Interlayer staggered stacking path planning method for additive manufacturing

Abstract

The invention discloses an interlayer staggered stacking path planning method for additive manufacturing. Obtaining a filling area contour of a model plane slice polygon, calculating a feature vector, and determining a grid arrangement direction, a starting point and a starting filling line segment; searching an adjacent line segment set connected with the end point of the previous line segment on the lower layer or the upper layer, marking all the adjacent line segments, selecting a transition line segment adjacent to the line segment, and if the other layer of branch line segments connected with the transition line segment are not marked, taking the transition line segment as the next line segment, and taking the transition line segment as the next line segment; and connecting the end points of the line segments end to end to form a continuous line segment as a filling path line formed by final planning until the other layer of branch line segments connected with all the adjacent transition line segments are marked. According to the method, in the additive manufacturing process, the number of short paths and idle strokes can be reduced, the frequency of frequent starting and stopping is reduced, and the working efficiency is improved. And meanwhile, the excessive accumulation condition of materials at the intersection point and the molding instability at the start-stop point are reduced.

Description

Technical Field

[0001] This invention relates to a method for planning interlayer staggered stacking paths in additive manufacturing, belonging to the field of additive manufacturing technology. Background Technology

[0002] In the field of additive manufacturing (AM), thin-walled mesh structures are a very common and important design strategy, especially suitable for components requiring lightweighting, specific mechanical properties, or functional characteristics (such as heat dissipation and fluid flow). Material is placed only along the critical path that bears the load or achieves the function, reducing unnecessary material buildup and lowering material costs and manufacturing time. It has broad application prospects in aerospace lightweight components, high-performance energy-absorbing structures, heat exchangers, and medical implants. The unique advantages of additive manufacturing make it possible to fabricate complex internal thin-walled mesh structures that are impossible to process using traditional manufacturing methods.

[0003] Directed Energy Deposition (DED) additive manufacturing uses a high-energy beam (laser / electron beam / electric arc) to melt and deposit synchronously fed metal filaments or powders, creating layers one by one. Its unique process characteristics give it significant advantages in manufacturing specific types of mesh structures, especially suitable for large-scale, functionally integrated, multi-material, or repair / hybrid manufacturing applications. Due to its extremely high material deposition rate and typically larger formed-size dimensions, it is suitable for macroscopic mesh structures. It rapidly fills large-volume mesh areas, significantly shortening manufacturing cycles and reducing the cost of large, lightweight structures. DED has extremely broad material compatibility, allowing for easy switching between metal powders or filaments, and supports coaxial or off-axis feeding.

[0004] In Directed Energy Deposition (DED) additive manufacturing, path planning directly impacts heat input distribution, material deposition, cooling rate, and geometric accuracy. At grid nodes (path intersections), the nozzle needs to repeatedly stop, leading to severe local heat accumulation, exacerbating material overheating, grain coarsening, residual stress, and deformation. Furthermore, at nodes, the convergence of multiple paths can easily cause over-deposition due to molten pool overlap, resulting in incomplete fusion and porosity. In addition, the grid structure contains numerous short paths, frequent start-stop cycles, and significant idle travel, significantly reducing deposition efficiency and affecting interlayer bonding due to frequent thermal cycling. Therefore, it is necessary to specifically design the scanning paths at nodes to avoid excessive material deposition or defects, generate the longest possible continuous paths, reduce start-stop cycles, improve efficiency, and enhance heat distribution. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a method for planning interlayer staggered stacking paths for additive manufacturing.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for planning interlayer staggered stacking paths in additive manufacturing includes the following steps: Step 1. Obtain the outline of the filled region of a series of planar slice polygons of the model; the outer outline of the filled region is formed by the outer surface of the model, and the inner outline of the filled region is formed by the mesh surface of the model. Step 2. Calculate the feature vectors based on the contours within the filled region of the polygon; determine the mesh layout direction based on the feature vectors; Step 3. Generate the skeleton lines of the filled area of ​​the polygon. Each skeleton line branch consists of a series of sequential skeleton points, and the skeleton line branches are connected by skeleton branch points. Step 4. Designate the line segment connecting the nearest branch points of two adjacent floors as the inter-floor transition line segment; Step 5. Set the skeleton branch line segment set of the filled region of the lower-level polygon. , define the first Branch line segment The processing flag is 0 indicates no processing, 1 indicates processing; determine the starting point and the starting fill segment; Step 6. Search for the set of adjacent segments connected to the endpoint of the previous segment in the lower layer. If there are unmarked segments with similar layout directions, use them as the next segment and perform inter-layer path connection, and mark them as processed. If there are no unmarked segments, select the transition segment adjacent to the segment. If there are unmarked upper-layer branch segments connected to the transition segment, use the transition segment as the next segment and proceed to Step 7. Otherwise, proceed to Step 8. A line segment whose orientation is similar to the corresponding grid layout direction is defined as the line segment's orientation relative to the grid layout. The line segment with the smallest included angle; Step 7. Search for the set of adjacent segments connected to the endpoints of the previous segment in the upper layer. If there are unmarked segments with similar layout direction, use them as the inter-layer path connection method for the next segment and mark them as processed. If there are no unmarked segments, select the transition segment adjacent to the segment. If there are unmarked lower-level branch segments connected to the transition segment, use the transition segment as the next segment and repeat Step 6 until all the lower-level branch segments connected to the adjacent transition segments are marked, then proceed to Step 8. Step 8. Connect all the unprocessed line segments in the upper layer into continuous line segments based on the endpoints of the line segments, which will be used as the final planned fill path lines.

