Spraying method for surface of vacuum cup

Abstract

The invention relates to the technical field of spraying of surfaces of vacuum cups, and discloses a spraying method for the surfaces of vacuum cups. The method comprises the following steps: establishing a space coordinate system, collecting a structured light three-dimensional point cloud, mapping the point cloud to a two-dimensional parameter domain, calculating a first-order derivative and a normal vector, further calculating a second-order derivative and a basic form coefficient, extracting a Gaussian curvature and an average absolute curvature, generating a spray point spacing function according to the curvature, generating spray points in the parameter domain, and mapping the spray points into three-dimensional coordinates. And finally, path planning and spraying instruction output are carried out. According to the method, through high-precision non-contact modeling and differential geometric analysis, the geometric change of the curved surface is accurately recognized, self-adaptive adjustment of the spraying point density is guided, the spraying efficiency and uniformity are improved through path optimization, the bottlenecks of a traditional manual or mechanical path setting method in the aspects of spraying uniformity and consistency are broken through, and the method is suitable for large-scale popularization and application. And the device is particularly suitable for intelligent and high-precision spraying operation of personalized products and complex structure surfaces.

Description

Technical Field

[0001] This invention relates to the field of spray coating technology for the surface of thermos cups, specifically a spray coating method for the surface of thermos cups. Background Technology

[0002] Currently, the spraying process for curved containers such as thermos cups mainly relies on manual experience or simple trajectory control, making it difficult to achieve a consistent and precise coating thickness distribution. Traditional spraying methods typically employ a uniform spiral or reciprocating spraying path, maintaining a constant distance between the spray gun and the object surface, spray flow rate, and moving speed. However, significant differences in curvature and surface morphology across different areas result in uneven coating thickness distribution. Especially at edges with high curvature and crank joints, coating accumulation or thinning often occurs, affecting appearance and performance.

[0003] In existing technologies, some spraying systems introduce process compensation, which adjusts the spray thickness by adding local pauses or accelerations to a preset robotic arm trajectory. However, this compensation method relies on human experience or pre-tested data and cannot precisely control each discrete point. Furthermore, conventional systems often use 2D or 3D CAD models to directly generate the spraying path, neglecting detailed analysis of point cloud data. This makes it difficult to dynamically adjust for subtle surface changes, resulting in a lack of overall process adaptability. In the field of digital spraying, existing research has used 3D scanned point clouds for surface reconstruction and performed mesh discretization and surface fitting in a CAD environment to form a discrete parameter domain. However, subsequent spray point generation and path planning still primarily rely on regular meshes or fixed spacing, failing to fully utilize surface geometric information. While point cloud parametric mapping methods can transform discrete 3D coordinates into a unified 2D parameter domain, facilitating meshing operations, without incorporating derivative information such as local curvature, simply uniformly dividing parameters is insufficient to meet the detailed requirements of complex surfaces. Regarding curvature calculation, existing literature uses difference or fitting methods to obtain the first and second derivatives of the surface, and then calculates the Gaussian curvature and mean curvature, attempting to guide the coating thickness distribution. However, in actual spraying, these methods often only remain at the numerical analysis stage, lacking a strategy to directly couple the curvature field with the spray point spacing function, making it difficult to form a closed-loop, integrated spraying control process. Furthermore, existing systems often rely on polynomial fitting or machine learning models to predict the optimal spacing, but the dependence on model training data increases the barrier to industry application. In terms of path planning, commonly used optimization strategies include global or local optimization methods such as genetic algorithms, ant colony algorithms, or simulated annealing algorithms. These methods can optimize the total travel or spraying time under multiple objectives, but they are often computationally expensive and require repeated parameter tuning, making them unsuitable for online adaptive spraying scenarios. In contrast, greedy nearest neighbor or shortest path heuristic algorithms, while computationally simple, fail to embed the curvature-driven spray point spacing into the path generation logic, resulting in insufficient matching between the spraying effect and surface features. Furthermore, existing spraying command outputs typically only include discrete path points and fixed spraying sequences, lacking a refined combination of spray gun movement speed and trigger delay. This leads to asynchrony between tool movement and spray gun activation during the spraying process. This asynchrony not only affects the uniformity of spraying but may also cause over-spraying or missed areas due to delayed spray gun switching.

[0004] Therefore, this project aims to propose a spraying method for the surface of thermos cups, integrating multiple algorithm modules such as 3D scanning, parameter mapping, curvature analysis, adaptive spray point generation, and path planning to form a complete automated spraying system. This solves the problems of uneven spray points, overlapping coatings, or omissions in existing spraying methods when dealing with uneven surfaces, and is particularly suitable for complex surface structures such as thermos cups with cylindrical, arc-shaped transitions, and local micro-curvature variations. Through computer-controlled path planning and spraying control command output, manual intervention can be significantly reduced, improving spray uniformity and surface consistency, and achieving automation and intelligence in industrial-grade customized coating. Summary of the Invention

[0005] This invention provides a spraying method for the surface of a thermos cup, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a spraying method for the surface of a thermos cup, comprising:

[0007] A spatial coordinate system is established and point cloud data of the target object surface is collected. A structured light 3D scanner is used to obtain the discrete point cloud of its surface, wherein the target object is a thermos cup.

