A method for optimizing the empty cut distance of the region-filling trajectory based on the latent point greedy algorithm.

Abstract

This invention relates to the field of machining technology, specifically to a method for optimizing the empty cutting stroke of a region-filling trajectory based on a latent point greedy algorithm. First, multiple contour curves of all areas to be processed are selected. The intersection of parallel scan lines and offset contour curves is calculated, and the regions are grouped according to the number of intersection points. Then, to address anomalies such as scan lines coinciding with contour curves or an odd number of intersection points, a method is adopted to offset the scan lines slightly without affecting the machining distance, thus improving the efficiency of the method in handling these anomalies. Furthermore, the latent point greedy algorithm is used to select different orientations for the scan line filling trajectory within each group. Each time, the scan line filling trajectory of the nearest group is connected to construct a jump-cutting trajectory, ensuring that each selection is locally optimal, thereby optimizing the empty cutting stroke of the machining trajectory and improving overall machining efficiency.

Description

Technical Field

[0001] This invention relates to the field of machining technology, specifically to a method for optimizing the empty cutting stroke of a region filling trajectory based on a potential point greedy algorithm. Background Technology

[0002] With the development of technology, machining has transformed from a manual operation to a highly automated process. In this process, trajectory planning plays a crucial role, determining the movement trajectory of the cutting tool throughout the machining process and directly affecting machining efficiency, accuracy, and cost.

[0003] Toolpath generation is a core function of CAM software, using algorithms to generate the movement trajectory of the tool on the workpiece surface. Toolpath planning and optimization techniques aim to reduce machining time and improve machining quality. Through algorithm optimization, the idle cutting stroke of the machining trajectory can be reduced, while ensuring that cutting forces and heat are controlled within reasonable ranges during the machining process.

[0004] When planning the filling trajectory for complex processing areas, it is necessary not only to ensure the processing integrity of the entire selected area (i.e., there should be no unprocessed areas or areas exceeding the selected area), but also to minimize the number of tool jumps and the empty cutting distance between different processing areas. This requires optimizing the empty cutting stroke of the processing trajectory. Therefore, how to quickly generate effective filling trajectories within complex areas and optimize the connection order of filling trajectories in different areas to reduce the empty cutting stroke of the processing trajectory and improve overall processing efficiency are currently challenging problems that need to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the empty cutting stroke of a region filling trajectory based on a latent point greedy algorithm. This method uses a grouping strategy to construct the region filling trajectory in a divide-and-conquer manner, and optimizes the connection order of the region filling trajectory based on the latent point greedy algorithm, thereby reducing the empty cutting stroke of the processing trajectory and improving the overall processing efficiency.

[0006] To achieve the above objectives, this invention provides a method for optimizing the empty cut distance of a region-filling trajectory based on a latent point greedy algorithm, comprising the following steps:

[0007] Step 1: Select multiple contour curves for all areas to be processed;

[0008] Step 2: Determine the inner and outer contours of the multiple contour curves and perform contour offset;

[0009] Step 3: Use the intersection of parallel scan lines and offset contour curves to form the scan line filling trajectory after grouping;

[0010] Step 4: Using the latent point greedy algorithm, perform air cutting stroke optimization of the machining trajectory, and finally connect to form a high-efficiency machining trajectory.

[0011] Optionally, the contour curve is a region contour curve drawn or imported in CAD / CAM software, used to generate the trajectory for region trenching.

[0012] Optionally, the nesting relationships between contour curves in step 2 can be categorized into the following two types:

[0013] Separation: If contour L1 and contour L2 do not contain each other, then contour L1 and contour L2 are separated.

[0014] In-containment / inclusion: If contour L1 is inside contour L2, then contour L1 and contour L2 are in-containment; otherwise, contour L2 and contour L1 are inclusion.

[0015] Optionally, the execution process of step 2 includes the following steps:

[0016] Step 2.1: For the set of contour curves collected in Step 1, start from the first contour curve and traverse the nesting relationship between it and other contour curves in turn, and traverse all contour curves in turn.

[0017] Step 2.2: Construct a contour curve depth information tree to obtain the depth information relationship between each contour curve and other contour curves, thereby determining the information of the inner and outer contours. The formula is as follows:

[0018]

[0019] Where n is the depth of the contour curve, and when n is equal to 0, it means that the contour curve is the outermost contour curve.

