Femtosecond laser processing method based on micro-nano array attachment

Abstract

The invention belongs to the technical field of laser application, and relates to a femtosecond laser processing method based on micro-nano array attachment, which comprises the following steps of: 1) acquiring a three-dimensional curved surface workpiece to be processed; 2) extracting a target curved surface on the surface of the three-dimensional model, performing discretization processing, and generating a triangular patch mesh model; 3) performing shape fidelity mapping to a two-dimensional plane domain to obtain a two-dimensional plane model; 4) importing a two-dimensional processing array and carrying out Boolean intersection operation on the two-dimensional processing array to obtain a public area of the two-dimensional plane model and the two-dimensional processing array; 5) performing triangulation processing to obtain a plane region before inverse mapping; 6) mapping to a three-dimensional space to obtain an attached and segmented three-dimensional model; 7, a laser machining path is generated, and femtosecond laser machining is conducted on the three-dimensional curved surface workpiece to be machined through the laser machining path. According to the femtosecond laser machining method, the calculation complexity can be reduced, the expression accuracy of the two-dimensional micro-nano array attachment pattern boundary in the three-dimensional space can be improved, and different machining requirements can be flexibly met.

Description

Femtosecond laser processing method based on micro / nano array attachment Technical Field

[0001] This invention belongs to the field of laser application technology and relates to a femtosecond laser processing method based on micro-nano array attachment, and more particularly to a femtosecond laser processing method based on micro-nano array attachment for complex curved surfaces. Background Technology

[0002] In the field of femtosecond laser processing, complex functional surfaces composed of numerous micron- and nano-scale micro-units have become key carriers for advanced optical devices and electronic systems. The final performance of such surfaces directly depends on the accurate reproduction of the theoretically designed configuration by a large number of micro- and nano-arrays. In such applications, one of the core steps is to precisely attach a pre-defined two-dimensional processing array pattern to the surface of a three-dimensional model, and then segment and fill it to ultimately generate a controllable laser processing path. To this end, the industry has drawn on texture mapping technology from computer graphics, which essentially involves "attaching" two-dimensional graphics to the surface of a three-dimensional model through a specific mapping function.

[0003] However, existing methods mostly rely on direct projection attachment or general model parameterization. These methods lack active control over the geometric properties of the array during the mapping process. When the curvature of the surface changes drastically, it can lead to unexpected stretching and compression distortion of the two-dimensional array after projection, resulting in a severe deterioration in the dimensional accuracy and geometric shape reproduction accuracy (shape fidelity) of the processed pattern. Therefore, existing technologies cannot meet the requirements of high-precision femtosecond laser processing applications for shape fidelity and dimensional accuracy of micro / nano arrays. There is an urgent need for an innovative processing method that can ensure high shape fidelity reproduction of micro / nano arrays on three-dimensional curved surfaces through controllable shape fidelity mapping and precise inverse mapping. Summary of the Invention

[0004] To address the aforementioned technical problems in the background art, this invention provides a femtosecond laser processing method based on micro-nano array attachment that can reduce computational complexity, improve the accuracy of representing the graphical boundaries of two-dimensional micro-nano array attachments in three-dimensional space, and flexibly meet different processing requirements.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a femtosecond laser processing method based on micro-nano array attachment, characterized in that: the femtosecond laser processing method based on micro-nano array attachment includes the following steps: 1) obtaining a three-dimensional curved surface workpiece to be processed; 2) extracting the target surface of the three-dimensional model of the three-dimensional curved surface workpiece obtained in step 1), performing discretization processing, and generating a triangular facet mesh model; 3) performing shape-fidelity mapping of the triangular facet mesh model to a two-dimensional planar domain to obtain a two-dimensional planar model; 4) importing a two-dimensional processing array into the two-dimensional planar model and performing Boolean intersection operation on the two to obtain the common area of ​​the two-dimensional planar model and the two-dimensional processing array; 5) performing triangulation processing on the common area obtained in step 4) to obtain the planar area before inverse mapping; 6) mapping the planar area before inverse mapping obtained in step 5) to three-dimensional space to obtain a three-dimensional model with attachment segmentation; 7) generating a laser processing path based on the three-dimensional model with attachment segmentation obtained in step 6), and using the laser processing path to perform femtosecond laser processing on the three-dimensional curved surface workpiece to be processed.

