity, and then incorporates these parameters into path optimization. Through a feedback mechanism, the system monitors ink distribution in real time and adjusts the printing speed to match the pattern mapping requirements.

[0104] For example, in areas with a high degree of curvature on the hat body, the speed is reduced to control diffusion and ensure that the edges of the pattern are clear.

[0105] One possible implementation considers scenarios with irregular brim shapes. When detecting misalignment, a mesh model is used to represent the geometry at the connection points, and then a correction algorithm generates a smooth transition path. After final path integration, seamless pattern mapping and uniform control of diffusion are achieved. This approach is effective when printing custom hats, maintaining structural stability.

[0106] Understandably, this technical solution achieves precise control of path optimization through the aforementioned steps, improving the quality of curved surface connections in the field of 3D printing. Particularly when integrating patterns and diffusion requirements, it leads to improved printing efficiency while effectively suppressing positional deviations. Furthermore, in another implementation, path optimization also includes compensation for environmental factors.

[0107] For example, when detecting misalignment, the influence of temperature is incorporated, and the correction algorithm adjusts the coordinates accordingly to counteract the thermal expansion effect. The final path fully meets the requirements of pattern mapping and ink control, ensuring the reliability of the printing results.

[0108] S107. Drive the digital inkjet printing device to perform pattern printing operation through the final optimized printing path, obtain real-time feedback data to judge whether the ink adhesion is uniform during the printing process, and obtain a complete high-precision three-dimensional curved surface printing result, wherein the result satisfies the personalized gradient effect and fabric comfort.

[0109] The process involves acquiring pattern printing execution data from the digital device driver, including ink adhesion position information. Through preset printing path optimization, the ink adhesion positions in the pattern printing execution data are compared to determine ink adhesion uniformity, resulting in a uniformity evaluation index. Using a real-time feedback acquisition method, ink distribution data is extracted from the uniformity evaluation index to determine ink distribution deviation during the 3D curved surface printing process, obtaining a high-precision result calibration value. Based on the high-precision result calibration value, personalized gradient effect parameters are integrated, and color gradient data is extracted from these parameters. Fabric comfort is adjusted to meet requirements, generating a printing density map. Color penetration control is performed using this printing density map, and the penetration depth in the color penetration control is compared for uniformity to determine gradient transition uniformity, resulting in a 3D curved surface printing result. If the gradient transition uniformity is lower than a preset threshold, the printing path is adjusted according to the ink distribution deviation, and the printing density map is regenerated.

[0110] Specifically, in one implementation, the final optimized printing path is obtained by meshing and path planning the three-dimensional surface model.

[0111] Specifically, the first step is to digitally model the three-dimensional curved surface of the target fabric. Point cloud data of the surface is collected using a scanning device, and then a surface mesh model is generated based on this data. Next, path optimization algorithms, such as those based on minimum path coverage, are applied to calculate the printing path on the mesh model, ensuring that the path covers all areas and avoids overlap. This path planning considers the printhead movement speed and surface curvature variations of the printing equipment, thereby driving the digital inkjet printer to perform the pattern printing operation. In this way, an efficient printing process can be achieved, suitable for printing needs on various textile fabrics. Furthermore, the printing path optimization process includes multiple steps.

[0112] For example, firstly, key points on the surface are calculated, determined based on a curvature threshold, with more path points assigned to high-curvature regions to ensure accuracy. Then, an initial path is generated using dynamic programming, and the path is iteratively optimized to minimize printing time and ink consumption.

[0113] For example, when processing spherical surfaces, the path spirals upwards from the equator, gradually covering the entire surface. This optimization not only improves printing efficiency but also ensures pattern continuity.

[0114] In one possible implementation, the path can further integrate gradient effect parameters, such as adjusting the ink jet density based on a user-customized color gradient model, thereby directly reflecting personalized designs in the printing operation.

[0115] Obtaining real-time feedback data is a crucial step in the printing process.