[0020] Step 2.3: Offset all contour curves. Specifically, based on the information in Step 2.2, perform two contour offsets, with the outer contour offset inward and the inner contour offset outward, with an offset distance of f.

[0021] Optionally, the execution process of step 3 includes the following steps:

[0022] Step 3.1: Obtain the minimum bounding box of the outermost contour curve. Based on the data, calculate the number of scan lines N, using the following formula:

[0023]

[0024] Where N is the total number of scan lines, y max and y min y represents the maximum and minimum values ​​of the bounding box along the y-axis, while d is the offset distance;

[0025] Step 3.2: From ymin The position begins to generate scan lines parallel to the X-axis. Each scan line is offset by a distance of (N-1)*d. Steps 3.3 and 3.4 are repeated until N scan lines are generated.

[0026] Step 3.3: Find the intersection of the scan line with all the offset contour curves, keep the coordinates of the intersection points of the scan line and the contour curves, sort them by the size of the X-axis of the intersection point coordinates in ascending order, and record the number of intersection points.

[0027] Step 3.4: When the number of intersections between the scan line and the contour curve is odd, or when the scan line and the contour curve coincide, enter a loop operation. The loop operation is as follows: discard the intersection information generated by the scan line, offset the scan line by a small distance that does not affect the processing, and then repeat step 3.3. The loop stops when the number of intersections between the scan line and the contour curve is even and the scan line and the contour curve do not coincide.

[0028] Step 3.5: Group the scan lines based on the number of intersections between the scan lines and the contour curve; let L i Fill in the number of intersection points between the i-th scan line and the contour curve, where {L i ,0<=i<=N}, when L i With L i+1 If they are not equal, a grouping operation occurs, and L is grouped. i The previous curves are treated as a large group. By repeating this operation, all scan lines can be divided into m large groups, and the grouping formula is as follows:

[0029]

[0030] Step 3.6: After the large groups are formed, the effective scan line filling trajectory needs to be formed based on the intersection of each large group. Therefore, it is necessary to further divide the group into smaller subgroups.

[0031] Optionally, step 4.1: Construct a group information structure container, where the group information structure includes the following information: the number F1 recording whether it is a first or last point, the number F2 recording the pose, and the potential two first points P. Start1 and P Start2 The two potential endpoints are P. End1 and P End2 ;

[0032] Step 4.2: Iterate through all group members, store the information in the group information structure container, and use the first group's P as the starting point. End1 As a starting point, let's begin searching for starting point information;

[0033] Step 4.3: For the remaining groups, use the potential point greedy algorithm to select the group closest to the starting point, and determine whether the group should maintain its original posture or reverse its posture based on the potential point distance comparison.

[0034] Step 4.4: When the distance between two points is less than 1.5d, it is assumed that the filling trajectory can be directly connected; when it is greater than 1.5d, a jump operation is performed, and then the operation of step 4.3 is repeated until all group information is traversed.

[0035] Step 4.5: After step 4.4, only two adjacent scan lines in each group have not yet been connected. There are two ways to connect two adjacent scan lines: connect the first point to the first point or connect the last point to the last point, corresponding to the bridging curve L. Mode1 and L Mode2 Two kinds;

[0036] Step 4.6: Based on the information obtained in Step 4.3, determine which group maintained its original attitude or underwent an attitude reversal, and then connect them using bridging curves. The connection methods for the two cases are as follows:

[0037] The original orientation group connection method: odd-numbered scan lines connecting even-numbered scan lines is L. Mode2 The connection between even-numbered scan lines and odd-numbered scan lines is L. Mode1 connect;

[0038] The group connection method for attitude reversal: odd-numbered scan lines connecting even-numbered scan lines is L. Mode1 The connection between even-numbered scan lines and odd-numbered scan lines is L. Mode2 connect;

[0039] Step 4.7: Repeat step 4.6 until all group members have been traversed to generate the final processing trajectory.

[0040] Optionally, the potential point distance comparison operation in step 4.3 corresponds to the following four cases:

[0041] If P Start1 Recently, they have maintained their original stance and changed the starting point to P. End1 ;

[0042] If P Start2 Recently, the attitude has been reversed, and the next starting point has been changed to P. End2 ;

[0043] If P End1 Recently, it has maintained its original stance and changed the previous starting point to P. Start1 ;

[0044] If P End2Recently, the attitude has been reversed, and the previous starting point has been changed to P. Start2 .