[0006] The specific implementation of step 2) above is as follows: 2.1) Obtain the target surface M of the three-dimensional model of the workpiece to be processed from step 1); 2.2) Use a high-precision triangulation algorithm to discretize the target surface M to generate a triangular mesh model M. 3D The triangular mesh model M 3D It is composed of numerous triangular facets.

[0007] The specific implementation method of step 3) above is as follows: 3.1) Select the mapping method; the mapping method is angle-preserving mapping or area-preserving mapping; 3.2) Apply the triangular mesh model M obtained in step 2) to the mapping method. 3D Mapping onto the two-dimensional planar domain D, construct the vertices P of each triangular facet on the three-dimensional surface. 3D And the point P mapped onto the two-dimensional plane 2D The one-to-one correspondence between them yields a two-dimensional planar model; the vertex P of the triangular facet... 3D The coordinates of point P on the two-dimensional plane are (x, y, z). 2D The coordinates are (u, v).

[0008] The specific implementation of step 4) above is as follows: 4.1) Establish a two-dimensional coordinate system in the two-dimensional planar domain D; 4.2) Import the two-dimensional micro / nano array G into the two-dimensional coordinate system obtained in step 4.1), and align the two-dimensional micro / nano array G with the two-dimensional planar model obtained in step 3) to obtain the oriented two-dimensional micro / nano array G'; 4.3) Perform a Boolean intersection operation between the oriented two-dimensional micro / nano array G' obtained in step 4.2) and the two-dimensional planar domain D to obtain the common area G of the two-dimensional planar model and the two-dimensional array. clip .

[0009] The specific implementation of step 4.1) above is as follows: 4.1.1) Define the two-dimensional planar domain D as an effective strobe attachment region; 4.1.2) Use the theoretical center point of the effective strobe attachment region obtained in step 4.1.1) or a preset corner point as the origin D0 (x0, y0) to establish a two-dimensional coordinate system.

[0010] The specific implementation of step 4.2) above is as follows: 4.2.1) Input the two-dimensional micro / nano array G to be attached; 4.2.2) Calculate the offset vector between the geometric center point G(x', y') of the two-dimensional micro / nano array G and the coordinate origin D0(x0, y0) of the two-dimensional planar domain D; 4.2.3) Based on the offset vector obtained in step 4.2.2), translate the two-dimensional micro / nano array G as a whole so that the reference point of the two-dimensional micro / nano array G is precisely aligned with the coordinate origin D0 of the two-dimensional planar domain D; the reference point is the geometric center point G(x', y') in step 4.2.2); 4.2.4) Rotate the two-dimensional micro / nano array G that has been aligned with the coordinate origin D0 of the two-dimensional planar domain D to obtain the oriented two-dimensional micro / nano array G'.

[0011] The specific implementation of step 4.3 above is as follows: perform a Boolean intersection operation between the oriented two-dimensional micro / nano array G' and the two-dimensional planar domain D, discard the part falling outside the effective region, and finally obtain the common region G of the two-dimensional planar model and the two-dimensional fabricated array. clip .

[0012] The specific implementation method of step 5) above is as follows: 5.1) For the common area G of the two-dimensional planar model and the two-dimensional machining array clip Perform triangulation constraints; 5.2) Divide the result of the triangulation constraints into a set of several non-overlapping two-dimensional triangles. The set constitutes a planar region before the inverse mapping.

