Multi-directional Random Polishing Path Generation Method Based on Tree Topology Structure

Abstract

The present invention discloses a method for generating multi-directional random polishing paths based on a tree-like topological structure. The generation steps are as follows: According to the geometric and process parameters of the workpiece to be polished, a discrete uniformly distributed dot matrix that completely covers the workpiece surface is generated, and the points within the workpiece area are marked as valid points; A main trunk is generated based on the valid dot matrix, and connecting branches are generated with the same logic. The branch generation is repeated, and finally a multi-directional random guiding curve with a tree-like topological structure is formed; Then, for the tree-like guiding curve, it is processed to obtain a tree-like random polishing path with multiple directions; The tree-like random polishing path is re-interpolated and sampled and smoothed, etc., and finally a random polishing path that can be used for processing is generated. The present invention can obtain a random tree-like guiding curve according to the requirements of intermediate frequency error suppression for the randomness and uniformity of the polishing path direction, and then extract the path points to obtain a tree-like random path with uniform distribution, multiple directions and continuity, forming an efficient and feasible path generation method.

Description

Technical Field

[0001] The present invention relates to the technical field of precision and ultra-precision polishing, and particularly to a method for generating a multi-directional random polishing path based on a tree-like topological structure. Background Art

[0002] With the wide application of ultra-precision optical components in high-power lasers, astronomical observations, ultraviolet lithography systems and other cutting-edge fields, higher and higher requirements are put forward for the surface shape accuracy, surface roughness, mid-frequency error, subsurface damage and other indicators of optical components, and at the same time, more challenges are brought to the ultra-precision manufacturing of optical components. Among them, the mid-frequency error on the surface of optical components will cause instability of precision tools and systems, trigger small-angle scattering, reduce image contrast, or generate light spots, damaging the optical components and seriously affecting the safe operation of the tool system. Therefore, suppressing the mid-frequency error of the optical surface is an urgent manufacturing problem to be solved in the manufacturing of ultra-precision optical components.

[0003] Polishing is the last process in the surface precision machining of optical components, and plays a crucial role in reducing surface roughness, improving surface quality, and suppressing mid-frequency error. Traditional manual polishing has a harsh environment, is time-consuming and laborious, and highly depends on the experience of workers, resulting in poor quality consistency, low efficiency, and high cost. With the development of the automation industry, automated polishing has great advantages over manual methods in terms of improving productivity, improving processing quality, and reducing manufacturing costs, thus attracting the attention of many researchers. Researchers have conducted extensive research on automated polishing, including new polishing technologies, polishing tool systems, polishing force control strategies, edge effects in polishing, polishing material removal models, and polishing path planning. The polishing removal mechanism is very complex, especially for curved surfaces, and there are many factors affecting the polishing effect. Among them, the path planning in the polishing process is one of the important factors affecting the polishing effect, which plays a crucial role in achieving uniform material removal, improving polishing efficiency, and suppressing mid-frequency error. The mid-frequency error on the surface of optical components is mainly caused by polishing tool wear, uneven polishing liquid concentration, path convolution, etc. Among them, the mid-frequency error generated on the workpiece surface due to path convolution is particularly significant. Therefore, discovering and finding better polishing paths is of great significance for improving the surface quality of workpieces and suppressing the mid-frequency error on the surface of optical components.