[0007] Furthermore, the inter-layer path connection method includes the following steps: Suppose that in the current layer, the path segment is filled. The endpoint is The corresponding centroid is The corresponding arrangement direction is ,in The direction of this arrangement is... or The determination is made by adjusting the remainder of the g value. still If in If there are unmarked branch segment endpoints in the neighborhood, then Calculate the endpoint Using the centroid point Starting from, with The direction of the ray ; In order to be in Calculate the endpoints of unlabeled branch segments in the neighborhood. Using the centroid point Starting from, with The direction of the ray ; And according to and Based on the relationship, select fill line segment; If there are no unmarked branch line segment endpoints, select the transition line segment adjacent to that line segment. If there are unmarked branch line segments in another layer connected to the transition line segment, use that transition line segment as the next line segment and repeat the above steps until all branch line segments in another layer connected to the transition line segment are marked, then stop the inter-layer path connection.

[0008] Furthermore, if and The relationship is At that time, choose the centroid point. Starting from, with The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. At the same time, update the centroid point to the centroid point. , centroid point It is based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, , It is a centroid point, taking values ​​from the set of centroid points. The corresponding arrangement direction is: Then repeat step i until all the endpoints of the branch segments are marked.

[0009] Furthermore, if and The relationship is At that time, choose the centroid point. Starting from The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. Simultaneously update the centroid point to the centroid point. , centroid point Based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, The corresponding arrangement direction is: Then repeat step i until all the endpoints of the branch segments are marked.

[0010] Furthermore, step 5, determining the starting point and the starting fill segment, includes the following steps: Step 51) Select the endpoint of the skeleton segment with the smallest coordinate value , is the starting point; at the same time, the centroid point closest to this starting point is selected as . ; Step 52) Starting from the point In the set of adjacent branches, select the direction that is consistent with the mesh layout. Similar branch segments are the starting fill segments And mark it as processed; calculate the branch segment and... When the included angle is at its minimum, the branch line segment is perpendicular to the direction of the grid arrangement. resemblance.

[0011] Furthermore, the filling path is determined based on the spacing between the grids.

[0012] Furthermore, the filling path is either the filling path of the skeleton line of the polygonal filling area or a filling path that swings along the skeleton line diameter, so that the swing range completely covers the spacing between the grids.

[0013] Furthermore, the specific steps of step 2 include: 21) Let the set of centroids of the contour within the filled region be... , among which, the Centroid of the inner contour R is the set of real numbers. The number of inner contours, Let the set of centroids of the contour within the filled region be represented; then the first... The centroid of the inner contour ;in: It is the first The first inner contour polygon One vertex, It is the first The first inner contour polygon One vertex, It is the total number of its vertices; It is the total area of ​​the h-th inner contour polygon; It is the first The directed area of ​​each vertex; 22) The covariance matrix of the set of centroid points of the contour within the filled region is: ,in The centroid is the set of the mass center; 23) Covariance matrix The eigenvalues ​​and eigenvectors satisfy: ;in, For eigenvalues, Let be the eigenvectors; let the eigenvalues ​​be . and Then the corresponding eigenvector and This indicates the orientation of the grid.