[0013] The specific implementation method of step 6) above is as follows: 6.1) Select any two-dimensional triangle T obtained in step 5.2). 2d Based on the vertices P of each triangular facet on the three-dimensional surface obtained in step 3.2), 3D And the point P mapped onto the two-dimensional plane 2D Find the one-to-one correspondence between them and the two-dimensional triangle T. 2d The three vertices of the given triangle correspond to the three 3D vertices in the original 3D mesh, which in turn determine a corresponding curved triangle T in 3D space. 3d 6.2) For triangle T lying on the curved surface 3d For the internal vertices, calculate the corresponding positions of the vertices in three-dimensional space using the centroid interpolation method; 6.3) Based on the corresponding positions obtained in step 6.2), construct the two-dimensional triangle T. 2dThe corresponding planar region before inverse mapping is mapped to three-dimensional space; 6.4) Repeat steps 6.1) to 6.3) to traverse all two-dimensional triangles T of the planar region before inverse mapping. 2d All planar regions before inverse mapping are mapped to three-dimensional space, ultimately obtaining a three-dimensional model with attachment and segmentation; preferably, the specific implementation of step 6.2) is as follows: 6.2.1) Let a two-dimensional triangle T 2d The vertex coordinates are A 2d B 2d C 2d Two-dimensional triangle T 2d The points corresponding to the vertices on the three-dimensional surface are A and B, respectively. 3d B 3d C 3d 6.2.2) For a two-dimensional triangle T 2d Any point P inside 2d Calculate the value of any point relative to A. 2d B 2d C 2d If the centroid coordinates (α, β, γ) are given, then the corresponding point P in three-dimensional space is given by this arbitrary point. 3d From the same centroid coordinates at A 3d B 3d C 3d The value of the insertion is: P 3d =α×A 3d +β×B 3d +γ×C 3d .

[0014] The specific implementation method of step 7) above is as follows: 7.1) For the 3D model obtained by attachment segmentation in step 6), the closed contour of the points generated after attachment is used as the boundary constraint for automatic segmentation processing, and the complex 3D model of attachment segmentation is divided into a series of independent sub-regions that do not overlap with each other and have clear boundaries, so as to realize the accurate block division of the 3D model of attachment segmentation; 7.2) Based on step 7.1), a laser processing path with high shape fidelity on the surface of the 3D model is obtained, and the laser processing path is exported as a standard path file format; 7.3) The laser processing path obtained in step 7.2) is imported into the femtosecond laser processing CNC system, and the 3D curved surface workpiece to be processed is processed by the femtosecond laser processing CNC system.