[0004] Traditional polishing paths, such as Figure 1The scanning paths, spiral paths, Hilbert paths, etc. shown have strict regularity. Due to their uniformity and strong traversability, the polishing effect on the workpiece surface is good. For example, Tam H Y, Cheng H, Dong Z. Peano-like paths for subaperture polishing of optical aspherical surfaces[J]. Applied Optics, 2013, 52(15): 3624-3636. H. Y. Tam, “Toward the uniform coverage of surfaces by scanning curves,” Computer Aided Design 31, 585–596 (1999). Therefore, they have very wide applications in automated polishing. However, these regular paths cannot only eliminate the mid-frequency errors on the surface of optical elements, but may even exacerbate the generation of mid-frequency errors. Therefore, optimizing the polishing path is of great significance for suppressing the mid-frequency errors on the surface of optical elements. Again, Tam H. Toward the uniform coverage of surfaces by scanning curves[J]. Computer Aided Design, 1999, 31(9): 585-596, proposed an extended scanning path that can uniformly cover the curved surface and can cover the curved surface more uniformly than the traditional scanning path. Also, Zhang L, Han Y, Fan C, et al. Polishing path planning for physically uniform overlap of polishing ribbons on freeform surface[J]. The International Journal of Advanced Manufacturing Technology, 2017, 92(9): 4525-4541, proposed a path optimization method for uniform overlap of polishing ribbons, which greatly suppresses phenomena such as over-polishing and under-polishing generated by traditional polishing paths during the polishing process.For another example, Tam HY, Cheng H, Dong Z. Peano-like paths for subaperture polishing of optical aspherical surfaces[J]. Applied Optics, 2013, 52(15): 3624-3636 further studies show that some non-periodic uniform paths, such as Peano, Hilbert and Peano-like, as well as some combined paths can effectively suppress the generation of mid-frequency errors. However, Dunn C R, Walker D D. Pseudo-random tool paths for CNC sub-aperture polishing and other applications[J]. Optics express, 2008, 16(23): 18942-18949 first proposed six-directional pseudo-random paths in 2008, which have higher randomness and non-periodicity. Compared with traditional combined paths, their effect of suppressing mid-frequency errors is more obvious. In the same year, Dunn C R, Walker D D. Pseudo-random tool paths for CNC sub-aperture polishing and other applications[J]. Optics express, 2008, 16(23): 18942-18949 proposed an eight-directional random path, improving the randomness of the path and the effect of suppressing mid-frequency errors. Recently, Zhao Q, Zhang L, Fan C. Six-directional pseudo-random consecutive unicursal polishing path for suppressing mid-spatial frequency error and realizing consecutive uniform coverage[J]. Applied Optics, 2019, 58(31): 8529-8541 proposed a six-directional pseudo-random consecutive unicursal polishing path and its generation method, and the results show that the polishing effect has been further improved compared with that of traditional polishing paths.

[0005] In summary, after processing the optical element with a polishing path having obvious periodic characteristics, obvious periodic ripples, i.e., medium-frequency errors, will be formed on the surface of the optical element. In the existing random path generation methods, there are generally problems such as complex algorithms, low operation efficiency, relatively single randomness of directions, and it is difficult to ensure the uniformity and traversability of the path for different workpiece surfaces. There is an urgent need to propose a polishing path generation method with strong direction randomness, uniform coverage, and high operation efficiency. Summary of the Invention

[0006] To solve the existing technical problems, the present invention aims to propose a multi-direction random polishing path generation method based on a tree-like topological structure, which can meet the traversability and uniformity while ensuring randomness, and at the same time solves the problem of slow path generation efficiency.

[0007] The technical solution of the present invention is as follows:

[0008] A multi-direction random polishing path generation method based on a tree-like topological structure, characterized by the following steps:

[0009] Step 1, according to the geometric parameters of the workpiece to be polished and the selected process parameters (such as path spacing, adjacent point spacing, etc.), generate a discrete uniformly distributed dot matrix that completely covers the surface of the workpiece, that is, a control dot matrix, and mark the points within the workpiece area as valid points. All valid points form a valid dot matrix;

[0010] Step 2, randomly select a point from the valid dot matrix as the starting point, and generate a random curve that continuously passes through discrete points and does not self-intersect as the main trunk;

[0011] Step 3, randomly select a used valid point in the valid dot matrix as the starting point of the branch, and then loop to search for unused valid points in the valid dot matrix, and generate a random curve that continuously passes through discrete points and does not self-intersect as the branch; repeat the branch generation process until there are no unused valid points in the dot matrix. Finally, the main trunk and all branches form a tree trunk, that is, a multi-direction random guiding curve with a tree-like topological structure is formed;

[0012] Step 4, take any point on the edge contour of the multi-direction random guiding curve as the starting point, process the generated tree trunk data, and then generate a tree-like random polishing path with multiple directions; the processing method can adopt methods such as stroke drawing, ants climbing a tree, image recognition, and equidistant offset;

[0013] Step 5, perform re-interpolation sampling and post-processing of arc smooth transition on the generated random path, and finally generate a random polishing path that can be used for processing.

