Reconstruction optimization method for two-dimensional irregular parts

Abstract

The invention belongs to the field of part reconstruction, and particularly relates to a two-dimensional irregular part-oriented reconstruction optimization method, which comprises the following steps of: reading vertex information and plate information of an irregular part; calculating the center of mass and the area of each part; solving a convex hull set of each part; solving the minimum enclosing rectangle of the convex hull set, and calculating the effective area ratio of the preprocessed part reconstruction; all the parts are classified; establishing a two-dimensional irregular part reconstruction strategy, preprocessing the part, and reconstructing a plurality of new matrix-shaped parts; establishing a rectangular piece layout coding sequence and sorting; a dynamic layout strategy is adopted, and a layout result is obtained; and inputting the geometric vertexes of the two-dimensional irregular parts to automatically obtain the layout mode corresponding to the highest plate utilization rate. According to the method, the optimal layout can be obtained only by inputting the plate information and the information of the two-dimensional irregular parts, the layout time is saved, the layout efficiency of the two-dimensional irregular parts is improved, and the labor intensity of workers is reduced.

Description

Technical Field

[0001] This application belongs to the field of part reconstruction, specifically involving a reconstruction optimization method for two-dimensional irregular parts. Background Technology

[0002] Reassembly is a crucial step in industrial production, from design to automated manufacturing, and its quality directly impacts raw material utilization. Traditional part reassembly relies on manual operations. Technicians manually input part drawings and then translate or rotate them in a CAD environment. The goal is to maximize the total area of ​​the material that accommodates the drawings or the remaining usable area, while ensuring that the drawings do not overlap or exceed the material's boundaries. This method is inefficient, and the reassembly results heavily depend on the experience and skill level of the technicians.

[0003] Two-dimensional part reconstruction is the most common reconstruction problem in practical applications. Based on the shape of the parts, they can be divided into regular parts and irregular parts. Reconstruction of regular two-dimensional parts is usually a rectangular or circular part layout problem, mainly studying how to lay out rectangular parts on a rectangular sheet. Because the shapes of rectangular and circular parts are relatively regular, the rotation angle of rectangular parts is limited during layout, only 0° or 90°. Each part can be laid out according to a uniform rule, making the calculation relatively simple and the sheet material utilization rate high. However, for two-dimensional irregular parts composed of arc segments, spline curves, and straight lines, the complexity of their geometry makes the reconstruction calculation very complex. For example, patent publication number CN118196356A, entitled "A Reconstruction and Analysis Method and System for Irregular Object Images Based on Point Clouds," discloses: This invention relates to a reconstruction and analysis method and system for irregular object images based on point clouds, belonging to the field of graphic visualization technology. The method includes: importing an image; image point cloud computing processing; obtaining the center point B of the object in the image in the world coordinate system; constructing an object coordinate system with the origin at the object's center point B relative to the object; calculating the object's maximum diameter; calculating the camera coordinate point; calculating the camera rotation angle; assigning the calculated camera coordinate point and camera rotation angle to a virtual 3D camera, and the camera viewpoint outputs the front view of the object. However, the above-mentioned existing technology has a relatively low material utilization rate when reconstructing irregular parts, which can no longer meet the production requirements of today's fierce market competition. Summary of the Invention

[0004] To address the problem of reconstructing two-dimensional irregular parts in actual production, this invention proposes a reconstruction optimization method for two-dimensional irregular parts. This method can improve the utilization rate of sheet metal and reconstruction efficiency, reduce the labor intensity of technical personnel, and improve the economic benefits of enterprises.

[0005] To achieve the above effects, the technical solution of this application is as follows: A reconstruction optimization method for two-dimensional irregular parts includes the following steps: Step 1: Read in the vertex information and sheet material information of the irregular part; Step 2: Calculate the centroid and area of ​​each part; Step 3: Solve for the convex hull set R of each part; Step 4: Find the minimum bounding rectangle of the convex hull set R, and calculate the effective area ratio of the reconstructed part AB after preprocessing. ; Step 5: Classify each part according to its effective area ratio and whether there are concave corners; Step 6: Establish a two-dimensional irregular part reconstruction strategy and preprocess the parts to reconstruct multiple new matrix-shaped parts; Step 7: Establish and sort the layout coding sequence for the rectangular components; Step 8: Adopt a dynamic layout strategy and obtain the layout result; Step 9: By inputting the geometric vertices of the two-dimensional irregular part through the above steps, the layout method corresponding to the highest material utilization rate can be automatically obtained.

[0006] Furthermore, in step 1, the length of the sheet material is input. ,width And detailed information on the irregular parts involved in the reconstruction, including: part number, coordinates of the part vertices; Furthermore, the coordinates of the vertices of the parts are recorded clockwise. If the parts have holes, the outer vertices are recorded counterclockwise, and the inner vertices are recorded counterclockwise. Each part is represented as a set of multiple scattered points.