[0116] Specifically, during operation of the digital inkjet printing equipment, an integrated high-speed camera or optical sensor captures image data of the printing area in real time. This data includes pixel values ​​and reflectivity information of the ink distribution, used to determine whether the ink adhesion is uniform. The judgment process involves image processing techniques, such as calculating the grayscale histogram of the image and analyzing the variance. If the variance is below a preset threshold, it is considered uniform adhesion; otherwise, an adjustment mechanism is triggered. This feedback data is transmitted in real time through the equipment control system, achieving closed-loop control. This method is particularly suitable for the textile printing industry, effectively addressing the challenges posed by uneven fabric texture and ensuring printing quality.

[0117] In one embodiment, the judgment of real-time feedback data further refines the evaluation process of ink adhesion uniformity. First, the data collected by the sensor is converted into digital signals, for example, frequency features are extracted through Fourier transform to identify patterns of uneven adhesion, such as spots or streaks. Then, these features are classified based on a machine learning model, which is pre-trained on similar fabric samples, with image feature vectors as input and uniformity scores as output. The specific process includes a data preprocessing stage, removing noise and extracting edge features; next, the model calculates the probability distribution of adhesion uniformity. If the probability is below 0.8, the system automatically pauses printing and adjusts printhead parameters, such as increasing ink pressure or changing the spray angle. This detailed judgment mechanism ensures high-precision printing, especially when dealing with complex three-dimensional curved surfaces, and can correct deviations in real time to obtain complete results. The innovation of this process lies in the seamless integration of real-time data with the control system, which significantly improves the reliability and accuracy of printing and brings greater fabric adaptability in personalized textile customization.

[0118] Preferably, the high-precision three-dimensional curved surface printing result is a complete output obtained by integrating path optimization and feedback data.

[0119] Specifically, after printing, the system scans and verifies the entire curved surface to ensure no areas are missed and high-precision pattern reproduction. This result particularly emphasizes the achievement of gradient effects, such as a pattern that transitions from dark blue to light blue on fabric, achieved by controlling the ink mixing ratio and printing density. Fabric comfort is ensured by selecting low-penetration inks and optimizing the adhesion process to avoid excessive ink causing fabric stiffness. This method demonstrates versatility in various textile printing scenarios, such as custom clothing or home textiles.

[0120] For example, when printing on tubular fabrics such as sleeves, the printing path can be designed as a wraparound path, with real-time feedback to adjust the ink volume to maintain uniform adhesion. The result satisfies personalized gradient requirements while maintaining the fabric's soft feel. Furthermore, in another implementation, the gradient effect can be personalized through user-input parameters.

[0121] Specifically, users provide a gradient color sequence and a mapped surface area, based on which the system generates printing instructions. During printing, real-time feedback data is used to monitor the smoothness of the gradient transition, such as calculating color gradient values ​​and comparing them with expectations. If the deviation exceeds 5%, the path is fine-tuned. This approach expands the flexibility of the technical solution and is suitable for printing operations on different textile materials.

[0122] Understandably, the fabric comfort assessment results include post-processing steps, such as heat setting to fix the ink, while simultaneously testing the fabric's flexural modulus to ensure it does not exceed standard values. This assessment process objectively verifies the impact of printing on comfort.

[0123] In one possible implementation, the entire printing operation can be scaled up to multi-device collaborative scenarios, such as multiple printheads working in parallel, path optimization algorithms allocating sub-paths, and real-time feedback data aggregation to determine overall uniformity. This scenario demonstrates the application potential of the technical solution in large-scale textile printing.

[0124] Specifically, the realization of high-precision 3D curved surface printing also involves curved surface unfolding technology. First, the 3D curved surface is projected onto a 2D plane, the unfolded diagram is calculated, and then a path is planned on the unfolded diagram and mapped back to 3D space. This process ensures the pattern is distortion-free; for example, when dealing with irregular curved surfaces such as human body models, accuracy is maintained by minimizing projection errors. Feedback data is used at this stage to verify the mapping accuracy; if uneven adhesion is detected, the unfolding parameters are iteratively adjusted. This detailed technical path not only supports the core features of the claims but also provides a general framework for various implementations in the textile field, enhancing the scope of protection of the solution through objective step descriptions.

[0125] The above are only some preferred embodiments of the present invention, but the present invention is not limited thereto, and many improvements and modifications can be made. Any improvements and modifications made based on the basic principles of the present invention should be considered to fall within the protection scope of the present invention.