[0014] Furthermore, step 3 includes the following specific steps: Step 31) Given the set of outline polygons for the filled region Its skeleton line ;in, It is a point Time Euclidean distance; Represents polygons The boundary; Step 32) Set and Given two unequal contour polygons representing the set of contour polygons for the filled region, any skeleton line branch B is represented as: ; Step 33) If the skeleton branches They are connected by a common skeletal branch point. Connect, then about that point The set of adjacent branches is: So, skeleton branches Regarding its skeletal branch points The set of adjacent branches is: “ " indicates not included; N represents the neighborhood, the first The first branch k The branch points are ; It is the first The first branch k Branch points The neighborhood representation of a node is that the branches within this neighborhood are first related to the branch point. Connected, but not containing this. Branches; and It is a branch point The neighborhood of a node is all the branches connected to the branch point. Represents the neighborhood of a branch with respect to the branch point; Represents the neighborhood of the branch point.

[0015] The beneficial effects achieved by this invention are as follows: The interlayer staggered stacking path planning method disclosed in this invention has significant advantages in the additive manufacturing process, especially for the manufacturing of specific types of mesh structures. It can reduce the number of short paths and idle strokes, decrease the frequency of start-stop operations, and improve work efficiency. It also reduces the over-stacking of material at intersections and the instability of forming at start-stop points. Furthermore, the interlayer staggered forming improves heat distribution and enhances the bonding ability between material layers. Attached Figure Description

[0016] Figure 1 Schematic diagram showing the selection of the starting point and corresponding centroid point; Figure 2 This is a schematic diagram of the selection of the starting path segment; Figure 3 This is a schematic diagram showing the selection of fill path segments and layout direction; Figure 4 This is a schematic diagram of the interlayer staggered filling path of a quadrilateral grid array; Figure 5 This is a schematic diagram of the interlaced filling paths between layers of a hexagonal grid array. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0018] This embodiment discloses a method for planning interlayer staggered stacking paths in additive manufacturing, including the following steps: Step 1. Obtain a series of planar slice polygonal fill region outlines of the model. The outer outline of the fill region is formed by the outer surface of the model, while the inner outline of the fill region is formed by the inner surface of the model's mesh.

[0019] Step 2. First, calculate the eigenvectors based on the contours within the polygon-filled area. Then, determine the mesh layout direction based on the eigenvectors.

[0020] 21) Assume that the set of centroids of the contour within the filled region is... , among which, the Centroid of the inner contour R is the set of real numbers. The number of inner contours, This represents the set of centroids of the contour within the filled region. Then the... The centroid of the inner contour .in: It is the first The first inner contour polygon There are vertices, whose coordinates are... , It is the first The first inner contour polygon There are vertices, whose coordinates are... , It is the total number of its vertices, and . It is the total area of ​​the h-th inner contour polygon. . It is the first The directed area of ​​each vertex .

[0021] 22) The covariance matrix of the set of centroid points of the contour within the filled region is: ,in For the centroid point set to the mass center, .

[0022] 23) Covariance matrix The eigenvalues ​​and eigenvectors satisfy: .in, For eigenvalues, Let be the eigenvector. Since the contour points within the filled region of a planar slice polygon are a two-dimensional point set, we assume the eigenvalues ​​are . and ( Then the corresponding eigenvector and This indicates the orientation of the grid.

[0023] Step 3. Generate the skeleton lines of the polygonal fill area. Each skeleton line branch is composed of a series of sequential skeleton points, and the skeleton line branches are connected by skeleton branch points.

[0024] Step 31) Given the set of outline polygons for the filled region Its skeleton line .in, It is a point Time Euclidean distance. Represents polygons The boundary.

[0025] Step 32) Set and Given two unequal contour polygons representing the set of contour polygons for the filled region, any skeleton line branch B can be represented as: .