[0045] This invention provides a method for optimizing the empty-cut travel of a region filling trajectory based on a latent point greedy algorithm. First, multiple contour curves of all areas to be processed are selected. The inner and outer contours of these contour curves are determined, and contour offsets are applied. The intersection of parallel scan lines and the offset contour curves is used to form grouped scan line filling trajectories. The latent point greedy algorithm is then used to optimize the empty-cut travel of the processing trajectory, ultimately connecting them to form a high-efficiency processing trajectory. Specifically, the intersection of parallel scan lines and the offset contour curves is used, and grouping is performed based on the number of intersection points. Then, the entire area to be processed is divided into multiple smaller areas and numbered to improve the efficiency of filling trajectory generation. Since there are abnormal situations during grouping, such as scan lines coinciding with contour curves or an odd number of intersection points, a method is used to offset the scan lines by a small segment without affecting the processing distance, thereby improving the execution efficiency of the method when facing abnormal situations. Furthermore, by utilizing a latent point greedy algorithm, different orientations are selected for the scan line filling trajectory within each group. Each time, the scan line filling trajectory of the nearest group to the current group is connected to construct the skip cut trajectory, making each selection locally optimal. This optimizes the skip cut travel of the machining trajectory, significantly reduces the number of skip cuts and the skip cut distance, and improves the overall machining efficiency. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating the steps of a region-filling trajectory empty-cutting journey optimization method based on a latent point greedy algorithm according to the present invention.

[0048] Figure 2 This is a schematic diagram of the design pattern outline curve in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the contour curve depth information tree in an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of the minimum bounding box of the contour curve in an embodiment of the present invention.

[0051] Figure 5 This is a schematic diagram of an embodiment of the present invention when the number of intersection points between the scan line and the contour curve is odd.

[0052] Figure 6 This is a schematic diagram of the scan line coinciding with the contour curve in an embodiment of the present invention.

[0053] Figure 7 This is a schematic diagram of partitioning in a partitioning-direction scanning embodiment of the present invention.

[0054] Figure 8 This is a schematic diagram of potential endpoints in a group in an embodiment of the present invention.

[0055] Figure 9 This is a schematic diagram of the original posture of the group in an embodiment of the present invention.

[0056] Figure 10 This is a schematic diagram of attitude reversal in a group in an embodiment of the present invention.

[0057] Figure 11 These are schematic diagrams of two bridging curves in embodiments of the present invention.

[0058] Figure 12 This is a schematic diagram illustrating the final effect in an embodiment of the present invention.

[0059] Figure 13 This is a schematic diagram of the second final effect in an embodiment of the present invention. Detailed Implementation

[0060] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0061] Please see Figure 1 This invention provides a method for optimizing the empty cut distance of a region-filling trajectory based on a latent point greedy algorithm, comprising the following steps:

[0062] S1: Select multiple contour curves for all areas to be processed;

[0063] S2: Determine the inner and outer contours of the multiple contour curves and perform contour offset;

[0064] S3: Use the intersection of parallel scan lines and offset contour curves to form the scan line filling trajectory after grouping;

[0065] S4: Using a greedy algorithm for potential points, the machining trajectory is optimized by performing air cutting stroke, and finally connected to form a high-efficiency machining trajectory.

[0066] The following description, in conjunction with implementation steps and specific embodiments, provides further details. Please refer to the provided text for further information. Figures 2 to 13 :

[0067] Step S1: Select multiple contour curves for all areas to be processed;

[0068] In this embodiment, several region contour curves are first drawn or imported into CAD / CAM software, such as... Figure 2 The design pattern outline curve is shown, which is used to generate trajectories for areas including but not limited to trenching.

[0069] Step S2: Determine the inner and outer contours of the multiple contour curves and perform contour offset. The specific operation is as follows:

[0070] S201. The nesting relationships between contour curves are divided into the following two categories:

[0071] 1. Separation. If contour L1 and contour L2 do not contain each other, then contour L1 and contour L2 are separated.