[0015] The advantages of this invention are: This invention provides a femtosecond laser processing method based on micro / nano array attachment, comprising: 1) acquiring a three-dimensional curved surface workpiece to be processed; 2) extracting the target surface of the three-dimensional model of the three-dimensional curved surface workpiece obtained in step 1), performing discretization processing, and generating a triangular facet mesh model; 3) performing shape-fidelity mapping of the triangular facet mesh model to a two-dimensional planar domain to obtain a two-dimensional planar model; 4) importing a two-dimensional processing array into the two-dimensional planar model and performing Boolean intersection operation on the two to obtain the common area of ​​the two-dimensional planar model and the two-dimensional processing array; 5) performing triangulation processing on the common area obtained in step 4) to obtain the planar area before inverse mapping; 6) mapping the planar area before inverse mapping obtained in step 5) to three-dimensional space to obtain an attached and segmented three-dimensional model; 7) generating a laser processing path based on the attached and segmented three-dimensional model obtained in step 6), and using the laser processing path to perform femtosecond laser processing on the three-dimensional curved surface workpiece to be processed. This invention supports uniform processing of arbitrary free-form and composite surfaces without relying on specific surface types for attachment strategies. Its core principle is to prevent distortion of micro / nano array patterns through a dimensionality reduction-dimensional expansion shape fidelity strategy, ensuring that the shape, size proportions, and relative positional relationships of the processed pattern on the 3D model remain highly consistent with the original design. After achieving high shape fidelity 3D attachment of the micro / nano array pattern, this invention needs to discretize the complex 2D array into physical motion trajectories that can be precisely and continuously executed by the laser galvanometer. This invention automatically and optimally divides the attached model into a series of non-overlapping, seamlessly connected line segments or filled regions strictly constrained within the surface boundaries through constrained triangulation and center coordinate interpolation. Furthermore, by performing triangulation and constraint processing on the planar region after Boolean intersection operations, this invention generates a series of seamless, continuous laser scanning paths strictly confined within the processing area, avoiding path breakage or out-of-bounds processing, thus ensuring the accurate implementation of the attachment results from the execution level. Clearly, the femtosecond laser processing method based on micro / nano array attachment provided by this invention actively selects a specific mathematical mapping method according to processing requirements, reducing complex three-dimensional spatial calculations to a two-dimensional planar domain for processing. Precise positioning and trimming within the two-dimensional plane ensures the expected position and orientation of the micro / nano array on the curved surface. Re-constraining triangulation within the plane ensures that the boundaries of the micro / nano array pattern are not destroyed during the inverse mapping process, maintaining the integrity and shape fidelity of the micro / nano array pattern distribution. Flattening the complex three-dimensional model into a two-dimensional plane allows for intuitive and precise positioning of the micro / nano array pattern to the designated area, reducing computational complexity. Re-triangulation in the two-dimensional plane ensures that the vertices of the trimmed micro / nano array pattern all serve as vertices of triangles, avoiding interpolation errors caused by elongated triangles and ensuring the accuracy of the two-dimensional micro / nano array attachment pattern boundary representation in three-dimensional space. Based on the theory of triangular meshes and shape-fidelity mapping, it can handle arbitrarily complex free-form surface models, and by autonomously selecting the unfolding algorithm, it can flexibly respond to different processing requirements. Attached Figure Description

[0016] Figure 1 is an overall flowchart of the femtosecond laser processing method based on micro / nano array attachment provided by the present invention; Figure 2 is a flowchart of the micro / nano array attachment algorithm used in the present invention; Figure 3 is a schematic diagram of the three-dimensional model and the mesh model generated by discretization processing used in the present invention; Figure 4 is a schematic diagram of mapping the model to a two-dimensional plane using the conformal parameterization method used in the present invention; Figure 5 is a schematic diagram of performing Boolean intersection and clipping between the flattened plane model and the array to be attached in the present invention; Figure 6 is a schematic diagram of re-triangulating the clipped model in the present invention; Figure 7 is a schematic diagram of inversely mapping the two-dimensional plane attached array graphic back to three-dimensional space to generate a three-dimensional attached model in the present invention. Detailed Implementation

[0017] The present invention will be further described below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0018] Existing methods for attaching 2D micro / nano array patterns to 3D model surfaces require high-precision 3D models. While these methods achieve high accuracy on surfaces with minimal curvature changes or standard curved surfaces, they suffer from problems when attaching to free-form surfaces or areas with high curvature. This leads to changes in the relative angles between features within the micro / nano array pattern, causing deformation at line intersections, compromising the geometric accuracy of the micro / nano array pattern, and failing to accurately fit the surface boundaries, resulting in reduced processing accuracy and consistency. This invention provides a femtosecond laser processing method based on micro / nano array attachment. This method performs controllable shape-fidelity mapping of 2D micro / nano arrays onto the 3D model surface, processes the array pattern and model in 2D space, and finally inversely maps it back to 3D space, achieving high shape-fidelity attachment of the 2D micro / nano array pattern. Through constrained triangulation and center coordinate interpolation, the attached model is automatically and optimally segmented into a series of non-overlapping, seamlessly connected line segments or filled regions strictly constrained within the surface boundaries. By performing triangulation and constraint processing on the planar region after Boolean intersection operation, a series of seamless, continuous and strictly limited femtosecond laser scanning paths are generated within the processing area. Based on the femtosecond laser processing method based on micro-nano array attachment provided by this invention, the continuity and processing accuracy of freeform surface laser processing can be improved.