[0008] The collected point cloud data is parametrically mapped to establish the correspondence between the point cloud and the two-dimensional parameter domain;

[0009] Calculate the first derivative and normal vector of each point in the parameter domain based on its neighborhood points.

[0010] Further calculations were performed on the second derivative and the coefficients of the basic surface form.

[0011] Calculate the Gaussian curvature and mean absolute curvature at each point;

[0012] The spraying point spacing function is determined based on information such as Gaussian curvature, and the spraying spacing of different areas is generated.

[0013] According to the spray dot spacing function, spray dots are generated in the parameter domain and three-dimensional mapping is performed to obtain the three-dimensional coordinates of the actual spray dots.

[0014] The system performs path planning and outputs spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation.

[0015] Optionally, the step of establishing a spatial coordinate system and acquiring point cloud data of the target object's surface, and using a structured light 3D scanner to obtain its discrete point cloud, specifically includes:

[0016] The surface of the thermos cup is cylindrical;

[0017] The center points of the two circular bases of the thermos are identified and marked as center point 1 and center point 2, respectively. The line connecting center point 1 and center point 2 is perpendicular to the two circular bases.

[0018] Choose the center point of one of the circular bases as the origin of the coordinate system.

[0019] The line connecting the first center point and the second center point is taken as the Z-axis of the coordinate system;

[0020] The X-axis passes through the origin. The horizontal direction points towards the front of the scanner, and the Y-axis is determined by the right-hand rule;

[0021] The discrete point cloud of the cup surface was acquired using a structured light 3D scanner, resulting in the following discrete point set:

[0022] in, The point cloud set is the data collected; N is the total number of points in the point cloud set; P i Let X be the i-th data collection point; i ,Y i Z i Point P i The coordinate values ​​on the X, Y, and Z axes.

[0023] Optionally, the step of parametrically mapping the acquired point cloud data to establish a correspondence between the point cloud and the two-dimensional parameter domain specifically includes:

[0024] Calculate the minimum and maximum heights: Among them, Z min Z is the minimum Z-coordinate of all collected points; max The maximum value of the Z-coordinate of all collected points;

[0025] Set parameter coordinates (u i ,v i ):

[0026] The mapping result is (u i ,v i )∈[0,1]×[0,1], and each (u i ,v i One-to-one correspondence P i ; where u i v is the normalized angle of the i-th point in the horizontal rotation direction; i Here is the normalized height of the i-th point in the vertical direction; arctan2(Y) i ,X i Return point (Y) i ,X iThe angle between the plane and the X-axis.

[0027] Optionally, calculating the first derivative and normal vector of each point based on its neighborhood points in the parameter domain specifically includes:

[0028] In the parameter plane, for each (u i ,v i The six points closest to each other by Euclidean distance are selected to form an index set. in, Let j be the set of neighborhood indices of the i-th point used for difference computation; each j k This is the index of the k-th point in the neighborhood;

[0029] For u j ≠u i v j ≠v i Calculate the directional steering parameter:

[0030] Where, r u r v Given the surface first-order partial derivative approximation vector functions along the u and v directions respectively, output a three-dimensional vector;

[0031] Calculate the surface normal vector: Where n(·) is the unit normal vector function, and the input P i Output a three-dimensional unit vector; ||·|| is the Euclidean norm of the three-dimensional vector.

[0032] Optionally, the further calculation of the second derivative and the surface fundamental form coefficients specifically includes:

[0033] Calculate the second-order finite difference:

[0034]

[0035] Where, r uu r uv r vv These are the second-order partial derivative approximation vector functions, used to calculate the second-order surface changes;

[0036] Calculate the first fundamental form:

[0037] E i =r u (P i )·r u (P i ), F i =r u (P i )·r v (P i ), Gi =r v (P i )·r v (P i );

[0038] Among them, E i F i G i These are the coefficients of the first fundamental form at point i;

[0039] Calculate the second fundamental form:

[0040] L i =n(P i )·r uu (P i M i =n(P i )·r uv (P i ), N i =n(P i )·r vv (P i );

[0041] Among them, L i M i N i These are the coefficients of the second fundamental form at point i.

[0042] Optionally, the calculation of the Gaussian curvature and mean absolute curvature at each point specifically includes:

[0043] Calculate the Gaussian curvature at each point: Among them, K i Let be the Gaussian curvature of the surface at point i;

[0044] Calculate the global mean absolute curvature: Among them, K avg The global mean absolute Gaussian curvature; |K i |For K i Absolute value.