[0072] 2. Inside / Containing. If contour L1 is inside contour L2, then contour L1 and contour L2 have an inside relationship; otherwise, contour L2 and contour L1 have a containment relationship.

[0073] S202, First, collect data according to S1, such as... Figure 2 The set of contour curves shown is traversed by iterating through the nesting relationships between the first contour curve and other contour curves in this manner until all contour curves have been traversed.

[0074] S203, construct as follows Figure 3 The contour curve depth information tree shown obtains the contour curve depth information of each contour curve, including other contours, thereby determining the information of the inner and outer contours. The formula is as follows:

[0075]

[0076] Where n is the depth of the contour curve. If n equals 0, it means that the contour curve is the outermost contour curve.

[0077] S204. Offset all contour curves. Based on the information in S203, perform two contour offsets, with the outer contour offset inward and the inner contour offset outward, with an offset distance of f.

[0078] Step S3: Use the intersection of parallel scan lines and offset contour curves to form the scan line filling trajectory after grouping. The specific operation is as follows:

[0079] S301. Based on the information in S2, obtain the minimum bounding box of the outermost contour curve, specifically as follows: Figure 4 As shown, based on the data, the number of scan lines N is calculated using the following formula:

[0080]

[0081] Where N is the total number of scan lines, y max and y min y represents the maximum and minimum values ​​of the bounding box along the y-axis, while d represents the offset distance.

[0082] S302, Based on S301, the number of scan lines N is known, from y min The position begins to generate a scan line parallel to the X-axis. The scan line is offset by a distance of (N-1)*d each time. Steps S303 and S304 are repeated until N scan lines are generated.

[0083] S303. Find the intersection of the scan line with all the offset contour curves, retain the coordinates of the intersection points of the scan line and the contour curves, sort them by the size of the X-axis of the intersection point coordinates in ascending order, and record the number of intersection points.

[0084] S304, if as follows Figure 5 As shown, when the number of intersections between the scan line and the contour curve is odd, or as... Figure 6 As shown, when the scan line coincides with the contour curve, a loop operation is entered. The loop process is as follows: discard the intersection information generated by the scan line, offset the scan line by a small distance that does not affect the processing, and then repeat step S303. The loop stops when the number of intersections between the scan line and the contour curve is even and the scan line and the contour curve no longer coincide.

[0085] S305. Group the scan lines based on the number of intersections between the scan lines and the contour curve. Let L... i Fill in the number of intersection points between the i-th scan line and the contour curve, where {L i ,0<=i<=N}, when L i With L i+1 If they are not equal, a grouping operation occurs, and L is grouped. i The previous curves are treated as a large group. By repeating this operation, all scan lines can be divided into m large groups, and the grouping formula is as follows:

[0086]

[0087] S306. After grouping into large groups, it is necessary to form effective scan line filling trajectories based on the intersections of each large group. This requires further subdivision into smaller groups. Although the number of intersections between the scan line and the contour curve within the same large group is equal, they are divided into smaller groups based on the different positions of the filling line segments formed by pairing even and odd intersections on the scan line. For example, if a large group has 4 intersections, and one scan line intersects the contour curve at points P1, P2, P3, and P4, then according to the pairing even and odd intersection principle, line segments P1 and P2 form the first group, and line segments P3 and P4 form the second group. This process is repeated until all scan lines within the current large group have been traversed, ultimately resulting in two smaller groups. Figure 7 As shown, the final division is into 5 groups. The dividing lines shown in the diagram do not actually exist; they are only used to distinguish the dividing areas in the diagram.

[0088] Step S4: Using the latent point greedy algorithm, optimize the empty cutting stroke of the machining trajectory, and finally connect them to form a high-efficiency machining trajectory. The specific operation is as follows:

[0089] S401. Construct a group information structure container, where the group information structure includes the following information: a record of whether it is a first or last point (F1); a record of the pose (F2); and the potential two first points (P). Start1 and P Start2 The two potential endpoints are P. End1 and P End2 The definition of group information is explained as follows: (e.g.) Figure 8 As shown, under each group of members, there are four endpoints and four potential points. The top two points are designated as potential first points, and the bottom two points are designated as potential last points. The relationships are then mapped accordingly. Further, as follows... Figure 9 As shown and Figure 10 As shown, P Start1 and P End1 This corresponds to the first and last points under the original posture, P Start2 and P End2 This corresponds to the first and last points under the reversed posture.