[0019] Referring to Figure 1, the femtosecond laser processing method based on micro / nano array attachment provided by this invention includes: 1) acquiring a three-dimensional curved surface workpiece to be processed; 2) extracting the target surface of the three-dimensional model of the workpiece obtained in step 1), discretizing it, and generating a triangular mesh model, as shown in Figure 3. This step aims to flatten the complex three-dimensional curved surface model into a two-dimensional parametric plane and establish a precise correspondence, laying the geometric foundation for subsequent array attachment processing. Specifically:

[0020] 2.1) Obtain the target surface M of the 3D model of the workpiece to be processed from step 1); 2.2) Discretize the target surface M using a high-precision triangulation algorithm to generate a triangular mesh model M. 3D Triangular mesh model M 3D It is composed of numerous triangular facets, and based on this mesh model M 3D This yields a set of triangular facets and the vertex coordinates of each triangular facet.

[0021] 3) The triangular mesh model is shape-preservingly mapped to a two-dimensional planar domain, as shown in Figure 4, resulting in a two-dimensional planar model. Specifically: 3.1) Select the mapping method; the mapping method is angle-preserving mapping or area-preserving mapping; select the core requirement for angle-preserving mapping or area-preserving mapping based on the processing requirements, and choose the corresponding mapping method: angle-preserving mapping is suitable for processing scenarios that require strictly maintaining the local angles of the elements to minimize angular distortion. Area-preserving mapping is suitable for scenarios with strict requirements on the element area, striving to ensure that the area of ​​each element in the two-dimensional parameter domain is proportional to its physical model on the three-dimensional curved surface.

[0022] 3.2) The triangular mesh model M obtained in step 2) 3D Mapping onto the two-dimensional planar domain D, construct the vertices P of each triangular facet on the three-dimensional surface. 3D And the point P mapped onto the two-dimensional plane 2D The one-to-one correspondence between them yields a two-dimensional planar model; the vertex P of the triangular facet. 3D The coordinates of point P on the two-dimensional plane are (x, y, z). 2D The coordinates are (u, v).

[0023] 4) Referring to Figure 2, import the two-dimensional machining elements into the two-dimensional planar model and perform a Boolean intersection operation on the two to obtain the common area of ​​the two-dimensional planar model and the two-dimensional machining elements. Specifically, this includes: 4.1) Establishing a two-dimensional coordinate system in the two-dimensional planar domain D, specifically: 4.1.1) Defining the two-dimensional planar domain D as the effective element attachment area; 4.1.2) Using the theoretical center point of the effective element attachment area obtained in step 4.1.1) or a preset corner point (such as the lower left point) as the origin D0 (x0, y0) to establish a two-dimensional coordinate system.

[0024] 4.2) Import the two-dimensional micro / nano array G into the two-dimensional coordinate system constructed in step 4.1), and align the two-dimensional micro / nano array G with the two-dimensional planar model obtained in step 3) to obtain the oriented two-dimensional micro / nano array G'. Specifically: 4.2.1) Input the two-dimensional micro / nano array G to be attached; 4.2.2) Calculate the offset vector between the geometric center point G(x', y') of the two-dimensional micro / nano array G and the origin D0(x0, y0) of the two-dimensional planar domain D; 4.2.3 Based on the offset vector obtained in step 4.2.2), the two-dimensional micro-nano array G is translated as a whole so that the reference point of the two-dimensional micro-nano array G is precisely aligned with the origin D0 of the coordinate system of the two-dimensional planar domain D; where the reference point is the geometric center point G(x', y') of step 4.2.2); 4.2.4) According to the processing requirements, a rotation angle is input to rotate the two-dimensional micro-nano array G that has been aligned with the origin D0 of the coordinate system of the two-dimensional planar domain D, so as to obtain the oriented two-dimensional micro-nano array G'.