[0014] For the above steps, the further design is as follows:

[0015] Step 1: The geometric parameters of the workpiece to be polished include at least the contour boundary of the surface of the workpiece to be polished and the dimensions of the circumscribed rectangle of the contour. The process parameters include the path spacing p and the spacing between adjacent points along the path Δs . Inside the circumscribed rectangle of the contour is a control point matrix, inside the contour boundary is an effective point matrix, and the points between the circumscribed rectangle of the contour and the contour boundary are invalid points.

[0016] In Step 2, the specific process of generating the main trunk is as follows:

[0017] A1. Randomly select a point in the effective point matrix as the main reference point, mark the main reference point as used, and search whether there are unused effective points near the main reference point;

[0018] A2. If there are unused effective points, update the main reference point, that is, take the searched unused effective point as the new main reference point and mark it as used;

[0019] A3. Search whether there are unused effective points near the new main reference point, repeat the process of A2 until there are no unused effective points around the new main reference point, then jump out of the loop;

[0020] A4. Connect all the main reference points in sequence to generate a continuous and non-intersecting curve, which is the only main trunk.

[0021] In Step 3, the specific process of generating the branches is as follows:

[0022] B1. Randomly select a marked and used effective point as the initial branch reference point, and search whether there are unused effective points near the initial branch reference point; the initial branch reference point is a point on the main trunk or a point on the generated branches;

[0023] B2. If there are unused effective points, update the branch reference point, that is, take the searched new effective point as the new branch reference point and mark it as used;

[0024] B3. Search whether there are unused effective points near the new branch reference point, repeat the process of B2 until there are no unused effective points around the new branch reference point, then jump out of the loop;

[0025] B4. Connect all the branch reference points in sequence to generate a continuous and non-intersecting curve connected to the generated trunk, which is a branch;

[0026] B5. Search whether there are unused effective points in the effective point matrix. If so, repeat steps B1 - B4 to generate all other possible branches;

[0027] B6. When there are no unused valid points in the valid dot matrix, this loop is exited, and all branches are generated.

[0028] In step 4, assume that the spacing of the tree-shaped guiding curve is equal to twice the spacing of the process path. Starting from any point on the edge contour, methods such as stroke drawing, ants climbing a tree, image recognition, or equidistant offset are used on the generated tree-shaped random guiding curve to extract the edge contour points of the trunk, and a multi-directional random polishing path based on the tree-shaped topological structure is initially obtained.

[0029] Furthermore, the specific process of path extraction using the stroke drawing method:

[0030] C1. Take the right contour point of the starting point of the generated multi-directional random guiding curve as the initial path starting point; start walking along the right side of the tree-shaped random guiding curve from the starting point, set the walking direction as the positive direction, and then determine whether the edge contour has been extracted, that is, determine whether the current path point returns to the path starting point.

[0031] C11. If the current path point has not returned to the starting point, is not a branch point, nor an end point, then walk along the current branch to the next path point and set it as the current path point, with the direction along the current direction.

[0032] C12. If the current path point has not returned to the starting point and is just a branch point, then assume that the next point adjacent to the current trunk of the current path point is P1 , and the next point adjacent to the current path point on the branch trunk is P2 , select P1 、 P2 the point on the right side as the next path point: (1) If P1 is on the right side of P2 , then walk along the current branch direction to the next point without changing the direction, set the next point as the current point, and then return to determine whether the current point returns to the starting point; (2) If P2 is on the right side of P1 and along the reverse direction of the branch trunk, then walk along the reverse direction of the branch trunk to the next point, set the branch trunk as the current trunk, the adjacent point on the branch trunk as the current point, with the direction as negative, and then return to determine whether the current point returns to the starting point; (3) If P2 is on the right side of P1 , then walk along the forward direction of the branch trunk, set the branch trunk as the current trunk, the adjacent point on the branch trunk as the current point, with the direction as positive, and return to determine whether the current point returns to the starting point.