[0045] Optionally, the step of determining the spray dot spacing function based on information such as Gaussian curvature to generate the spray spacing for different regions specifically includes:

[0046] Obtain the diameter of a single droplet from the nozzle, and denote it as D0;

[0047] Let the distance between the spray points at point i be: Among them, s i Let be the spray spacing corresponding to the i-th point.

[0048] Optionally, the step of generating spray points in the parameter domain according to the spray point spacing function and performing three-dimensional mapping to obtain the three-dimensional coordinates of the actual spray points specifically includes:

[0049] Set grid step size Where Δ is the uniform step size for parameter domain meshing;

[0050] Generate parameter points {(u) uniformly in the [0,1]×[0,1] area with a step size Δ. m ,v n )};

[0051] Among them, u m =mΔ,v n = nΔ, and satisfy 0≤u m ,v n ≤1;

[0052] For each grid point (u m ,v n Find the nearest original point index i. * ;

[0053] like Then keep i * ;

[0054] For each retained point, its three-dimensional coordinates are calculated using linear interpolation:

[0055] in, is the interpolated 3D coordinate of the spray point; j is the indexed grid point number;

[0056] Summary of all Forming a set of spray points

[0057] Optionally, the step of performing path planning and outputting spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation specifically includes:

[0058] Calculate the distance between any two spray points: a,b∈{1,2,...,M}; where d ab For spray point and The Euclidean distance between them;

[0059] Select the starting point index j1 = 1;

[0060] In order Generate path sequence

[0061] Let the spray gun move at a constant speed of v. move ;

[0062] For each pair of adjacent spray points Calculate the trigger interval: Where, τ k The time interval for triggering the k-th spraying;

[0063] Output spraying commands in sequence: (X) jk ,Y jk Z jk ,τ k ), k∈{1,2,...,M-1};

[0064] The spraying equipment drives the spray gun to move to (X) jk ,Y jk Z jk And delay τ k Post-coating.

[0065] The present invention has the following beneficial effects:

[0066] 1. An adaptive spatial coordinate system was established based on the structural characteristics of the thermos cup. A structured light 3D scanner was used to accurately acquire surface point cloud data, and the origin and axis directions of the coordinate system were correlated with physical geometric features (the line connecting the center of the bottom surface) to ensure geometric consistency in subsequent parameter processing. Compared to traditional fixed-platform spraying systems, this avoids complex alignment and calibration problems, achieving highly robust modeling with "deformation-free" operation. This strategy significantly improves system adaptability, eliminating the need for recalibration each time. It is applicable to cups of different sizes and tilt angles, or similar structural appliances, providing a stable reference system for the entire digital process and a technological foundation for large-scale automatic identification and processing.

[0067] 2. By mapping 3D point clouds to a 2D parameter domain, a normalized mapping method of "angle + height" is introduced, effectively eliminating the influence of cup height and diameter variations on spraying calculations and exhibiting good scalability. This mapping strategy essentially unfolds irregular curved surfaces into "quasi-rectangular meshes," greatly simplifying subsequent differential calculations and mesh generation. Compared to existing algorithms that require complex surface fitting, this method can achieve geometric control of spray point distribution without constructing a complete mesh structure, offering high computational efficiency and strong stability, making it particularly suitable for real-time industrial processing scenarios. This low-dimensional mapping not only improves algorithm efficiency but also provides a more stable computational space for curvature-based local feature extraction.

[0068] 3. A first-order steering vector calculation method based on local Euclidean neighborhood construction is proposed to estimate surface tangential and normal vectors. Compared with traditional global least squares or surface reconstruction methods, this method's local difference calculation in the parameter domain is more suitable for processing dense but unstructured point cloud data. Its greatest advantage is that it can efficiently obtain point normals without constructing complex topological structures, and is applicable to any local region. As the basis for subsequent second-order derivative and curvature calculations, the normal vector has a direct impact on the adjustment of spray density and path accuracy control. Therefore, the high stability and high accuracy of this module provide key support for the entire system, and it is particularly suitable for scenarios where the product surface has arc transitions or depressions.

[0069] 4. Continuing the idea of ​​local finite difference, this invention introduces the calculation of coefficients for the first and second fundamental forms, constructing a complete differential geometric description framework. This is a rare feature in traditional spraying path design; existing systems often rely on simple heightmap modeling, lacking a precise understanding of surface curvature. This invention accurately characterizes the bending characteristics of surfaces through differential geometry, not only improving the adaptability of spray point arrangement but also providing theoretical support for intelligent identification of areas requiring focused coverage. This structure enables the method to map from structural features to process parameters, enhancing the precision of spraying control.

[0070] 5. By calculating the Gaussian curvature at all points and obtaining the global average absolute curvature, the system introduces for the first time an adaptive spray dot control mechanism based on the intensity of geometric changes. Traditional systems mostly use fixed-spacing grids or rely on empirical formulas to set spray dot density, making it difficult to achieve sufficient coverage in areas with micro-curvature or wasting resources in flat areas. This method adjusts density by curvature-driven adjustment, automatically identifying surface microstructures to achieve the precision-efficiency optimization goal of "densifying necessary areas and sparsening in flat areas." In practical engineering, this on-demand spray dot distribution mechanism can significantly reduce the number of spraying passes and improve spray uniformity, making it particularly suitable for customized coating processes that combine aesthetics and functionality.