[0025] 4.3) Referring to Figure 5, perform a Boolean intersection operation between the oriented two-dimensional micro / nano array G' obtained in step 4.2) and the two-dimensional planar domain D, discarding the parts falling outside the effective area to ensure that the final attached pattern is strictly within the surface boundary. Depending on the processing requirements, choose to retain or remove the processing array to obtain the common area G of the two-dimensional planar model and the two-dimensional processing array. clip For example, it could be: performing a Boolean intersection operation between the oriented two-dimensional micro / nano array G' and the two-dimensional planar domain D, discarding the portion falling outside the effective region, and finally obtaining the common region G of the two-dimensional planar model and the two-dimensional fabricated array. clip .

[0026] 5) Triangulate the common region obtained in step 4) to obtain the planar region before inverse mapping, as shown in Figure 6. Specifically, this includes: 5.1) Triangulating the common region G between the two-dimensional planar model and the two-dimensional machining array. clip Perform triangulation constraints; it should be noted that the constraints here refer to the requirement that G must be set during the triangulation process. clip All boundary line segments are used as constraint edges to ensure that these boundaries are not split or crossed during the partitioning process, thereby strictly maintaining the geometric contour of the processing area.

[0027] 5.2) Divide the result of the triangulation constraint into a set of several non-overlapping two-dimensional triangles. The set constitutes a planar region before the inverse mapping.

[0028] 6) Map the planar region obtained in step 5) before inverse mapping to three-dimensional space to obtain the attached segmented three-dimensional model, as shown in Figure 7. Specifically: 6.1) Select any two-dimensional triangle T obtained in step 5.2). 2dBased on the vertices P of each triangular facet on the three-dimensional surface obtained in step 3.2), 3D And the point P mapped onto the two-dimensional plane 2D Find the one-to-one correspondence between them and the two-dimensional triangle T. 2d The three vertices of the given triangle correspond to the three 3D vertices in the original 3D mesh, which in turn determine a corresponding curved triangle T in 3D space. 3d 6.2) For triangle T lying on the curved surface 3d For the internal vertices, the corresponding positions of the vertices in three-dimensional space are calculated using the centroid interpolation method. For example, this step can be performed as follows: 6.2.1) Let a two-dimensional triangle T 2d The vertex coordinates are A 2d B 2d C 2d Two-dimensional triangle T 2d The points corresponding to the vertices on the three-dimensional surface are A and B, respectively. 3d B 3d C 3d 6.2.2) For a two-dimensional triangle T 2d Any point P inside 2d Calculate the value of any point relative to A. 2d B 2d C 2d If the centroid coordinates (α, β, γ) are given, then the corresponding point P in three-dimensional space is given by this arbitrary point. 3d From the same centroid coordinates at A 3d B 3d C 3d The value of the insertion is: P 3d =α×A 3d +β×B 3d +γ×C 3d .

[0029] 6.3) Based on the corresponding positions obtained in step 6.2), the two-dimensional triangle T 2d The corresponding planar region before inverse mapping is mapped to three-dimensional space; 6.4) Repeat steps 6.1) to 6.3) to traverse all two-dimensional triangles T of the planar region before inverse mapping. 2d7) Based on the three-dimensional model obtained in step 6), a laser processing path is generated, and the three-dimensional curved surface workpiece to be processed is processed using femtosecond laser. Specifically, this includes: 7.1) For the three-dimensional model obtained in step 6), the closed contour of the points generated after attachment is used as boundary constraints for automatic segmentation processing, dividing the complex three-dimensional model into a series of independent sub-regions that do not overlap and have clear boundaries, thereby achieving accurate block division of the three-dimensional model; 7.2) Based on step 7.1), a high shape fidelity laser processing path is generated on the surface of the three-dimensional model, and the laser processing path is exported as a standard path file format (such as G code, NC code); 7.3) The laser processing path obtained in step 7.2) is imported into the femtosecond laser processing CNC system, and the three-dimensional curved surface workpiece to be processed is processed through the femtosecond laser processing CNC system. For example, the femtosecond laser processing CNC system sets and calls the corresponding laser process parameters according to the material properties and processing requirements. Under the coordinated control of a multi-axis linkage laser processing machine tool or a galvanometer scanning system, high-shape fidelity micro-nano arrays are precisely etched on real three-dimensional curved workpieces.