[0033] C13. If the current point does not return to the starting point and is only an end point, walk back along the current tree trunk to the previous point, set the previous point as the current point, set the direction as the reverse of the current direction, and then return to determine whether the current point is the return starting point;

[0034] C2. If the current point returns to the starting point, jump out of the loop judgment and generate a complete tree-shaped random polishing path.

[0035] In step five, the interpolation is to perform parametric subdivision interpolation on the path points on the tree-shaped random polishing path, that is, according to the path points generated in step five, calculate and insert new path points at the positions of adjacent path points among them to obtain a new sequence of path points, and finally obtain a smooth path curve.

[0036] The beneficial effects of the present invention are as follows:

[0037] According to the requirements of intermediate frequency error suppression for the randomness and uniformity of the polishing path direction, the present invention simulates the topological rules of branch growth to obtain a random tree-shaped guiding curve. According to the generated random guiding curve, the method of tracing the tree trunk is adopted to obtain a tree-shaped random path with uniform distribution, multiple directions and continuity, providing an efficient and feasible path generation method for effectively suppressing the intermediate frequency error on the surface of the microcrystalline glass optical element in the follow-up. Description of the Drawings

[0038] Figure 1 Schematic diagrams of three traditional typical polishing paths.

[0039] Figure 2 General flowchart of the present invention.

[0040] Figure 3 Schematic diagram of the main trunk and branches in the present invention.

[0041] Figure 4 Schematic diagram of the control point matrix, effective boundary, effective points and invalid points in the present invention.

[0042] Figure 5 Flowchart for generating a multi-direction random guiding curve in the present invention.

[0043] Figure 6 Schematic diagram of the main trunk generated in the embodiment of the present invention.

[0044] Figure 7 Schematic diagram of the multi-direction random guiding curve generated in the embodiment of the present invention.

[0045] Figure 8 Flowchart for generating a tree-shaped random polishing path in the embodiment of the present invention.

[0046] Figure 9Schematic diagram of producing tree-shaped random polishing path points by using the stroke method in the embodiment of the present invention.

[0047] Figure 10 It is generated according to Figure 9 Schematic diagram of the generated tree-shaped random polishing path.

[0048] Figure 11 Schematic diagram of the fairing four-direction polishing path in the embodiment of the present invention.

[0049] Figure 12 Schematic diagram of the fairing six-direction polishing path in the embodiment of the present invention. Detailed implementation manners

[0050] Embodiment 1

[0051] As Figure 2 shown, the basic steps of the multi-direction random polishing path generation method with a tree-shaped topological structure provided in this embodiment are as follows:

[0052] Step 1: Generate a discrete uniformly distributed dot matrix that completely covers the surface of the workpiece, that is, a control dot matrix, according to the geometric parameters of the workpiece to be polished and the selected process parameters, and mark the points within the workpiece area as valid points. All valid points form a valid dot matrix;

[0053] Step 2: Randomly select a point from the valid dot matrix as the starting point, and generate a random curve that continuously passes through discrete points and does not intersect itself as the main trunk;

[0054] Step 3: Randomly select a point on the main trunk as the starting point, and generate a random curve that continuously passes through discrete points and does not intersect itself as a branch; then circularly search for unused valid points on the main trunk or the generated branches, and repeat the branch generation process. Finally, the main trunk and all branches form a tree trunk, that is, a multi-direction random guiding curve with a tree-shaped topological structure is formed

[0055] Step 3: Randomly select a used valid point in the valid dot matrix as the starting point of the branch, and then circularly search for unused valid points in the valid dot matrix, and generate a random curve that continuously passes through discrete points and does not intersect itself as a branch; repeat the branch generation process until there are no unused valid points in the dot matrix. Finally, the main trunk and all branches form a tree trunk, that is, a multi-direction random guiding curve with a tree-shaped topological structure is formed, as Figure 7 shown;