[0007] Furthermore, the vertex set of any part in step 2 is represented as... ,in Let x be the nth x-coordinate of the part. Let be the nth ordinate of the part. The calculation methods for the area and centroid of each part are as follows: Based on the principle that there exists a line segment connecting any two points within the polygon that is either inside or on the edge of that polygon, the irregular polygon is subdivided into convex and concave polygons. Any convex polygon part can be divided into multiple triangles. Assume that a certain triangle has vertex . , and The formula for the area of ​​the triangle is: The centroid of the triangle Represented as , .

[0008] For convex polygons, the centroid is calculated by weighting the areas of the decomposed triangles and then averaging the results. , ,in This represents the number of triangles that a convex polygon can be decomposed into. Indicates , and A general expression for calculating the area of ​​a triangle with vertex A; Then it represents the first decomposition of the convex polygon. The area of ​​each triangle, and Let x and y represent the x and y coordinates of the centroids of the triangles decomposed from the convex polygon, respectively. .

[0009] Similarly, for a concave polygon, it is decomposed into several non-overlapping small convex polygons. For each small convex polygon obtained from the decomposition, its corresponding area and centroid are calculated. The centroid of the final concave polygon is obtained by weighting the area of ​​the decomposed convex polygons.

[0010] Furthermore, the specific method for solving the convex hull using the Jarvis step method in step 3 is as follows: for the part coordinates Organize the information and find the answer using Jarvis's stepwise method. convex hull: First find middle The point with the smallest value ,save Add to the convex hull set R, and from Remove from the middle; take The remaining points in the middle are sequentially connected with Connect and record with Based on the angles of the axis, sort the remaining points in ascending order of angle, and then select the point corresponding to the smallest angle. Add it to the convex hull set R, and put from Eliminate from the middle; and so on, searching for... Until the entire process is completed. All points, until There is only one point left to choose from. Let R be the set of points of the convex hull. Connecting the points in R end to end forms the convex hull of the point. The convex hull.

[0011] Furthermore, from When searching for the next point, if a straight line appears... There's another dot above. In this situation, at this time and All are added to the convex hull set R, and the distances are... The point that is furthest away by a straight line is used as the starting point for finding the next point.

[0012] Furthermore, in step 4, the minimum bounding rectangle is solved and the effective area ratio is calculated. The specific method is as follows: First, arbitrarily select two adjacent points on the convex hull set R. and Calculate the straight line passing through these two points. , and for The x and y coordinates, in Using straight lines as the sides of a rectangle, calculate the distance from all points on the convex hull to the rectangle. distance , past Longest distance Points to make Parallel lines, obtain the second side of the rectangle and The height of the rectangle Project the remaining points on the convex hull to Above, record the two points that are furthest apart in the X-axis from the projection point. and Calculate the width of the rectangle. At this time, the area of ​​the envelope rectangle is ; Traverse all adjacent points on the convex hull, , Let the number of points on the convex hull be the minimum area rectangle. The rectangle with the smallest area is then taken as the minimum bounding rectangle. The effective area ratio of this part is... ,in This indicates the actual area of ​​the part.

[0013] Furthermore, in step 5, an effective area ratio indicator is introduced. ,in For the first The area of ​​each part The minimum bounding rectangle of the part; when or If a part has no concave corners and is classified as a rectangle, then this type of part will not participate in subsequent reconstruction steps; when And without concave angles, it is judged to be a triangular-like shape; when Furthermore, the presence of concave angles indicates that it is a concave polygon. It is determined to be a concave angle.

[0014] Furthermore, step 6 specifically includes: 1) If part A is determined to be a rectangle, proceed directly to steps 3 and 4 to reconstruct it into the corresponding minimum bounding rectangle. ; 2) If part A It is a polygon containing defects such as holes, where This represents the outermost vertices of part A, recorded in clockwise order. This represents the innermost vertex, i.e., the inner hole, recorded counter-clockwise. First, determine the area of ​​the inner hole. The shortest diagonal inside the hole Or the shortest adjacent side inside the hole The calculation method is as follows: ,in , Let represent the coordinates of any two distinct vertices within the inner hole, and .

[0015] Specific aperture area small parts Select according to area from largest to smallest, that is To select parts Longest diagonal and longest adjacent edge Not exceeding the shortest diagonal of the inner hole with the shortest adjacent edge Here are the constraints, where Select the candidate part and fill it into the inner hole of part A for reconstruction. The centroid of the candidate part is aligned with the centroid of part A as the placement method. Reconstruct the candidate part and part A into a rectangular part with the following constraints:

[0016]

[0017] 3) If part B is judged to be a defect-free concave polygon, first process the part in step 3 to form a convex hull set, and use the smallest bounding rectangle as its reconstructed rectangular part to solve the effective area ratio of the convex hull set. 4) If part B If the shape is determined to be a triangle, first consider reconstructing it with other parts of the same type (B) to form a new minimum bounding rectangle. If no part B of the same type exists, then it is compared with other types of triangles, such as part C. Reconstruct the structure and calculate the longest diagonal of part B. and longest adjacent edge Calculate the longest diagonal of part C. and longest adjacent edge And record the lines containing these four line segments. , , , The longest sides of parts B and C are respectively and and determine and The line in question is and Fix part B, according to and The parallel directions and the line connecting the centers of mass of the two parts are perpendicular to each other. and Place parts B and C according to the principle, and determine the distance between parts B and C after placement as required. satisfy: :

[0018] in Represents the coordinates of all points in part B. Represents the coordinates of all points in part C. Let each represent a point in part B and part C respectively. This means finding the shortest distance between part B and part C.