Claims

1. A femtosecond laser processing method based on micro / nano array attachment, characterized in that: The femtosecond laser processing method based on micro / nano array attachment includes the following steps: 1) acquiring the three-dimensional curved surface workpiece to be processed; 2) extracting the target surface of the three-dimensional model of the three-dimensional curved surface workpiece obtained in step 1), discretizing it, and generating a triangular mesh model; 3) mapping the triangular mesh model to a two-dimensional planar domain with shape fidelity to obtain a two-dimensional planar model; 4) importing two-dimensional processing arrays into the two-dimensional planar model and performing Boolean intersection operation on the two to obtain the common area of ​​the two-dimensional planar model and the two-dimensional processing arrays; 5) performing triangulation on the common area obtained in step 4) to obtain the planar area before inverse mapping; 6) mapping the planar area before inverse mapping obtained in step 5) to three-dimensional space to obtain the attached segmented three-dimensional model; 7) generating a laser processing path based on the attached segmented three-dimensional model obtained in step 6), and using the laser processing path to perform femtosecond laser processing on the three-dimensional curved surface workpiece to be processed.

2. The femtosecond laser processing method based on micro / nano array attachment according to claim 1, characterized in that: The specific implementation of step 2) is as follows: 2.1) Obtain the target surface M of the three-dimensional model of the workpiece to be processed from step 1); 2.2) Use a high-precision triangulation algorithm to discretize the target surface M to generate a triangular mesh model M. 3D The triangular mesh model M 3D It is composed of numerous triangular facets.

3. The femtosecond laser processing method based on micro / nano array attachment according to claim 2, characterized in that: The specific implementation of step 3) is as follows: 3.1) Select the mapping method; the mapping method is angle-preserving mapping or area-preserving mapping; 3.2) Apply the triangular mesh model M obtained in step 2) to... 3D Mapping onto the two-dimensional planar domain D, construct the vertices P of each triangular facet on the three-dimensional surface. 3D And the point P mapped onto the two-dimensional plane 2D The one-to-one correspondence between them yields a two-dimensional planar model; the vertex P of the triangular facet... 3D The coordinates of point P on the two-dimensional plane are (x, y, z). 2D The coordinates are (u, v).

4. The femtosecond laser processing method based on micro / nano array attachment according to claim 3, characterized in that: The specific implementation of step 4) is as follows: 4.1) Establish a two-dimensional coordinate system in the two-dimensional planar domain D; 4.2) Import the two-dimensional micro / nano array G into the two-dimensional coordinate system obtained in step 4.1), and align the two-dimensional micro / nano array G with the two-dimensional planar model obtained in step 3) to obtain the oriented two-dimensional micro / nano array G'; 4.3) Perform a Boolean intersection operation between the oriented two-dimensional micro / nano array G' obtained in step 4.2) and the two-dimensional planar domain D to obtain the common area G of the two-dimensional planar model and the two-dimensional array. clip .

5. The femtosecond laser processing method based on micro / nano array attachment according to claim 4, characterized in that: The specific implementation of step 4.1) is as follows: 4.1.1) Define the two-dimensional planar domain D as an effective array attachment region; 4.1.2) Using the theoretical center point of the effective matrix attachment area obtained in step 4.1.1) or a preset corner point as the origin D0(x0, y0), establish a two-dimensional coordinate system.