[0071] 6. The spray dot generation algorithm dynamically adjusts the spray dot spacing based on local curvature information and precisely sets it in conjunction with the nozzle's physical parameters. This ensures enhanced coating density in areas of micro-curvature and avoids coating breakage or excessive thickness due to surface changes. It innovatively combines two-dimensional parameter domain meshing with curvature-guided filtering, guaranteeing coverage integrity while significantly reducing computational load. Compared to traditional methods of spraying dots at equal diameter intervals, this invention establishes a precise mapping mechanism between spatial distribution and physical realization. The generated spray dot set better matches the actual surface requirements, making it particularly suitable for high-end customized coating tasks or complex surface feature enhancement coating scenarios.

[0072] 7. By calculating the distance between spray points and establishing an approximate shortest path sequence, and combining this with the spray gun's movement speed to derive the trigger time for each pair of spray points, precise time-space coupling control is achieved. Traditional spraying systems often execute sequentially at a fixed speed, neglecting the impact of spatial distance on spraying quality, which easily leads to overlapping or skipped-point spraying problems. This method introduces a TSP-like approach to optimize the path structure and further controls the spray gun's movement rhythm through trigger time intervals, achieving a dynamic balance between spraying quality and efficiency. This has significant implications for applications in intelligent manufacturing, unmanned spraying, and personalized painting. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the process of the present invention.

[0074] Figure 2 This is a schematic diagram of the coordinate system of the present invention.

[0075] In the diagram: 1-Surface of the thermos cup, 2-Origin of the coordinate system, 3-Lower circular base of the thermos cup, 4-Upper circular base of the thermos cup, 5-Z-axis, 6-X-axis, 7-Y-axis, 8-Scanner, 9-Front of the scanner. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] Example, refer to Figure 1 A spraying method for the surface of a thermos cup, comprising:

[0078] A spatial coordinate system is established and point cloud data of the target object surface is collected. A structured light 3D scanner is used to obtain the discrete point cloud of its surface, wherein the target object is a thermos cup.

[0079] The collected point cloud data is parametrically mapped to establish the correspondence between the point cloud and the two-dimensional parameter domain;

[0080] Calculate the first derivative and normal vector of each point in the parameter domain based on its neighborhood points.

[0081] Further calculations were performed on the second derivative and the coefficients of the basic surface form.

[0082] Calculate the Gaussian curvature and mean absolute curvature at each point;

[0083] The spraying point spacing function is determined based on information such as Gaussian curvature, and the spraying spacing of different areas is generated.

[0084] According to the spray dot spacing function, spray dots are generated in the parameter domain and three-dimensional mapping is performed to obtain the three-dimensional coordinates of the actual spray dots.

[0085] The system performs path planning and outputs spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation.

[0086] An automated spraying method for curved surfaces such as thermos cups is proposed. Starting with coordinate system establishment and point cloud acquisition, the method sequentially completes parameter mapping, derivative calculation, curvature analysis, spray dot generation, path planning, and command output, constructing a complete digital spraying process chain. High-precision point cloud information is obtained through structured light scanning, enabling non-contact surface modeling. Parameter mapping transforms complex curved surfaces into an operable two-dimensional parameter domain, facilitating algorithm processing. The degree of surface geometric change is identified by calculating derivatives and curvature information, guiding the distribution of spray dot density. Finally, path planning optimizes the spraying sequence, improving spray gun movement efficiency and reducing spraying errors. This overall process breaks through the traditional method of setting paths manually or using mechanical fixtures, solving problems such as uneven spraying, localized missed spraying, or repeated spraying on curved surfaces. While improving automation, it also enhances spraying quality and consistency, making it suitable for intelligent manufacturing scenarios involving customized products or complex shapes and processes.

[0087] Reference Figure 2 The establishment of a spatial coordinate system and acquisition of point cloud data of the target object's surface, followed by the use of a structured light 3D scanner to obtain its discrete point cloud, specifically includes:

[0088] The surface of the thermos cup is cylindrical;

[0089] The center points of the two circular bases of the thermos are identified and marked as center point 1 and center point 2, respectively. The line connecting center point 1 and center point 2 is perpendicular to the two circular bases.

[0090] Choose the center point of one of the circular bases as the origin of the coordinate system.