[0019] Determine the internal diagonal or adjacent sides of the part. Then, the placement of parts B and C in the two groups can be confirmed; based on this, part B remains stationary, so that... By flipping part C along the axis of symmetry, we can determine the other two placement methods. Find the minimum bounding rectangle of these four placement methods. The rectangle with the smallest area is the optimal reconstruction layout BC between part B and part C. Traverse other triangular rectangular parts to find the optimal reconstruction layout between each part and part B. Use the optimal reconstruction layout with the smallest area as the optimal reconstruction layout between part B and another part. After completing the above steps, the optimal reconstruction method between each part is obtained. The minimum bounding rectangle corresponding to the reconstructed part vertex information is then calculated as a whole, transforming the problem into a solution. The layout method for rectangular components with different heights and widths, each rectangular component can be represented as follows: , , The designation indicating the rectangular component. These represent the width, height, and effective area ratio of the rectangular component, respectively.

[0020] Furthermore, the sorting method in step 7 is as follows: place the rectangular pieces involved in the layout vertically, ensuring that all rectangular pieces have a height greater than or equal to their width when placed. Sort the rectangular pieces from largest to smallest according to their area. Based on the previous sorting, sort the rectangular pieces from largest to smallest according to their height and label them.

[0021] Furthermore, the implementation method of the dynamic layout strategy in step 8 is as follows: the rectangular parts are laid out sequentially according to the order of step 7. Each time the rectangular part is laid out, it is placed upright at the leftmost and bottommost position of the board, and the coordinates of the bottom right vertex of the rectangular part are recorded. and top left vertex Calculate the remaining width between this coordinate and the rightmost boundary of the board. Determine the next rectangular piece Is the width less than or equal to the remaining width? If so, then the second rectangular piece Place it according to its lower left vertex at the lower right coordinate. The position of the rectangular component is determined and placed within the board; otherwise, the second rectangular component is not placed first, and a rectangular component with a width less than or equal to the remaining width is found in the sequence to be arranged. ,Will Place it in the remaining space of this layer, if there is no suitable space. Then do not place them; at this point, the arrangement of the first layer is temporarily finished, and the height of the rectangular pieces in each layer decreases from left to right; Create a new layer to place the rectangular pieces that weren't placed earlier. Calculate the top left vertex With the remaining height of the highest point of the board, if If the height is less than or equal to the remaining height, then Start by inserting the board from the top right corner, moving it left and down until... No further movement is allowed; then determine the highest horizontal position of the new layer. The coordinates of the bottom right vertex are used to wait for the next rectangular component to be placed; if If the height is greater than the remaining height, then consider [doing something]. Rotate 90 degrees before placing; if If both the height and width are greater than the remaining height, then... Place the board directly from the top right corner downwards, or rotate it 90° before placing it. Move it close to the right side of the board and as low as possible, then ignore it. Whether or not it can be placed, it will move on to the next rectangle to be arranged. The smallest outer rectangle of the part will be laid out one by one until all rectangles are arranged.

[0022] Furthermore, the utilization rate formula in step 9 is: ,in Indicates the number of parts.

[0023] The beneficial effects of this application are as follows: 1. The reconstruction optimization method for two-dimensional irregular parts proposed in this invention aims to maximize the utilization rate of two-dimensional irregular parts on the plate. Only the plate information and the information of the two-dimensional irregular parts need to be input to obtain the optimal layout. This method effectively saves layout time, improves the layout efficiency of two-dimensional irregular parts, and reduces the labor intensity of workers. 2. This invention establishes a two-dimensional irregular part reconstruction strategy. In practical applications, based on the set vertex information of the two-dimensional irregular parts, the geometric structural features are analyzed to establish constraints for the reconstruction of irregular parts. The parts are adaptively pre-processed—combined and filled. Hollow areas such as holes are filled to maximize the effective area ratio of the reconstructed parts after pre-processing, thereby maximizing the utilization rate of the sheet metal. 3. This invention is simple to operate, requiring only the input of the set of vertex information of two-dimensional irregular parts and the basic information of the plate material. It is highly practical, easy to implement, and feasible and effective.

[0024] 4. This invention adaptively performs reconstruction preprocessing—combination and filling—based on the geometric features of the parts. Then, it solves for the optimal layout of the reconstructed parts and finds the minimum bounding rectangle corresponding to the optimal layout, forming new rectangular components. This maximizes the effective area ratio of the reconstructed parts. The rectangular components are sorted by their area and height, and a greedy algorithm is used to sequentially place them, thereby maximizing the utilization of the sheet metal. The reconstruction optimization algorithm proposed in this invention requires no manual adjustment; only basic information about the parts and sheet metal is input, and the layout is adaptively completed.