[0090] S402. Iterate through all group members, store the information in the group information structure container, and use the first group's P as the starting point. End1 Let's start by looking for starting point information.

[0091] S403. For the remaining groups, select the group closest to the starting point. Here, a greedy algorithm for potential points is used. For each group, there are four potential points. Based on the distance comparison of the four potential points for each group collected in step S401, determine which of the four potential points is closest to the current starting point. There are four possible cases as follows:

[0092] 1. If P Start1 Recently, they have maintained their original stance and changed the starting point to P. End1 .

[0093] 2. If P Start2 Recently, the attitude has been reversed, and the next starting point has been changed to P. End2 .

[0094] 3. If P End1 Recently, it has maintained its original stance and changed the previous starting point to P. Start1 .

[0095] 4. If P End2 Recently, the attitude has been reversed, and the previous starting point has been changed to P. Start2 .

[0096] S404. When the distance between two points is less than 1.5d, for this type of air cut stroke, it is assumed that the filling trajectory can be directly connected, thereby reducing the number of tool jumps; when it is greater than 1.5d, tool jump operation is performed, and then the operation of step S403 is repeated until all group information is traversed.

[0097] S405. Further connections are made using a bridging curve. After step S404, only two adjacent scan lines in each group have not yet been connected. There are two ways to connect two adjacent scan lines: connecting the first point to the first point or connecting the last point to the last point. Here, the corresponding method is defined as the bridging curve L. Mode1 and L Mode2 Two types, specifically as follows Figure 11 As shown.

[0098] S406. Based on the information obtained in step S403, determine which group maintained its original attitude or underwent an attitude reversal. Connect them using bridging curves. The connection methods for the two cases are as follows:

[0099] The original orientation group connection method: odd-numbered scan lines connecting even-numbered scan lines is L. Mode2 The connection between even-numbered scan lines and odd-numbered scan lines is L. Mode1 connect.

[0100] The group connection method for attitude reversal: odd-numbered scan lines connecting even-numbered scan lines is L. Mode1 The connection between even-numbered scan lines and odd-numbered scan lines is L. Mode2 connect;

[0101] S407. Repeat step S406 until all group members have been traversed, thus generating the final processing trajectory. The final result of the algorithm is as follows: Figure 12 and Figure 13As shown, where Figure 13 For better 3D observation, the tool jump trajectory can be more easily observed. It is evident that the selected machining area is completely covered by the scan line filling trajectory, with no unprocessed areas or areas extending beyond the selected region. Furthermore, a greedy algorithm using latent points optimizes the connection between the filling trajectories of different regions, effectively reducing the number of tool jumps and the empty cutting distance, thus improving overall machining efficiency.

[0102] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A method for optimizing an air cutting stroke of a region filling trajectory based on a potential point greedy algorithm, characterized in that, It comprises the following steps: Step 1: selecting a plurality of contour curves of all areas to be processed; Step 2: judging the inner and outer contours of the plurality of contour curves, and performing contour offsetting; Step 3: obtaining intersection of parallel scanning lines and offset contour curves to form scanning line filling tracks after grouping; Step 4: using a potential point greedy algorithm to perform machining track air travel optimization, and finally connecting to form high-efficiency machining tracks; Step 4.1: Constructing a group information structure body container, wherein the group information structure body includes information as follows: a number F1 recording whether it is a first point or a last point, a number F2 recording which posture the record is, potential two first points P Start1 and P Start2 , potential two last points P End1 and P End2 ; Step 4.2: Iterate through all group members, store information in group information structure container, and set the first group's P End1 As a starting point, let's find some starting point information; Step 4.3: for the remaining groups, use the potential point greedy algorithm to select the group closest to the starting point, and determine whether the group remains in the original posture or undergoes posture inversion according to the potential point distance comparison; Step 4.4: when the distance between two points is less than 1.5d, it is defaulted that the filling tracks can be directly connected; for more than 1.5d, a tool jump operation is performed, and then the operation of step 4.3 is repeated until all group information is traversed; Step 4.5: After step 4.4, only two adjacent scan lines in each group have not been connected. There are two ways to connect the two adjacent scan lines, i.e., connecting the start point with the start point or connecting the end point with the end point, which correspond to the bridge curve L Mode1 and L Mode2 ​ Step 4.6: according to the information obtained in step 4.3, it is known which group remains in the original posture or undergoes posture inversion, and then a bridge curve is used for connection, and the connection methods of the two cases are as follows: The original posture of the team connection mode: odd number of scan lines connecting even number of scan lines is L Mode2 Connection, even number of scan lines connecting odd number of scan lines is L Mode1 Connection; Orientation-reversing team connection: odd-numbered scan lines connect even-numbered scan lines is L Mode1 Connection; even-numbered scan lines connect odd-numbered scan lines is L Mode2 Connection; Step 4.7: repeat step 4.6 until all group members are traversed to realize the generation of the final machining track; The potential point distance comparison operation in step 4.3 corresponds to the following four cases: If P Start1 Recently, keep the original pose, and the next starting point becomes P End1 ; If P Start2 Recently, the posture is reversed and the next starting point becomes P End2 ; If P End1 Recently, keep the original pose, and the last start point becomes P Start1 ; If P End2 Recently, the posture is inverted and the previous starting point becomes P Start2 .