[0091] The line connecting the first center point and the second center point is taken as the Z-axis of the coordinate system;

[0092] The X-axis passes through the origin. The horizontal direction points towards the front of the scanner, and the Y-axis is determined by the right-hand rule;

[0093] Establish a unified spatial reference frame to ensure that all subsequent location calculations are performed in the same coordinate system;

[0094] The discrete point cloud of the cup surface was acquired using a structured light 3D scanner, resulting in the following discrete point set:

[0095] in, The point cloud set is the data collected; N is the total number of points in the point cloud set; P i Let X be the i-th data collection point; i ,Y i Z i Point P i The coordinate values ​​of the X, Y, and Z axes are used to obtain the three-dimensional geometric data of the surface, providing the raw input for subsequent curvature and spray point generation.

[0096] This paper describes the specific process of establishing a spatial coordinate system and acquiring point cloud data, including determining the center points of the two bottom surfaces of the thermos cup and constructing a rectangular coordinate system, and acquiring point cloud data using structured light scanning. By combining the product's geometric features (cylindrical cup body and its center line), the 3D spatial positioning task is simplified into a unified spatial reference system construction problem, effectively avoiding the error accumulation problem of traditional manual positioning or physical fixture alignment. The acquired point cloud data accurately reflects the true 3D structure of the thermos cup surface, providing the original geometric input for subsequent parameter mapping and curvature analysis. This step solves the problem of "difficulty in accurately capturing the surface shape of the appliance" in traditional spraying scenarios, while ensuring that different thermos cups have a unified calculation coordinate system in subsequent processes, thereby improving the reusability of the algorithm and the stability of the system, laying the foundation for accurate geometric modeling for the entire intelligent spraying process.

[0097] The parameter mapping of the collected point cloud data to establish the correspondence between the point cloud and the two-dimensional parameter domain specifically includes:

[0098] Calculate the minimum and maximum heights: Among them, Z min Z is the minimum Z-coordinate of all collected points; max The maximum value of the Z-coordinate of all sampling points is used; the vertical coordinate is normalized to eliminate the influence of different cup sizes.

[0099] Set parameter coordinates (u i ,v i ):

[0100] The mapping result is (u i ,v i )∈[0,1]×[0,1], and each (u i ,v i One-to-one correspondence P i ; where u i v is the normalized angle of the i-th point in the horizontal rotation direction; i Here is the normalized height of the i-th point in the vertical direction; arctan2(Y) i ,X i Return point (Y) i ,Xi The angle between the three-dimensional point and the X-axis on the plane; mapping the three-dimensional point to the two-dimensional parameter domain [0,1]×[0,1] facilitates meshing and difference calculation.

[0101] The parametric mapping process involving point cloud data maps 3D point clouds to 2D planar parametric coordinates, achieving normalized representations of angles and heights. This step constructs a 2D parameter domain by setting unified parameter axes (angle θ, normalized height z), thus mapping spatial data onto a computable meshed data structure. On one hand, normalization eliminates the influence of absolute coordinates caused by different thermos cup sizes, making the spraying strategy size-independent and facilitating batch deployment. On the other hand, the 2D parameter domain facilitates subsequent mesh generation, neighborhood search, and derivative calculation, improving algorithm efficiency and reducing implementation difficulty. This method effectively solves the problems of irregular structure and uneven data distribution in 3D point cloud processing, forming a unified input format suitable for numerical differential processing, and providing standardized support for spray density adjustment and path generation.

[0102] The calculation of the first derivative and normal vector of each point based on its neighborhood points in the parameter domain specifically includes:

[0103] In the parameter plane, for each (u i ,v i The six points closest to each other by Euclidean distance are selected to form an index set. in, Let j be the set of neighborhood indices of the i-th point used for difference computation; each j k This provides the index of the k-th point in the neighborhood; it also determines the point set within the local region, providing neighborhood support for finite difference finite differences.

[0104] For u j ≠u i v j ≠v i Calculate the directional steering parameter:

[0105] Where, r u r v The first-order partial derivatives of the surface along the u and v directions are approximate vector functions, and a three-dimensional vector is output. The first-order rate of change of the surface in the u and v directions is calculated and used for subsequent normal vectors and second-order derivatives.

[0106] Calculate the surface normal vector: Where n(·) is the unit normal vector function, and the input P i Output a three-dimensional unit vector; ||·|| is the Euclidean norm of the three-dimensional vector; obtain the surface unit normal vector at point i, which is used for the calculation of the coefficients of the second-order fundamental form.

[0107] This paper introduces a method for selecting neighboring points and calculating the first derivative and normal vector using local Euclidean distance. By constructing an index set of six nearest neighbors for each point in the two-dimensional parameter domain, finite difference calculations can be performed quickly to obtain the first-order guidance of the surface in two directions. This structure not only simplifies the traditional normal vector estimation process based on triangular meshes but also avoids computational instability caused by fitting bias and topological disconnection. The obtained first derivative and normal vector are used to describe the local surface tangential variation trend and normal orientation, which are the basis for curvature calculation and spraying direction control. This method solves the problem of "difficulty in efficiently extracting derivative features from discrete point clouds," thereby improving the surface analysis accuracy and spraying consistency, and is particularly suitable for processing the surfaces of appliances with micro-curved structures.