[0025] 5. This invention establishes a two-dimensional irregular part reconstruction strategy. Based on the geometric features and other characteristics of two-dimensional irregular parts, the parts are classified, the structural features of different types of parts are analyzed, constraints are automatically established, and parts that meet the constraints are combined and filled to reconstruct a rectangular part, thus transforming the problem into a simple rectangular part layout method.

[0026] 6. The reconstruction optimization algorithm proposed in this invention can automatically complete the layout by only reading the geometric vertex information of the two-dimensional irregular parts and the basic information of the sheet metal, thereby improving the utilization rate of the sheet metal and meeting the needs of actual application scenarios. Attached Figure Description

[0027] Figures 1-6 The diagram shows six parts A, B, C, D, E, and F in a specific embodiment of the present invention.

[0028] Figures 7-8 This is a schematic diagram of vertex information annotation and convex hull R_A of part A in a specific embodiment of the present invention.

[0029] Figures 9-12The present invention relates to four reconstruction methods for parts A1 and A2 in specific embodiments.

[0030] Figure 13 This is a flowchart illustrating the specific implementation method.

[0031] In the figure, 1. Part A, 2. Part B, 3. Part C, 4. Part D, 5. Part E, 6. Part F, 7. Vertex labeling information of Part A, 8. Vertex labeling information of the convex hull R_A corresponding to Part A, 9. Longest diagonal of Part A1, 10. Longest diagonal of Part A1, 11. Straight line passing through the centroid of Part A1 and perpendicular to the two diagonals. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the invention clearer, the technical solutions of the embodiments of the invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0034] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0035] In the description of this invention, it should be noted that the terms "upper," "vertical," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0036] The present invention will now be described in detail with reference to the accompanying drawings: Example 1 A reconstruction optimization method for two-dimensional irregular parts includes the following steps: Step 1: Read in the vertex information and sheet material information of the irregular part; Step 2: Calculate the centroid and area of ​​each part; Step 3: Solve for the convex hull set R of each part; Step 4: Find the minimum bounding rectangle of the convex hull set R, and calculate the effective area ratio of the reconstructed part AB after preprocessing. ; Step 5: Classify each part according to its effective area ratio and whether there are concave corners; Step 6: Establish a two-dimensional irregular part reconstruction strategy and preprocess the parts to reconstruct multiple new matrix-shaped parts; Step 7: Establish and sort the layout coding sequence for the rectangular components; Step 8: Adopt a dynamic layout strategy and obtain the layout result; Step 9: By inputting the geometric vertices of the two-dimensional irregular part through the above steps, the layout method corresponding to the highest material utilization rate can be automatically obtained.

[0037] Furthermore, in step 1, the length of the sheet material is input. ,width The detailed information of the irregular parts involved in the reconstruction includes: part number, coordinates of part vertices, as shown in the table below: Parts type and quantity information table

[0038] Furthermore, the coordinates of the vertices of the parts are recorded clockwise. If the parts have holes, the outer vertices are recorded counterclockwise, and the inner vertices are recorded counterclockwise. Each part is represented as a set of multiple scattered points.

[0039] Furthermore, the vertex set of any part in step 2 is represented as... ,in Let x be the nth x-coordinate of the part. Let be the nth ordinate of the part. The calculation methods for the area and centroid of each part are as follows: Based on the principle that there exists a line segment connecting any two points within the polygon that is either inside or on the edge of that polygon, the irregular polygon is subdivided into convex and concave polygons. Any convex polygon part can be divided into multiple triangles. Assume that a certain triangle has vertex . , and The formula for the area of ​​the triangle is: The centroid of the triangle Represented as , .

[0040] For convex polygons, the centroid is calculated by weighting the areas of the decomposed triangles and then averaging the results. , ,in This represents the number of triangles that a convex polygon can be decomposed into. Indicates , and A general expression for calculating the area of ​​a triangle with vertex A; Then it represents the first decomposition of the convex polygon. The area of ​​each triangle, and Let x and y represent the x and y coordinates of the centroids of the triangles decomposed from the convex polygon, respectively. .

[0041] Similarly, for a concave polygon, it is decomposed into several non-overlapping small convex polygons. For each small convex polygon obtained from the decomposition, its corresponding area and centroid are calculated. The centroid of the final concave polygon is obtained by weighting the area of ​​the decomposed convex polygons.

[0042] In summary: for parts with arbitrary convex polygons The centroid of part C can be determined as follows: , The area of ​​part C is For any concave polygon, it is decomposed into several non-overlapping convex polygons. The centroid of the final concave polygon is then calculated by weighting the areas of the decomposed convex polygons. This represents the number of triangles that a convex polygon can be decomposed into. Indicates , and A general expression for calculating the area of ​​a triangle with vertex A; Then it represents the first decomposition of the convex polygon. The area of ​​each triangle, and Let x and y represent the centroid coordinates of the triangles decomposed from the convex polygon, respectively. .