[0026] Step 33) If the skeleton branches They are connected by a common skeletal branch point. Connect, then about that point The set of adjacent branches is: So, skeleton branches Regarding its skeletal branch points The set of adjacent branches is: “ "" indicates that it does not contain. N represents the neighborhood, the first... The first branch k The branch points are .therefore It is the first The first branch k Branch points The neighborhood representation of a node is that the branches within this neighborhood are first related to the branch point. Connected, but not containing this. Branches. And It is a branch point The neighborhood of a node is all the branches connected to the branch point. It represents the neighborhood of a branch with respect to the branch point. Represents the neighborhood of the branch point.

[0027] Step 4. The line segment connecting the nearest branch points between two adjacent layers is the inter-layer transition line segment. Given a set of branch points between two adjacent layers. and , For point The Euclidean distance between them, where , .definition Inter-layer nearest neighbor: The line segment connecting the two points is... , .

[0028] Step 5. Assume that the skeleton branch line segment set of the lower-level polygon filling region... , define the first Branch line segment The processing flag is 0 indicates no processing, and 1 indicates processing. The selection of the starting point and the starting fill segment is as follows: Step 51) Select the endpoint of the skeleton segment with the smallest coordinate value , is the starting point. Simultaneously, the centroid point closest to this starting point is selected as... .like Figure 1 As shown.

[0029] Step 52) Starting from the point In the set of adjacent branches, select the direction that is consistent with the mesh layout. Similar branch segments are the starting fill segments And mark it as processed. For example Figure 2 As shown. The formula is used to calculate the branch line segment and... When the included angle is at its minimum, the branch line segment is perpendicular to the direction of the grid arrangement. resemblance.

[0030] Step 6. Search for the set of adjacent segments connected to the endpoint of the previous segment in the lower layer. If there is an unmarked segment with a similar layout direction (similar meaning as explained in step 52), treat it as the next segment and perform inter-layer path connection, and mark it as processed. If there is no unmarked segment, select the transition segment adjacent to it. If there is an unmarked upper-layer branch segment connected to the transition segment, use the transition segment as the next segment and proceed to step 7; otherwise, proceed to step 8.

[0031] Step 7. Search for the set of adjacent segments connected to the endpoints of the previous segment in the upper layer. If there are unmarked segments with similar layout direction, use them as the inter-layer path connection method for the next segment and mark them as processed. If there are no unmarked segments, select the transition segment adjacent to the previous segment. If there are unmarked lower-level branch segments connected to the transition segment, use the transition segment as the next segment and repeat step 6 until all the lower-level branch segments connected to the adjacent transition segments are marked, then proceed to step 8.

[0032] Step 8. Connect all the unprocessed line segments in the upper layer into continuous line segments based on the endpoints of the line segments, which will be used as the final planned fill path lines.

[0033] Inter-layer path connection method: Step i. Assume that within the current layer (the current layer can be either the upper or lower layer; if the current layer is the upper layer, then the other layer is the lower layer; if the current layer is the lower layer, then the other layer is the upper layer), fill the path segment. The endpoint is The corresponding centroid is The corresponding arrangement direction is ,in The direction of this arrangement is... or The determination is made by adjusting the remainder of the g value. still This is the index corresponding to the previous layout direction, such as the grid layout direction in step 52). Then g = 0. If in If there are unmarked branch segment endpoints in the neighborhood, then Calculate the endpoint Using the centroid point Starting from, with The direction of the ray . In order to be in Calculate the endpoints of unlabeled branch segments in the neighborhood. Using the centroid point Starting from, with The direction of the ray And perform step ii, according to and Based on the relationship, select the fill line segment.

[0034] If there is no unmarked branch segment endpoint, select the transition segment adjacent to the segment. If there is an unmarked branch segment in another layer connected to the transition segment, use the transition segment as the next segment and repeat step i until all the branch segments in another layer connected to the transition segment are marked, then stop connecting the inter-layer paths.

[0035] Step ii. If Choose with the centroid point Starting from, with The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. At the same time, update the centroid point to the centroid point. , centroid point It is based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, , It is a centroid point, taking values ​​from the set of centroid points. The corresponding arrangement direction is... Then repeat step i until all endpoints of the branch segments are marked. For example... Figure 3 As shown in the figure, the outline is a thin line, the path line is a thick line, and the line segment mentioned above is a straight line segment of the path line.

[0036] if Choose with the centroid point Starting from The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. At the same time, update the centroid to the centroid point. , centroid point Based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, The corresponding arrangement direction is... Then repeat step i until all the endpoints of the branch segments are marked.