[0108] The further calculation of the second derivative and the surface fundamental form coefficients specifically includes:

[0109] Calculate the second-order finite difference:

[0110]

[0111] Where, r uu r uv r vv These are second-order partial derivative approximation vector functions, used to calculate the second-order surface change; and to calculate the second-order rate of change of the surface in the parameter domain to obtain surface curvature information.

[0112] Calculate the first fundamental form:

[0113] E i =r u (P i )·r u (P i ), F i =r u (P i )·r v (P i )), G i =r v (P i )·r v (P i );

[0114] Among them, E i F i G i These are the coefficients of the first fundamental form at point i; they describe the inner product between the first-order guiding quantities of the surface and provide the denominator for the curvature formula.

[0115] Calculate the second fundamental form:

[0116] L i =n(P i)·r uu (P i M i =n(P i )·r uv (P i ), N i =n(P i )·r vv (P i );

[0117] Among them, L i M i N i These are the coefficients of the second fundamental form at point i; by combining the second derivative with the normal vector, the second-order bending strength of the surface is extracted and used for curvature calculation.

[0118] The calculation of the second derivative and fundamental form coefficients is described in detail, and a method is proposed to obtain the second-order geometric information of the surface and calculate the first and second fundamental forms using the finite difference method. The first fundamental form provides in-plane metric information to characterize tangential changes, while the second fundamental form combines the second derivative and the normal vector to characterize the bending strength of the surface. This combination establishes a connection between the surface geometry and the spraying strategy. Compared to existing methods that only roughly distribute spray dots based on surface elevation or visual features, this method achieves a foundation for accurately assessing the necessity and density of spray dots based on surface structural changes. Through this technical step, the system can effectively identify areas of severe deformation, predict possible spraying dead zones, and thus dynamically adjust the spraying density and direction to achieve "on-demand spraying," saving materials and improving coating uniformity. It is particularly suitable for coating designs with high aesthetic or functional requirements.

[0119] The calculation of the Gaussian curvature and mean absolute curvature at each point specifically includes:

[0120] Calculate the Gaussian curvature at each point: Among them, K i Let be the Gaussian curvature of the surface at point i; calculate the Gaussian curvature at point i to reflect the local concavity and convexity of the surface;

[0121] Calculate the global mean absolute curvature: Among them, K avg The global mean absolute Gaussian curvature; |K i |For K i Absolute value; yields the global average curvature, used as a scale for subsequent nozzle spacing.

[0122] This paper introduces the calculation methods for Gaussian curvature and global average absolute curvature. By numerically estimating the Gaussian curvature at each point and calculating the mean of the absolute values ​​of curvature at all points, this step provides an objective geometric strength evaluation index for the spraying strategy. Gaussian curvature can accurately identify the "concave" and "convex" areas on the surface of a thermos cup, areas prone to thin coating or buildup in traditional spraying. The average absolute curvature provides a benchmark for evaluating overall complexity, used to normalize the local spray dot spacing function and form a scale. This step mathematically solves problems such as the inability to uniformly quantify spray spacing and unreasonable parameter distribution, providing data support for subsequent refined adjustments and improving the robustness and adaptability of spray dot control.

[0123] The step of determining the spray dot spacing function based on information such as Gaussian curvature to generate the spray spacing for different regions specifically includes:

[0124] Obtain the diameter of a single droplet from the nozzle, denoted as D0; provide a physical dimension reference to ensure that the distance between spray points does not exceed the range of a single droplet.

[0125] Let the distance between the spray points at point i be: Among them, s i Let the distance between the spray dots corresponding to the i-th point be 0; ensure 0. i ≤D0, and the larger the curvature, the smaller the spacing; dynamically adjust the spray spacing of the i-th point according to the curvature, the larger the curvature, the smaller the spacing, to achieve detail enhancement.

[0126] A method for establishing a spray dot spacing function based on local curvature and nozzle physical characteristics is proposed. By setting the single droplet diameter of the nozzle as a physical lower limit, the spray spacing at corresponding points decreases as curvature increases, forming a strategy of "dense spraying at high curvature and sparse spraying at low curvature." This allows for dynamic control of spray dot density, avoiding sparse or misaligned spraying in high curvature areas and ensuring coating continuity and thickness uniformity. Simultaneously, it allows for sparse spraying in flat areas, saving spraying resources and time and improving overall spraying efficiency. Essentially, this method constructs a functional model that maps geometric characteristics to physical control parameters, forming a crucial foundation for intelligent control of spraying process parameters and solving the problems of strong subjectivity and poor adaptability in traditional spray spacing settings.