6. The femtosecond laser processing method based on micro / nano array attachment according to claim 5, characterized in that: The specific implementation of step 4.2) is as follows: 4.2.1) Input the two-dimensional micro / nano array G to be attached; 4.2.2) Calculate the offset vector between the geometric center point G(x', y') of the two-dimensional micro / nano array G and the coordinate origin D0(x0, y0) of the two-dimensional planar domain D; 4.2.3) Based on the offset vector obtained in step 4.2.2), translate the two-dimensional micro / nano array G as a whole so that the reference point of the two-dimensional micro / nano array G is precisely aligned with the coordinate origin D0 of the two-dimensional planar domain D; the reference point is the geometric center point G(x', y') in step 4.2.2); 4.2.4) Rotate the two-dimensional micro / nano array G that has been aligned with the coordinate origin D0 of the two-dimensional planar domain D to obtain the oriented two-dimensional micro / nano array G'.

7. The femtosecond laser processing method based on micro / nano array attachment according to claim 6, characterized in that: The specific implementation of step 4.3) is as follows: perform a Boolean intersection operation between the oriented two-dimensional micro / nano array G' and the two-dimensional planar domain D, discard the part falling outside the effective region, and finally obtain the common region G of the two-dimensional planar model and the two-dimensional fabricated array. clip .

8. The femtosecond laser processing method based on micro / nano array attachment according to claim 7, characterized in that: The specific implementation of step 5) is as follows: 5.1) For the common area G of the two-dimensional planar model and the two-dimensional machining array... clip Perform triangulation constraints; 5.2) Divide the result of the triangulation constraints into a set of several non-overlapping two-dimensional triangles. The set constitutes a planar region before the inverse mapping.

9. The femtosecond laser processing method based on micro / nano array attachment according to claim 8, characterized in that: The specific implementation of step 6) is as follows: 6.1) Select any two-dimensional triangle T obtained in step 5.2). 2d Based on the vertices P of each triangular facet on the three-dimensional surface obtained in step 3.2), 3D And the point P mapped onto the two-dimensional plane 2D Find the one-to-one correspondence between them and locate the two-dimensional triangle T. 2d The three vertices of the given triangle correspond to the three 3D vertices in the original 3D mesh, which in turn determine a corresponding curved triangle T in 3D space. 3d 6.2) For triangle T lying on the curved surface 3d For internal vertices, the corresponding positions of the vertices in three-dimensional space are calculated using the centroid interpolation method; 6.3) Based on the corresponding positions obtained in step 6.2), the two-dimensional triangle T 2d The corresponding planar region before inverse mapping is mapped to three-dimensional space; 6.4) Repeat steps 6.1) to 6.3) to traverse all two-dimensional triangles T of the planar region before inverse mapping. 2d All planar regions before inverse mapping are mapped to three-dimensional space, ultimately obtaining a three-dimensional model with attachment and segmentation; preferably, the specific implementation of step 6.2) is as follows: 6.2.1) Let a two-dimensional triangle T 2d The vertex coordinates are A 2d B 2d C 2d Two-dimensional triangle T 2d The points corresponding to the vertices on the three-dimensional surface are A and B, respectively. 3d B 3d C 3d 6.2.2) For a two-dimensional triangle T 2d Any point P inside 2d Calculate the value of any point relative to A. 2d B 2d C 2d If the centroid coordinates are (α, β, γ), then the corresponding point P in three-dimensional space is... 3d From the same centroid coordinates at A 3d B 3d C 3d The value of the insertion is: P 3d =α×A 3d +β×B 3d +γ×C 3d .

10. The femtosecond laser processing method based on micro / nano array attachment according to claim 9, characterized in that: The specific implementation of step 7) is as follows: 7.1) For the 3D model obtained by attachment segmentation in step 6), the closed contour of the points generated after attachment is used as the boundary constraint for automatic segmentation processing, dividing the complex 3D model into a series of independent sub-regions that do not overlap and have clear boundaries, thereby achieving accurate block division of the 3D model; 7.2) Based on step 7.1), a high shape fidelity laser processing path is generated on the surface of the 3D model, and the laser processing path is exported as a standard path file format; 7.3) The laser processing path obtained in step 7.2) is imported into the femtosecond laser processing CNC system, and the 3D curved surface workpiece to be processed is processed by the femtosecond laser processing CNC system.

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