[0043] Furthermore, the method for solving the convex hull using the Jarvis stepwise method in step 3 specifically involves: processing the pre-classified part coordinates... Organize the information and find the answer using Jarvis's stepwise method. convex hull: First find middle The point with the smallest value ,save Add to the convex hull set R, and from Remove from the middle; take The remaining points in the middle are sequentially connected with Connect and record with Based on the angles of the axis, sort the remaining points in ascending order of angle, and then select the point corresponding to the smallest angle. Add it to the convex hull set R, and put from Eliminate from the middle; and so on, searching for... Until the entire process is completed. All points, until There is only one point left to choose from. Let R be the set of points of the convex hull. Connecting the points in R end to end forms the convex hull of the point. The convex hull.

[0044] Furthermore, from When searching for the next point, if a straight line appears... There's another dot above. The situation, namely straight line and When the angles formed by the straight lines are consistent, then... and All are added to the convex hull set R, and the distances are... The point that is furthest away by a straight line is used as the starting point for finding the next point.

[0045] Furthermore, in step 4, the minimum bounding rectangle is solved and the effective area ratio is calculated. The specific method is as follows: First, arbitrarily select two adjacent points on the convex hull set R. and Calculate the straight line passing through these two points. , and for The x and y coordinates, in Using straight lines as the sides of a rectangle, calculate the distance from all points on the convex hull to the rectangle. distance , past Longest distance Points to make Parallel lines, obtain the second side of the rectangle and The height of the rectangle Project the remaining points on the convex hull to Above, record the two points that are furthest apart in the X-axis from the projection point. and Calculate the width of the rectangle. At this time, the area of ​​the envelope rectangle is ; Traverse all adjacent points on the convex hull, , Let the number of points on the convex hull be the minimum area rectangle. The rectangle with the smallest area is then taken as the minimum bounding rectangle. The effective area ratio of this part is... ,in This indicates the actual area of ​​the part.

[0046] Furthermore, in step 5, an effective area ratio indicator is introduced. ,in For the first The area of ​​each part The minimum bounding rectangle of the part; when or If a part has no concave corners and is classified as a rectangle, then this type of part will not participate in subsequent reconstruction steps; when And without concave angles, it is judged to be a triangular-like shape; when Furthermore, the presence of concave angles indicates that it is a concave polygon. It is determined to be a concave angle.

[0047] Furthermore, step 6 specifically includes: 1) If part A is determined to be a rectangle, proceed directly to steps 3 and 4 to reconstruct it into the corresponding minimum bounding rectangle. ; 2) If part A It is a polygon containing defects such as holes, where This represents the outermost vertices of part A, recorded in clockwise order. This represents the innermost vertex, i.e., the inner hole, recorded counter-clockwise. First, determine the area of ​​the inner hole. The shortest diagonal inside the hole Or the shortest adjacent side inside the hole The calculation method is as follows: ,in , Let represent the coordinates of any two distinct vertices within the inner hole, and .

[0048] Specific aperture area small parts Select according to area from largest to smallest, that is To select parts Longest diagonal and longest adjacent edge Not exceeding the shortest diagonal of the inner hole with the shortest adjacent edge Here are the constraints, where Select a suitable candidate part and fill it into the inner hole of part A for reconstruction. The centroid of the candidate part is aligned with the centroid of part A as the placement method. Reconstruct the candidate part and part A into a rectangular part with the following constraints:

[0049]

[0050] 3) If part B is judged to be a defect-free concave polygon, first process the part in step 3 to form a convex hull set, and use the smallest bounding rectangle as its reconstructed rectangular part to solve the effective area ratio of the convex hull set. 4) If part B If the shape is determined to be a triangle, first consider reconstructing it with other parts of the same type (B) to form a new minimum bounding rectangle. If no part B of the same type exists, then it is compared with other types of triangles, such as part C. Reconstruct the structure and calculate the longest diagonal of part B. and longest adjacent edge Calculate the longest diagonal of part C. and longest adjacent edge And record the lines containing these four line segments. , , , The longest sides of parts B and C are respectively and and determine and The line in question is and Fix part B, according to and The parallel directions and the line connecting the centers of mass of the two parts are perpendicular to each other. and To place parts B and C according to the principle, the required distance between parts B and C after placement is... satisfy: :

[0051] in Represents the coordinates of all points in part B. Represents the coordinates of all points in part C. Let each represent a point in part B and part C respectively. This means finding the shortest distance between part B and part C.