[0127] The step of generating spray dots within the parameter domain according to the spray dot spacing function and performing three-dimensional mapping to obtain the three-dimensional coordinates of the actual spray dots specifically includes:

[0128] Set grid step size Where Δ is the uniform step size of the parameter domain meshing; the finest step size of the parameter domain meshing is determined to ensure that all local regions can be covered;

[0129] Generate parameter points {(u) uniformly in the [0,1]×[0,1] area with a step size Δ. m ,v​n )};

[0130] Among them, u m =mΔ,v n = nΔ, and satisfy 0≤u m ,v n ≤1; Initially establish the distribution of candidate spray points;

[0131] For each grid point (v) m ,v n Find the nearest original point index i. * ;

[0132] like Then keep i * ;Simplify the grid points according to curvature requirements, retaining only the spray points that meet the spacing constraints;

[0133] For each retained point, its three-dimensional coordinates are calculated using linear interpolation:

[0134] in, is the interpolated 3D coordinate of the spray point; j is the index of the grid point retained by the index; the retained parameter points are mapped back to 3D space to generate the actual spray point coordinates;

[0135] Summary of all Forming a set of spray points Complete the final spray point list to provide input for path planning.

[0136] This paper focuses on how to generate spray points based on the spray point spacing function and perform 3D coordinate back mapping. It proposes operational steps including parameter domain meshing, screening qualified spray points, and interpolation calculation of 3D coordinates. By generating candidate points through uniform step-size meshing and combining curvature constraints to screen and retain points, the number of redundant spray points is minimized while maintaining spray integrity, thus optimizing resource allocation. Linear interpolation back mapping to 3D space ensures that each spray point has accurate position and orientation information, avoiding spray path deviations or structural connection errors. Overall, this technology solves engineering pain points such as uneven spray point distribution, imprecise coordinates, and low generation efficiency, providing accurate input for path planning algorithms and serving as a core link in the intelligent spray control chain.

[0137] The process of path planning and outputting spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation specifically includes:

[0138] Calculate the distance between any two spray points: Where, d ab For spray point and The Euclidean distance between them; the spatial distance between the spray points is quantified to provide a basis for path optimization calculations;

[0139] Select the starting point index j1 = 1;

[0140] In order Generate path sequence Access all spray points using the shortest possible path, reducing mechanical movement time;

[0141] Let the spray gun move at a constant speed of v. move Provides spray gun motion parameters, which are combined with distance to generate trigger timing;

[0142] For each pair of adjacent spray points Calculate the trigger interval: Where, τ k Let k be the time interval for triggering the spraying; calculate the spraying trigger delay between two spray points to ensure uniform motion;

[0143] Output spraying commands in sequence: (X) jk ,Y jk Z jk ,τ k ), k∈{1,2,...,M-1}; output device can parse action sequences to achieve precise spraying control;

[0144] The spraying equipment drives the spray gun to move to (X) jk ,Y jk Z jk And delay τ k Post-coating.

[0145] This paper proposes a spray gun control method involving spray path planning and control command output. This method involves steps such as calculating the Euclidean distance between spray points, path sorting, generating trigger time intervals, and command output. By using path shortest-length sorting, spray gun movement redundancy can be minimized, increasing spraying speed. Combining spray gun speed with the calculation of trigger delays based on the distance between spray points achieves uniform speed control and precise alignment, ensuring consistent spray coverage. Finally, standardized spraying commands are output, enabling direct interface and efficient collaboration with the equipment. This solution effectively solves problems such as blind spraying, intermittent spraying, and command disconnection in traditional systems, and is an indispensable component for realizing end-to-end automated spraying systems.

[0146] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0147] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A spraying method for the surface of a thermos cup, characterized in that, include: A spatial coordinate system is established and point cloud data of the target object surface is collected. A structured light 3D scanner is used to obtain the discrete point cloud of its surface, wherein the target object is a thermos cup. The collected point cloud data is parametrically mapped to establish the correspondence between the point cloud and the two-dimensional parameter domain; Calculate the first derivative and normal vector of each point in the parameter domain based on its neighborhood points. Further calculations were performed on the second derivative and the coefficients of the basic surface form. Calculate the Gaussian curvature and mean absolute curvature at each point; The spraying point spacing function is determined based on information such as Gaussian curvature, and the spraying spacing of different areas is generated. According to the spray dot spacing function, spray dots are generated in the parameter domain and three-dimensional mapping is performed to obtain the three-dimensional coordinates of the actual spray dots. The system performs path planning and outputs spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation.

2. The spraying method for the surface of a thermos cup according to claim 1, characterized in that, The process of establishing a spatial coordinate system and acquiring point cloud data of the target object's surface, using a structured light 3D scanner to obtain its discrete point cloud, specifically includes: The surface of the thermos cup is cylindrical; The center points of the two circular bases of the thermos are identified and marked as center point 1 and center point 2, respectively. The line connecting center point 1 and center point 2 is perpendicular to the two circular bases. Choose the center point of one of the circular bases as the origin of the coordinate system. The line connecting the first center point and the second center point is taken as the Z-axis of the coordinate system; The X-axis passes through the origin. The horizontal direction points towards the front of the scanner, and the Y-axis is determined by the right-hand rule; The discrete point cloud of the cup surface was acquired using a structured light 3D scanner, resulting in the following discrete point set: P i =(X i ,Y i Z i ), i = {1, 2, ..., N}; where, The point cloud set is the data collected; N is the total number of points in the point cloud set; P i Let X be the i-th data collection point; i ,Y i Z i Point P i The coordinate values ​​on the X, Y, and Z axes.