[0056] That is to say, it is possible to first use the valid points on the main trunk as the starting points of the branches to generate branches; then search for unused valid points in the valid dot matrix on the main trunk or the generated branches, and continue to generate other branches;

[0057] As Figure 3As shown: The thick line is the main trunk; the thin lines are generated by randomly selecting a point on the already generated trunk as the starting point, and the other branches are generated according to this logic;

[0058] Step 4: Take any point on the edge contour of the multi-directional random guiding curve as the starting point, process the generated trunk data, and then generate a tree-shaped random polishing path with multiple directions; The processing methods can adopt methods such as stroke drawing, ants climbing a tree, image recognition, and equidistant offset;

[0059] Step 5: Re-insert and sample the generated random path, and perform post-processing of smooth transition of arcs to finally generate a random polishing path that can be used for processing.

[0060] Embodiment 2

[0061] Based on Embodiment 1, in the said Step 1, the geometric parameters of the workpiece to be polished at least include the contour boundary of the surface of the workpiece to be polished and the dimensions of the circumscribed rectangle of the contour, and the process parameters include the path spacing p and the spacing between adjacent points along the path Δs .

[0062] As Figure 4 shown, within the circumscribed rectangle of the contour is the control point matrix, within the contour boundary is the effective point matrix, and the points between the circumscribed rectangle of the contour and the contour boundary are invalid points.

[0063] Embodiment 3

[0064] On the basis of Embodiment 1 or 2, in the said Step 2, the specific process of generating the main trunk is as follows:

[0065] A1: Randomly select a point in the effective point matrix as the main reference point, mark the main reference point as already used, and search whether there are unused effective points near the main reference point;

[0066] A2: If there are unused effective points, update the main reference point, that is, take the searched unused effective point as the new main reference point and mark it as already used;

[0067] A3: Search whether there are unused effective points near the new main reference point, repeat the process of A2 until there are no unused effective points around the new main reference point, then jump out of the loop;

[0068] A4: Connect all the main reference points in sequence, and a continuous and non-intersecting curve can be generated, which is the only main trunk, as Figure 6 shown.

[0069] Embodiment 4

[0070] On the basis of any one of Embodiments 1-3, in Step 3, the specific process of generating branches is as follows:

[0071] B1. Randomly select a marked and used valid point as the initial branch reference point, and search for unused valid points near the initial branch reference point; the initial branch reference point is a point on the main trunk or a point on the generated branch.

[0072] B2. If there are unused valid points, update the branch reference point, that is, take the newly searched valid point as the new branch reference point and mark it as used.

[0073] B3. Search for unused valid points near the new branch reference point, and repeat the process of B2 until there are no unused valid points around the new branch reference point, then jump out of the loop.

[0074] B4. Connect all the branch reference points in sequence to generate a continuous non-intersecting curve connected to the generated tree trunk, which is a branch.

[0075] B5. Search whether there are unused valid points in the valid dot matrix. If so, repeat Steps B1-B4 to generate all other possible branches.

[0076] B6. When there are no unused valid points in the valid dot matrix, jump out of this loop, and all branches are generated.

[0077] Embodiment 5

[0078] On the basis of any one of Embodiments 1-4, as Figure 9 shown, in Step 4, assuming that the spacing of the tree-shaped guiding curve is equal to twice the path spacing, taking any point on the edge contour as the starting point, and then using methods such as stroke drawing, ants climbing a tree, image recognition or equidistant offset on the generated tree-shaped random guiding curve to extract the edge contour points of the tree trunk, and initially obtain a multi-directional random polishing path based on the tree-shaped topological structure.

[0079] Embodiment 6

[0080] On the basis of Embodiment 5, as Figures 8 - 10 shown, the specific process of path extraction for the generated tree-shaped random guiding curve by using the stroke drawing method is as follows:

[0081] C1. Take the right contour point of the starting point of the generated multi-directional random guiding curve as the initial path starting point; start walking along the right side of the tree-shaped random guiding curve from the starting point, set the walking direction as the positive direction, and then judge whether the edge contour extraction is completed, that is, judge whether the current path point returns to the path starting point.