[0037] The spacing between grids varies. For thin-walled mesh structures, the spacing between grids is generally smaller, and the fill path is the fill path of the skeleton lines of the polygonal fill area. If the spacing between grids is larger, the fill path can be oscillated along the skeleton line diameter to completely cover the spacing.

[0038] Figure 4 and Figure 5 This is a specific example of the application planning of this method, illustrating that the method of this invention can be applied to polygonal grid array shapes.

[0039] Figure 4 In step a, the starting path segment is determined in the next layer according to step 5, and then its neighboring path segments are determined according to step 6. Step b, if all path segments in the next layer have been marked, connects them to the path segments in the previous layer (represented by the thick solid line in the diagram), and then connects the next layer paths. If all path segments in the next layer have been marked, connect them to the path segments in the previous layer, and then connect the previous layer paths. Step c, connects all adjacent unmarked paths in the previous layer. Step d, selects an unmarked neighboring area in the next layer as the starting path to generate another row of path lines. Step e, continues to connect the unmarked neighboring path segments based on the path generated in step d, performing staggered connections between upper and lower layers. Step d, continues to develop paths within the unmarked neighboring areas in the previous layer, and finally... Figure 4 The path connections on layers a, b, c, d, e, and f generate complete continuous paths. This method can handle path planning not only for quadrilateral grid array regions but also for hexagonal grid array regions, such as... Figure 5 As shown in Figures a, b, c, d, e, f, g, and h, this method can handle path planning for n-sided grid array regions.

[0040] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for planning interlayer staggered stacking paths in additive manufacturing, characterized in that, Includes the following steps: Step 1. Obtain the outline of the filled region of a series of planar slice polygons of the model; The outer contour of the filled region is formed by the outer surface of the model, while the inner contour of the filled region is formed by the mesh surface of the model. Step 2. Calculate the feature vector based on the contour within the filled region of the polygon; according to Eigenvectors determine the orientation of the grid layout; Step 3. Generate the skeleton lines of the filled area of ​​the polygon. Each skeleton line branch consists of a series of sequential skeleton points, and the skeleton line branches are connected by skeleton branch points. Step 4. Designate the line segment connecting the nearest branch points of two adjacent floors as the inter-floor transition line segment; Step 5. Set the skeleton branch line segment set of the filled region of the lower-level polygon. , define the first Branch line segment The processing flag is 0 indicates that the data has not been processed, and 1 indicates that the data has been processed. Determine the starting point and the initial fill segment; Step 6. Search for the set of adjacent segments that connect to the endpoint of the previous segment in the lower layer. If there are segments that are similar to the corresponding layout direction but have not been marked, treat them as the next segment and perform inter-layer path connection, and mark them as processed. If there is no unmarked line segment, select the transition line segment adjacent to the line segment. If there is an unmarked upper branch line segment connected to the transition line segment, take the transition line segment as the next line segment and execute step 7; otherwise, execute step 8. A line segment whose orientation is similar to the corresponding grid layout direction is defined as the line segment's orientation relative to the grid layout. The line segment with the smallest included angle; Step 7. Search for the set of adjacent segments connected to the endpoints of the previous segment in the upper layer. If there are unmarked segments with similar layout direction, use them as the inter-layer path connection method for the next segment and mark them as processed. If there is no unmarked line segment, select the transition line segment adjacent to the line segment. If there is an unmarked lower branch line segment connected to the transition line segment, take the transition line segment as the next line segment and repeat step 6 until all the lower branch line segments connected to all the adjacent transition line segments are marked, and proceed to step 8. Step 8. Connect all the unprocessed line segments in the upper layer into continuous line segments based on the endpoints of the line segments, which will be used as the final planned fill path lines.

2. The interlayer staggered stacking path planning method for additive manufacturing according to claim 1, characterized in that, The inter-layer path connection method includes the following steps: Step i: In the current layer, fill the path segment. The endpoint is The corresponding centroid is The corresponding arrangement direction is ,in The direction of this arrangement is... or The determination is made by adjusting the remainder of the g value. still If in If there are unmarked branch segment endpoints in the neighborhood, then Calculate the endpoint Using the centroid point Starting from, with The direction of the ray ; In order to be in Calculate the endpoints of unlabeled branch segments in the neighborhood. Using the centroid point Starting from, with The direction of the ray ; And according to and Based on the relationship, select fill line segment; If there are no unmarked branch line segment endpoints, select the transition line segment adjacent to that line segment. If there are unmarked branch line segments in another layer connected to the transition line segment, use that transition line segment as the next line segment and repeat the above steps until all branch line segments in another layer connected to the transition line segment are marked, then stop the inter-layer path connection.