3. The spraying method for the surface of a thermos cup according to claim 2, characterized in that, The parameter mapping of the collected point cloud data to establish the correspondence between the point cloud and the two-dimensional parameter domain specifically includes: Calculate the minimum and maximum heights: Among them, Z min Z is the minimum Z-coordinate of all collected points; max The maximum value of the Z-coordinate of all collected points; Set parameter coordinates (u i ,v i ): The mapping result is (u i ,v i )∈[0,1]×[0,1], and each (u i ,v i One-to-one correspondence P i ; where u i v is the normalized angle of the i-th point in the horizontal rotation direction; i Here is the normalized height of the i-th point in the vertical direction; arctan2(Y) i ,X i Return point (Y) i ,X i The angle between the plane and the X-axis.

4. The spraying method for the surface of a thermos cup according to claim 3, characterized in that, The calculation of the first derivative and normal vector of each point based on its neighborhood points in the parameter domain specifically includes: In the parameter plane, for each (u i ,v i The six points closest to each other by Euclidean distance are selected to form an index set. in, Let j be the set of neighborhood indices of the i-th point used for difference computation; each j k This is the index of the k-th point in the neighborhood; For u j ≠u i u j ≠v i Calculate the directional steering amount of the parameters: Where, r u r v Given the surface first-order partial derivative approximation vector functions along the u and v directions respectively, output a three-dimensional vector; Calculate the surface normal vector: Where n(·) is the unit normal vector function, and the input P i Output a three-dimensional unit vector; ||·|| is the Euclidean norm of the three-dimensional vector.

5. A spraying method for the surface of a thermos cup according to claim 4, characterized in that, The further calculation of the second derivative and the surface fundamental form coefficients specifically includes: Calculate the second-order finite difference: Where, r uu r uv r vv These are the second-order partial derivative approximation vector functions, used to calculate the second-order surface changes; Calculate the first fundamental form: E i =r u (P i )·r u (P i ),F i =r u (P i )·r u (P i ),G i =r v (P i )·r v (P i ); Among them, E i F i G i These are the coefficients of the first fundamental form at point i; Calculate the second fundamental form: L i =n(P i )·r uu (P i ),M i =n(P i )·r uv (P i ),N i =n(P i )·r vv (P i ); Among them, L i M i N i These are the coefficients of the second fundamental form at point i.

6. A spraying method for the surface of a thermos cup according to claim 5, characterized in that, The calculation of the Gaussian curvature and mean absolute curvature at each point specifically includes: Calculate the Gaussian curvature at each point: Among them, K i Let be the Gaussian curvature of the surface at point i; Calculate the global mean absolute curvature: Among them, K avg The global mean absolute Gaussian curvature; |K i |For K i Absolute value.

7. A spraying method for the surface of a thermos cup according to claim 6, characterized in that, The step of determining the spray dot spacing function based on information such as Gaussian curvature to generate the spray spacing for different regions specifically includes: Obtain the diameter of a single droplet from the nozzle, and denote it as D0; Let the distance between the spray points at point i be: Among them, s i Let be the spray spacing corresponding to the i-th point.

8. A spraying method for the surface of a thermos cup according to claim 7, characterized in that, The step of generating spray dots within the parameter domain according to the spray dot spacing function and performing three-dimensional mapping to obtain the three-dimensional coordinates of the actual spray dots specifically includes: Set grid step size Where Δ is the uniform step size for parameter domain meshing; Generate parameter points {(u) uniformly in the [0,1]×[0,1] area with a step size Δ. m ,v n )}; Among them, u m =mΔ,v n = nΔ, and satisfy 0≤u m ,v n ≤1; For each grid point (u m ,v n Find the nearest original point index i. * ; like Then keep i * ; For each retained point, its three-dimensional coordinates are calculated using linear interpolation: in, is the interpolated 3D coordinate of the spray point; j is the indexed grid point number; Summary of all Form a spray point set 9. A spraying method for the surface of a thermos cup according to claim 8, characterized in that, The process of path planning and outputting spraying instructions to guide the spray gun to move at a constant speed in a predetermined sequence and perform the spraying operation specifically includes: Calculate the distance between any two spray points: a,b∈{1,2,...,M}; where d ab For spray point and The Euclidean distance between them; Select the starting point index j1 = 1; In order Generate path sequence Let the spray gun move at a constant speed of v. move ; For each pair of adjacent spray points Calculate the trigger interval: Where, τ k The time interval for triggering the k-th spraying; Output spraying commands in sequence: ( τ k k∈{1,2,...,M-1); The spray gun is driven to move by the spraying equipment to And delay τ k Post-coating.

Images