[0082] C11, if the current path point has not returned to the starting point, is not a branch point, nor an end point, then walk along the current trunk to the next path point and set it as the current path point, with the direction along the current direction;

[0083] C12, if the current path point has not returned to the starting point and is just a branch point, then assume that the next point adjacent to the current trunk and the current path point is P1 , and the next point adjacent to the current path point on the branch trunk is P2 , select P1 、 P2 the point on the right side as the next path point: (1) If P1 is on the right side of P2 , then walk along the current trunk direction unchanged to the next point, set the next point as the current point, keep the direction unchanged, and then return to determine whether the current point has returned to the starting point; (2) If P2 is on the right side of P1 and along the reverse direction of the branch trunk, then walk along the reverse direction of the branch trunk to the next point, set the branch trunk as the current trunk, the adjacent point on the branch trunk as the current point, with the direction negative, and then return to determine whether the current point is the starting point to return; (3) If P2 is on the right side of P1 , then along the forward direction of the branch trunk, walk along the forward direction of the branch trunk to the next point, set the branch trunk as the current trunk, the adjacent point on the branch trunk as the current point, with the direction positive, return and then determine whether the current point is the starting point to return;

[0084] C13, if the current point has not returned to the starting point and is just an end point, then walk along the reverse direction of the current trunk to the previous point, set the previous point as the current point, set the direction as the reverse of the current direction, return and then determine whether the current point is the starting point to return;

[0085] C2, if the current point returns to the starting point, then jump out of the loop judgment and generate a complete tree-shaped random polishing path.

[0086] Example 7

[0087] On the basis of any one of Examples 1-6, as Figures 11 - 12 shown, in step five, the interpolation is to perform parameter subdivision interpolation on the path points on the tree-shaped random polishing path, that is, according to the path points generated in step five, calculate and insert new path points at the positions of adjacent path points to obtain a new sequence of path points, and finally obtain a smooth path curve.

Claims

1. A method for generating multi-directional random polishing paths based on a tree-like topological structure, characterized in that the steps are as follows: Step 1, according to the geometric parameters of the workpiece to be polished and the selected process parameters, generate a discrete uniformly distributed dot matrix that completely covers the workpiece surface, that is, a control dot matrix, and mark the points within the workpiece area as valid points. All valid points form a valid dot matrix; Step 2, randomly select a point from the valid dot matrix as the starting point, and generate a random curve that continuously passes through discrete points and does not self-intersect as the main trunk; Step 3, randomly select a used valid point in the valid dot matrix as the starting point of the branch, and then loop to search for unused valid points in the valid dot matrix, and generate a random curve that continuously passes through discrete points and does not self-intersect as the branch; Repeat the branch generation process until there are no unused valid points in the dot matrix. Finally, the main trunk and all branches form a tree trunk, that is, a multi-directional random guiding curve with a tree-like topological structure is formed; Step 4, take any point on the edge contour of the multi-directional random guiding curve as the starting point, process the generated tree trunk data, and then generate a tree-like random polishing path with multiple directions; the processing uses a stroke method, ants climbing a tree, image recognition, or equidistant offset; Step 5, perform re-interpolation sampling and post-processing of arc smooth transition on the generated tree-like random polishing path, and finally generate a random polishing path that can be used for processing.

2. The multi-directional random polishing path generation method according to claim 1, characterized in that: In Step 1, the geometric parameters of the workpiece to be polished at least include the contour boundary of the surface of the workpiece to be polished and the dimensions of the circumscribed rectangle of the contour, and the process parameters include the path pitch p and the distance between adjacent points along the path Δs ; within the circumscribed rectangle of the contour is a control point matrix, within the contour boundary is an effective point matrix, and the points between the circumscribed rectangle of the contour and the contour boundary are invalid points.