[0052] Determine the internal diagonal or adjacent sides of the part. Then, the placement of parts B and C in the two groups can be confirmed; based on this, part B remains stationary, so that... By flipping part C along the axis of symmetry, we can determine the other two placement methods. Find the minimum bounding rectangle of these four placement methods. The rectangle with the smallest area is the optimal reconstruction layout BC between part B and part C. Traverse other triangular rectangular parts such as D, E, F, etc., and find the optimal reconstruction layout between each part and part B. The optimal reconstruction layout with the smallest area is taken as the optimal reconstruction layout between part B and another part. After completing the above steps, the optimal reconstruction method between each part is obtained. The minimum bounding rectangle corresponding to the reconstructed part vertex information is then calculated as a whole, transforming the problem into a solution. The layout method for rectangular components with different heights and widths, each rectangular component can be represented as follows: , , The designation indicating the rectangular component. These represent the width, height, and effective area ratio of the rectangular component, respectively.

[0053] Furthermore, the sorting method in step 7 is as follows: place the rectangular pieces involved in the layout vertically, ensuring that all rectangular pieces have a height greater than or equal to their width when placed. Sort the rectangular pieces from largest to smallest according to their area. Based on the previous sorting, sort the rectangular pieces from largest to smallest according to their height and label them.

[0054] Furthermore, the implementation method of the dynamic layout strategy in step 8 is as follows: the rectangular parts are laid out sequentially according to the order of step 7. Each time the rectangular part is laid out, it is placed upright at the leftmost and bottommost position of the board, and the coordinates of the bottom right vertex of the rectangular part are recorded. and top left vertex Calculate the remaining width between this coordinate and the rightmost boundary of the board. Determine the next rectangular piece Is the width less than or equal to the remaining width? If so, then the second rectangular piece Place it according to its lower left vertex at the lower right coordinate. The position of the rectangular component is determined and placed within the board; otherwise, the second rectangular component is not placed first, and a rectangular component with a width less than or equal to the remaining width is found in the sequence to be arranged. ,Will Place it in the remaining space of this layer, if there is no suitable space. Then do not place them; at this point, the arrangement of the first layer is temporarily finished, and the height of the rectangular pieces in each layer decreases from left to right; Create a new layer to place the rectangular pieces that weren't placed earlier. Calculate the top left vertex With the remaining height of the highest point of the board, if If the height is less than or equal to the remaining height, then Start by inserting the board from the top right corner, moving it left and down until... No further movement is allowed; then determine the highest horizontal position of the new layer. The coordinates of the bottom right vertex are used to wait for the next rectangular component to be placed; if If the height is greater than the remaining height, then consider [doing something]. Rotate 90 degrees before placing; if If both the height and width are greater than the remaining height, then... Start placing the boards directly from the top right corner downwards, or rotate them 90° before placing them (because the rectangle placed on the right side during layout will be smaller in height than the one on the left). Try to make... Move it close to the right side of the board and as low as possible, then ignore it. Whether or not it can be placed, it will move on to the next rectangle to be arranged. The smallest outer rectangle of the part will be laid out one by one until all rectangles are arranged.

[0055] The utilization rate formula in step 9 is: ,in Indicates the number of parts.

[0056] Example 2 like Figures 1-6 As shown, the present invention provides an optimization algorithm for reconstructing irregular two-dimensional parts, comprising the following steps: Step 1: Read in the geometric vertex information, quantity information, and plate height of the two-dimensional irregular parts A(1), B(2), C(3), D(4), E(5), and F(6). and width ; Parts type and quantity information table

[0057] Step 2: Determine the centroid and area of ​​each part. For example, part A (1), based on the principle that the line segment connecting any two points within the polygon is inside or on the edge of the polygon, part A is determined to be a concave polygon. The area of ​​part A calculated by triangulation is 5064.9704. The center of mass is Similarly, the areas and centroids of the remaining parts can be calculated as follows:

[0058] Step 3: Solve for the convex hull set of each part. The vertex information of part A (7) is as follows: Taking part A as an example, the convex hull set is calculated using the Jarvis step method, and then the convex hull set is found. middle The point with the smallest value ,Will Save to R, from Remove from the middle; take The remaining points in the middle are sequentially connected with Connect and record with Angle of axis Sort the remaining points according to their angle from smallest to largest. The point corresponding to the smallest angle Add it to the convex hull set R, and put from Remove from the middle, at which point the convex hull set is ;Bundle The remaining points in the middle are sequentially connected with Connect and record with Angle of axis Sort the remaining points according to their angle from smallest to largest. The point corresponding to the smallest angle Add it to the convex hull set R, and put from Remove from the middle, at which point the convex hull set is ;Bundle The remaining points in the middle are sequentially connected with Connect and record with Angle of axis Sort the remaining points according to their angle from smallest to largest. The point corresponding to the smallest angle Add it to the convex hull set R, and put from Remove from the middle, at which point the convex hull set is ;Bundle The remaining points in the middle are sequentially connected with Connect and record with Angle of axis Sort the remaining points according to their angle from smallest to largest. The point corresponding to the smallest angle Add it to the convex hull set R, and put from Remove from the middle, at which point the convex hull set is This concludes the solution for the convex hull set of part A; similarly, the convex hull information for the remaining parts can be obtained as follows:

[0059] Step 4: Find the minimum bounding rectangle of the convex hull set and calculate the area ratio. Take part A as an example to find the convex hull. (8) The ratio of the minimum bounding rectangle to the effective area: Choose any two adjacent points Calculate the straight line passing through these two points. ,by Using straight lines as the sides of a rectangle, calculate the distance from all points on the convex hull to the rectangle. distance , past Longest distance Points to make Parallel lines Get the second side of the rectangle and The height of the rectangle Project the remaining points on the convex hull to Above, record the two points that are furthest apart in the X-axis from the projection point. and Calculate the width of the rectangle. The area of ​​the envelope rectangle at this time is Traverse all adjacent points on the convex hull, i.e. The rectangle with the smallest area is taken as the minimum bounding rectangle obtained. The effective area ratio of the part is... . In the same way, the information of other parts can be obtained as follows:

[0060] Step 5: Classify the parts. Part A is a part with a concave corner and It is determined to be a concave polygon; part B has no concave corners and It is determined to be a triangular shape; part C has no concave corners. It is determined to be a rectangle; part D has a concave corner and It is determined to be a concave polygon; part E is a polygon with concave corners and The part is determined to be a concave polygon; part F is a concave polygon with a hole. Step 6: Part preprocessing - Reconstruct and fill the parts. (1) Part F is a concave polygon with a hole. The area of ​​the inner hole is calculated to be 2021.0811, and the longest diagonal is 59.12. The areas of parts C and E are 719.65510 and 1368.8441, respectively. The longest diagonals of parts C and E are 37.86 and 139.21, respectively. Therefore, part C is selected to fill part F. Considering that there is one part F, one part C and one part F are selected for filling. The filled part CF is processed together into a rectangular part RCF with a height of 88.4106 and a width of 124.0693 for layout. (2) Part C has no concave corner. , judged as a rectangle, processed into a rectangle with a height of 31.1662 and a width of 29.8586; (3) Parts A, D and E are concave polygons, and after calculating their convex hulls, the new effective area ratios are 0.6373, 0.7009 and 0.3973 respectively. The processed part A is called part A-convex hull, and the processed part E is called part E-convex hull. They all have no concave corners and The part is determined to be a triangular shape, and the processed part D is called part D-convex hull, which has no concave corners. (4) The number of convex hulls of part A is 2, and they are respectively denoted as parts. and parts Consider reconstructing the convex hull of part A pairwise. The longest diagonal of the convex hull of part A is... ,according to and The parallel directions and the line connecting the two centers of mass are perpendicular to each other. and For the principle of parts and parts Reconstruction is performed, and there are four reconstruction methods (9). Among them, the rectangular part with a height of 104.3726 and a width of 148.6432 is the rectangular part with the smallest area; (5) Part B is judged to be a triangular shape, and the number of parts B is 3. According to the principle of part filling reconstruction, we first consider reconstructing parts B in pairs. The longest adjacent edge of part B is ,according to and The parallel directions and the line connecting the two centers of mass are perpendicular to each other. and Based on the principle, the layout of parts B1 and B2 is reconstructed. The rectangular part with a height of 119.4460 and a width of 124.9576 is the rectangular part with the smallest area; (6) The other part B3 and part E-convex hull are reconstructed. The longest adjacent side of part B3 is The longest adjacent edge of the convex hull of part E is ,according to and The parallel directions and the line connecting the two centers of mass are perpendicular to each other. and Based on this principle, the convex hulls of parts B3 and E are reconstructed to form a rectangular component with a height of 92.0671 and a width of 140.3797. The problem is thus transformed into laying out this rectangular component, whose information is as follows:

[0061] Step 7: Establish and sort the layout coding sequence of rectangular pieces to ensure that all rectangular pieces have a height greater than or equal to their width when placed. The order is: RAA-RD-RD-RBE-RBB-RCF-RC; Step 8: Lay out the rectangular pieces in the order of RAA-RD-RD-RBE-RBB-RCF-RC in Step 7. Each time, place the rectangular piece upright at the bottom left of the board. Set the coordinates of the bottom left vertex of the board. Place RAA as the first element and record the coordinates of the bottom right vertex of the rectangular element RAA. and top left vertex Calculate the remaining width between this coordinate and the rightmost boundary of the board. Determine if the width of the next rectangular component RBB is less than or equal to the remaining width. Place the second rectangular piece RD at the bottom right coordinate according to its bottom left vertex. The positions of the rectangular components are then placed into the material; similarly, RD is reconstructed into the material. This temporarily concludes the arrangement of the first layer. The height of the rectangular components in each layer decreases from left to right. Similarly, RBE-RCF-RBB-RC is reconstructed according to the dynamic layout strategy, resulting in RAA-RD-RD-RCF-RBE-RBB-RC. Step 9: Through the above steps, input the geometric vertex information of irregular parts A, B, C, D, E, and F. According to the two-dimensional irregular part reconstruction strategy, parts C and F can be filled and reconstructed into rectangular parts RCF. Parts A and B can be reconstructed into rectangular parts with themselves. Parts B and E can be reconstructed into rectangular parts. Parts C and D can be reconstructed into minimum bounding rectangular parts. Input the height and width of the rectangular parts into the control system. The control system automatically completes the automatic layout of the rectangular parts according to the dynamic layout strategy. Finally, the utilization rate is 43.21%.