Claims

1. A method for digitally printing personalized hats based on a three-dimensional curved surface model, characterized in that, The method includes the following steps: S101. Obtain the three-dimensional scanning data of the hat body, and process the data through a surface reconstruction algorithm to obtain a complete three-dimensional surface model, wherein the model contains the geometric features of all curvature variation regions for subsequent analysis; S102. Calculate the local curvature value of each region based on the three-dimensional surface model, and determine the curvature variation distribution map using the Gaussian curvature calculation method, wherein the distribution map indicates the boundary line between high curvature regions and low curvature regions to guide pattern adjustment; S102 further includes: The set of surface point coordinates for each region is obtained from the three-dimensional surface model, and the set of surface point coordinates contains the three-dimensional coordinates of multiple surface points. The Gaussian curvature calculation method is used to obtain the local curvature value of each surface point by calculating the principal curvature product of the coordinates of the surface points; A curvature variation distribution map is generated based on the local curvature values, and the boundary lines of high curvature regions and low curvature regions are marked on the distribution map; The curvature gradient vector is calculated for the boundary line by calculating the difference between the local curvature values ​​on both sides of the boundary line. The smoothness of the region transition is determined by the curvature gradient vector. If the smoothness of the region transition is lower than a preset threshold, the position of the boundary line is adjusted to obtain the adjusted boundary line. A pattern optimization path is generated from the adjusted boundary line, and the pattern optimization path is used to guide the pattern adjustment; S103, the planar pattern is projected onto the curvature change distribution map using a surface mapping algorithm. If the projected pattern is distorted in the high curvature region, the mapping parameters are dynamically adjusted to obtain a non-deformed surface-fitting pattern, wherein the fitted pattern retains the color transition of the original gradient effect; S104, the ink adhesion process is simulated for the surface-fitting pattern, and a diffusion simulation algorithm is used to predict the ink penetration path in different curvature regions. If the predicted path shows that the lateral diffusion exceeds a preset threshold, the ink injection volume is optimized to obtain a diffusion control parameter set, wherein the parameter set includes the ink volume and velocity value of each injection point; S1015, from the expansion... The control parameter set extracts the nozzle motion trajectory data, and a path planning algorithm generates a 3D printing path, wherein the path ensures that the movement of the nozzle on the curved surface is synchronized with the curvature change to avoid positional deviation; S106, if the 3D printing path detects potential misalignment at the connection between the brim and the hat body, a correction algorithm is applied to adjust the trajectory coordinates to obtain the final optimized printing path, wherein the path integrates all requirements for accurate pattern mapping and ink diffusion control; S107, the final optimized printing path drives the digital inkjet printing equipment to perform pattern printing operation, obtains real-time feedback data to determine whether the ink adhesion is uniform during the printing process, and obtains a complete high-precision 3D curved surface printing result, wherein the result satisfies the personalized gradient effect and fabric comfort.

2. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S101 includes: Acquire 3D scan data of the hat body, and extract a point cloud set from the data; The point cloud set is preprocessed by using a filtering algorithm to remove noise, resulting in a first point cloud set. The first point cloud set is processed using a surface reconstruction algorithm to generate a preliminary three-dimensional surface model. For the preliminary three-dimensional surface model, the curvature gradient is calculated, the curvature variation region is identified, and the geometric feature set of the region is obtained; By integrating the set of geometric features, the preliminary three-dimensional surface model is processed using a mesh optimization algorithm to generate a complete three-dimensional surface model containing all curvature variation regions. The complete three-dimensional surface model is smoothed to obtain the final three-dimensional surface model.

3. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S103 includes: Acquire surface geometric data, including a curvature variation distribution map; The locations of high curvature regions are extracted from the curvature variation distribution map. The high curvature regions are those where the curvature value exceeds a preset threshold. If the projected pattern in the high curvature region is distorted, the least squares method is used to adjust the mapping parameters. The least squares method obtains a preliminary fit pattern by minimizing the sum of squared errors and fitting the surface points. Extract color gradient vectors from the initial adapted pattern, wherein the color gradient vectors represent the direction and intensity of color changes in the pattern; Dynamic interpolation is performed on the uneven transition of the color gradient vector in the high curvature region. The dynamic interpolation process calculates the intermediate color value through linear interpolation to obtain a uniform color transition pattern. The texture density distribution is calculated based on the uniform color transition pattern, whereby the texture density distribution represents the distribution density of texture elements in the pattern. If the texture density distribution exceeds a preset threshold, then the neighboring pixel values ​​are merged. The merged neighboring pixel values ​​are then combined by weighted averaging of the colors of adjacent points to obtain a texture-balanced pattern. Obtain the boundary contour of the texture equalization pattern, smooth the boundary contour using a Bezier curve, which generates a smooth path based on control points to obtain the final surface adaptation pattern.

4. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S104 includes: Obtain a surface mesh from surface geometry data, the surface mesh comprising multiple element meshes; The element mesh is processed using the finite element method, and the Gaussian curvature value of each element mesh is calculated to obtain the curvature distribution of the region. Based on the curvature distribution of the region, a diffusion simulation algorithm is used to simulate the ink flow path and obtain ink penetration prediction data. If the lateral diffusion value of the ink penetration prediction data exceeds a preset threshold, the injection volume is adjusted according to the lateral diffusion value, and the volume value adjustment and speed value setting are determined. Based on the volume value adjustment and velocity value setting, adhesion process control parameters and pattern adaptation verification parameters are generated to obtain a diffusion control parameter set. For the aforementioned diffusion control parameter set, the ink adhesion effect is verified, and the diffusion control parameter set is adjusted to obtain an optimized diffusion control parameter set.

5. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S105 includes: The nozzle motion trajectory data is obtained from the diffusion control parameter set, and the trajectory data is processed by the path planning algorithm to obtain a preliminary 3D printing path. Based on the preliminary 3D printing path analysis, the surface curvature changes are analyzed, curvature synchronization adjustment parameters are obtained, and the synchronous mapping relationship between nozzle movement and surface curvature changes is determined. For the synchronous mapping relationship, position deviation risk points are extracted. If the deviation risk points exceed a preset threshold, the path parameters are adjusted to obtain the printing path after deviation correction. Based on the deviation-corrected printing path, the material deposition rate is controlled by fusion material, and the rate value is adjusted using a preset deposition model to generate an interlayer fusion enhancement path. The integrity of the interlayer fusion enhancement path is determined by comparing the consistency between continuous segments of the path and points of curvature change, thus obtaining the final 3D printing path.

6. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S106 includes: The coordinate data of the connection point is obtained from the path misalignment detection, and the degree of potential misalignment is judged by a preset threshold to obtain the misalignment adjustment requirements. To address the aforementioned misalignment adjustment requirement, a coordinate transformation algorithm is applied to adjust the trajectory coordinates. The coordinate transformation algorithm takes the trajectory coordinates and the misalignment adjustment requirement as inputs to obtain the adjusted coordinates. By integrating the precise mapping parameters of the fusion pattern, the adjusted coordinate sequence is determined. Based on the adjusted coordinate sequence, ink diffusion control requirements are integrated to generate optimized printing path data; Using the optimized printing path data, the operating parameters of the printing equipment are adjusted to obtain the final printing path; If the deviation of the final printing path exceeds a preset threshold, the coordinate transformation is recalculated based on the deviation value, and the adjusted coordinate sequence is updated.

7. The personalized hat digital printing method based on a three-dimensional curved surface model according to claim 1, characterized in that, S107 includes: Acquire pattern printing execution data from the digital device driver, the pattern printing execution data including ink adhesion position information; By optimizing the preset printing path, the ink adhesion position of the pattern printing execution data is compared to determine the ink adhesion uniformity and obtain the uniformity evaluation index. By adopting a real-time feedback acquisition method, ink distribution data is extracted from the uniformity evaluation index, and ink distribution deviation is determined during the three-dimensional curved surface printing process to obtain high-precision result calibration values. Based on the high-precision calibration value, the personalized gradient effect parameters are integrated, color gradient data is extracted from the personalized gradient effect parameters, the fabric comfort is adjusted to meet the conditions, and a print density mapping is generated. By mapping the printing density, color penetration control is performed, and the uniformity of the penetration depth in the color penetration control is compared to determine the uniformity of the gradient transition, thus obtaining the three-dimensional curved surface printing result. If the uniformity of the gradient transition is lower than a preset threshold, the printing path is adjusted according to the ink distribution deviation, and the printing density mapping is regenerated.

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