3. The multi-directional random polishing path generation method according to claim 2, characterized in that, in the said Step 2, the specific process of generating the main trunk is: A1, randomly select a point in the valid dot matrix as the main reference point, and mark the main reference point as already used, and search whether there are unused valid points near the main reference point; A2, if there are unused valid points, update the main reference point, that is, take the searched unused valid point as the new main reference point and mark it as already used; A3, search whether there are unused valid points near the new main reference point, and repeat the process of A2 until there are no unused valid points around the new main reference point, then jump out of the loop; A4, connect all the main reference points in sequence, and a continuous non-intersecting curve can be generated, which is the only main trunk.

4. The multi-directional random polishing path generation method according to claim 3, characterized in that: in the said Step 3, the specific process of generating the branch is: B1, randomly select a marked and used valid point as the initial branch reference point, and search whether there are unused valid points near the initial branch reference point; the initial branch reference point is a point on the main trunk or a point on the already generated branch; B2, if there are unused valid points, update the branch reference point, that is, take the newly searched valid point as the new branch reference point and mark it as already used; B3, search whether there are unused valid points near the new branch reference point, and repeat the process of B2 until there are no unused valid points around the new branch reference point, then jump out of the loop; B4. Connect all the branch reference points in sequence, and a continuous non - intersecting curve connected to the generated tree trunk can be generated, which is a branch. B5. Search whether there are unused valid points in the valid dot matrix. If there are, repeat steps B1 - B4 to generate all other possible branches accordingly. B6. When there are no unused valid points in the valid dot matrix, jump out of this loop, and all branches are generated.

5. The multi - direction random polishing path generation method according to claim 1, characterized in that: the distance between adjacent points in the said valid dot matrix is set to twice the process path distance.

6. The multi - direction random polishing path generation method according to claim 1, characterized in that: in step four, the specific process of path extraction using the stroke - drawing method is as follows: C1. Take the right - hand contour point of the starting point of the generated multi - direction random guiding curve as the initial path starting point; start walking along the right - hand side of the tree - shaped random guiding curve from the starting point, set the walking direction as the forward direction, and then determine whether the edge contour has been extracted, that is, determine whether the current path point returns to the path starting point. C11. If the current path point does not return to the starting point, is not a branch point, nor an end point, then walk along the current branch to the next path point and set it as the current path point, with the direction along the current direction. C12. If the current path point does not return to the starting point and is just a branch point, then assume that the next point adjacent to the current tree trunk and the current path point is P1 , and the next point adjacent to the current path point on the branch tree trunk is P2 . Select P1 、 P2 . The point on the right side is the next path point: (1) If P1 is on the right side of P2 , then walk along the current branch direction to the next point, set the next point as the current point, keep the direction unchanged, and then return to determine whether the current point returns to the starting point; (2) If P2 is on the right side of P1 and along the reverse direction of the branch tree trunk, then walk along the reverse direction of the branch tree trunk to the next point, set the branch tree trunk as the current tree trunk, the adjacent point on the branch tree trunk as the current point, the direction is negative, and then return to determine whether the current point returns to the starting point; (3) If P2 is on the right side of P1 , then along the forward direction of the branch tree trunk, then walk along the forward direction of the branch tree trunk to the next point, set the branch tree trunk as the current tree trunk, the adjacent point on the branch tree trunk as the current point, the direction is positive, return to determine whether the current point returns to the starting point; C13. If the current point does not return to the starting point and is just an end point, then walk backward along the current tree trunk to the previous point, set the previous point as the current point, set the direction as the reverse of the current direction, and then return to determine whether the current point returns to the starting point. C2. If the current point returns to the starting point, jump out of the loop judgment to generate a complete tree - shaped random polishing path.

7. The multi - direction random polishing path generation method according to claim 1, characterized in that: the interpolation is to perform parametric subdivision interpolation on the path points on the tree - shaped random polishing path, that is, according to the path points generated in step five, calculate and insert new path points at the positions between adjacent path points to obtain a new sequence of path points, and finally obtain a smooth path curve.

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