3. The interlayer staggered stacking path planning method for additive manufacturing according to claim 2, characterized in that, like and The relationship is At that time, choose the centroid point. Starting from, with The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. ， Simultaneously update the centroid point to the centroid point. , centroid point It is based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, , It is a centroid point, taking values ​​from the set of centroid points. The corresponding arrangement direction is: ; Then repeat step i until all the endpoints of the branch segments are marked.

4. The interlayer staggered stacking path planning method for additive manufacturing according to claim 2, characterized in that, like and The relationship is At that time, choose the centroid point. Starting from The branch segment of a ray that is closest to its endpoint is a filled segment, i.e. ； Simultaneously update the centroid point to the centroid point. , centroid point Based on the centroid point Starting from The distance on the projection of the ray from the centroid point The nearest centroid, ； The corresponding arrangement direction is ; Then repeat step i until all the endpoints of the branch segments are marked.

5. The interlayer staggered stacking path planning method for additive manufacturing according to claim 1, characterized in that, Step 5, determining the starting point and the starting fill segment, includes the following steps: Step 51) Select the endpoint of the skeleton segment with the smallest coordinate value , is the starting point; at the same time, the centroid point closest to this starting point is selected as . ; Step 52) Starting from the point In the set of adjacent branches, select the direction that is consistent with the mesh layout. Similar branch segments are the starting fill segments And mark it as processed; calculate the branch segment and... When the included angle is at its minimum, the branch line segment is perpendicular to the direction of the grid arrangement. resemblance.

6. The interlayer staggered stacking path planning method for additive manufacturing according to claim 1, characterized in that, The filling path is determined based on the spacing between the grids.

7. The interlayer staggered stacking path planning method for additive manufacturing according to claim 6, characterized in that, The filling path is either the filling path of the skeleton line of the polygon filling area or a filling path that swings along the skeleton line diameter, so that the swing range completely covers the spacing between the grids.

8. The interlayer staggered stacking path planning method for additive manufacturing according to claim 1, characterized in that, Step 2 includes the following specific steps: 21) Let the set of centroids of the contour within the filled region be... , among which, the Centroid of the inner contour R is the set of real numbers. The number of inner contours, Let the set of centroids of the contour within the filled region be represented; then the first... The centroid of the inner contour ;in: It is the first The first inner contour polygon One vertex, It is the first The first inner contour polygon One vertex, It is the total number of its vertices; It is the total area of ​​the h-th inner contour polygon; It is the first The directed area of ​​each vertex; 22) The covariance matrix of the set of centroid points of the contour within the filled region is: ,in The centroid is the set of the mass center; 23) Covariance matrix The eigenvalues ​​and eigenvectors satisfy: ;in, For eigenvalues, Let be the eigenvectors; let the eigenvalues ​​be . and Then the corresponding eigenvector and This indicates the orientation of the grid.

9. The interlayer staggered stacking path planning method for additive manufacturing according to claim 1, characterized in that, Step 3 includes the following specific steps: Step 31) Given the set of outline polygons for the filled region Its skeleton line ;in, It is a point Time Euclidean distance; Represents polygons The boundary; Step 32) Set and Given two unequal contour polygons representing the set of contour polygons for the filled region, any skeleton line branch B is represented as: ； Step 33) If the skeleton branches They are connected by a common skeletal branch point. Connect, then about that point The set of adjacent branches is: So, skeleton branches Regarding its skeletal branch points The set of adjacent branches is: " " indicates not included; N represents the neighborhood, the first The first branch k The branch points are ; It is the first The first branch k Branch points The neighborhood representation of a node is that the branches within this neighborhood are first related to the branch point. Connected, but not containing this. Branches; and It is a branch point The neighborhood of a node is all the branches connected to the branch point. Represents the neighborhood of a branch with respect to the branch point; Represents the neighborhood of the branch point.

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