2. The region filling track air travel optimization method based on the potential point greedy algorithm according to claim 1, characterized in that, The contour curve is a region contour curve drawn or imported in CAD / CAM software, which is used to generate region groove machining tracks.

3. The region filling track air travel optimization method based on the potential point greedy algorithm according to claim 2, characterized in that, The nesting relationship between the contour curves in step 2 is divided into the following two categories: Separation: if the contours L1 and L2 do not contain each other, then the contours L1 and L2 are in a separated relationship; In / contain: if the contour L1 is inside the contour L2, then the contour L1 and the contour L2 are in an in relationship; then the contour L2 and the contour L1 are in a containing relationship.

4. The region filling track air travel optimization method based on the potential point greedy algorithm according to claim 3, characterized in that, The execution process of step 2 comprises the following steps: Step 2.1: for the contour curve set collected in step 1, start from the first contour curve to traverse the nesting relationship with other contour curves, and traverse all contour curves in turn; Step 2.2: construct a contour curve depth information tree to obtain the depth information relationship of each contour curve with other contour curves, so as to judge the information of inner and outer contours, and the formula is as follows: ； Where n is the contour curve depth, and when n is special and equal to 0, it means that the contour curve is the outermost contour curve; Step 2.3: offset all contour curves, and specifically offset twice according to the information of step 2.2, wherein the outer contour is offset inward, and the inner contour is offset outward, and the offset distance is f.

5. The region filling track air travel optimization method based on the potential point greedy algorithm according to claim 4, characterized in that, The execution process of step 3 comprises the following steps: Step 3.1: Obtain the curve minimum bounding box of the outermost contour, according to the data, calculate the number of scan lines N, the formula is as follows: ； where N is the total number of scan lines, y max and y min are the maximum and minimum values of the y-axis of the bounding box, and d is the offset distance. Step 3.2: From y min Start generating scan lines parallel to the X axis from the position, each time offset by a distance of (N-1)*d, repeat Step 3.3 and Step 3.4 until N scan lines are generated; Step 3.3: Intersect the scan line with all the offset contour curves, keep the intersection point coordinates of the scan line and the contour curve, and sort the intersection point coordinates according to the X axis size, the sorting rule is from small to large, and record the number of intersection points; Step 3.4: When the number of intersection points of the scan line and the contour curve is odd, or the scan line and the contour curve coincide, enter the loop operation, the loop content is: discard the intersection point information generated by the scan line, offset the scan line by a small distance that does not affect the processing, and then repeat step 3.3, until the number of intersection points of the scan line and the contour curve is even, and the scan line and the contour curve do not coincide, stop the loop; Step 3.5: Group the scan lines according to the number of intersection points with the contour curve; let L i be the number of intersection points for the i-th scan line, where {L i , 0 <= i <= N}, when L i is not equal to L i+1 , then grouping operation occurs, the curve before L i is taken as a large group, repeat such operation, then all scan lines can be divided into m large groups, and the grouping formula is as follows: ； Step 3.6: After completing the division of the large group, it is necessary to form effective scan line filling tracks according to the intersection points of each large group, which needs to be further divided into small groups.

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