Claims

1. A reconstruction optimization method for two-dimensional irregular parts, characterized in that, Includes the following steps: Step 1: Read in the vertex information and sheet material information of the irregular part; Step 2: Calculate the centroid and area of ​​each part; Step 3: Solve for the convex hull set R of each part; Step 4: Find the minimum bounding rectangle of the convex hull set R, and calculate the effective area ratio of the reconstructed part AB after preprocessing. ; Step 5: Classify each part according to its effective area ratio and whether there are concave corners; Step 6: Establish a two-dimensional irregular part reconstruction strategy and preprocess the parts to reconstruct multiple new matrix-shaped parts; Step 7: Establish and sort the layout coding sequence for the rectangular components; Step 8: Adopt a dynamic layout strategy and obtain the layout result; Step 9: By inputting the geometric vertices of the two-dimensional irregular part through the above steps, the layout method corresponding to the highest material utilization rate can be automatically obtained.

2. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, In step 1, the length of the board material is input. ,width And detailed information on the irregular parts involved in the reconstruction, including: part number, coordinates of the part vertices.

3. The reconstruction optimization method for two-dimensional irregular parts according to claim 2, characterized in that, The coordinates of the vertices of a part are recorded clockwise. If the part has holes, the outer vertices are recorded counterclockwise, and the inner vertices are recorded counterclockwise. Each part is represented as a set of multiple scattered points.

4. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, The vertex set of each part in step 2 is represented as follows: ,in Let x be the x-coordinate of the nth part. Let y be the ordinate of the nth part. The calculation methods for the part's area and centroid are as follows: Based on the principle that there exists a line segment connecting any two points within the polygon that is either inside or on the edge of the polygon, the irregular polygon is subdivided into convex polygons and concave polygons. Any convex polygonal part is divided into multiple triangles, and the vertex of a certain triangle is... , and The formula for the area of ​​the triangle is: The centroid of the triangle is ,in , For convex polygons, the centroid is calculated by weighting the areas of the decomposed triangles. , ,in This represents the number of triangles that a convex polygon can be decomposed into. Indicates , and A general expression for calculating the area of ​​a triangle with vertex A; Then it represents the first decomposition of the convex polygon. The area of ​​each triangle, This represents the x-axis coordinate of the centroid of each triangle decomposed from the convex polygon. Let represent the y-coordinate of the centroid of each triangle decomposed from the convex polygon, where . For a concave polygon, it is decomposed into several non-overlapping small convex polygons. For each small convex polygon obtained by decomposition, its corresponding area and centroid are calculated according to the above method. The centroid of the final concave polygon is obtained by weighting the area of ​​the decomposed convex polygons.

5. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, Step 3, specifically the method for solving the convex hull using the Jarvis step method, involves: for any part coordinates... Organize the information and find the answer using Jarvis's stepwise method. convex hull: First find middle The point with the smallest value ,save Add to the convex hull set R, and from Remove from the middle; take The remaining points in the middle are sequentially connected with Connect and record with Based on the angles of the axis, sort the remaining points in ascending order of angle, and then select the point corresponding to the smallest angle. Add it to the convex hull set R, and put from Eliminate from the middle; and so on, searching for... Until the entire process is completed. All points, until There is only one point left to choose from. Let R be the set of points of the convex hull. Connecting the points in R end to end forms the convex hull of the point. The convex hull.

6. The reconstruction optimization method for two-dimensional irregular parts according to claim 5, characterized in that, from When searching for the next point, if a straight line appears... There's another dot above. In this situation, at this time and All are added to the convex hull set R, and the distances are... The point that is furthest away by a straight line is used as the starting point for finding the next point.

7. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, In step 4, solve for the minimum bounding rectangle and calculate the effective area ratio. The specific method is as follows: First, arbitrarily select two adjacent points on the convex hull set R. and Calculate the straight line passing through these two points. , and They represent The x and y coordinates of the point, Using straight lines as the sides of a rectangle, calculate the distance from all points on the convex hull to the rectangle. distance , past Longest distance Points to make Parallel lines, obtain the second side of the rectangle and The height of the rectangle Project the remaining points on the convex hull to Above, record the two points that are furthest apart in the X-axis from the projection point. and Calculate the width of the rectangle. At this time, the area of ​​the envelope rectangle is ; Traverse all adjacent points on the convex hull, , Let the number of points on the convex hull be the minimum area rectangle. The rectangle with the smallest area is then taken as the minimum bounding rectangle. The effective area ratio of this part is... ,in This indicates the actual area of ​​the part.

8. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, In step 5, the effective area ratio indicator is introduced. ,in For the first The area of ​​each part The minimum bounding rectangle of the part; when or If a part has no concave corners and is classified as a rectangle, then this type of part will not participate in subsequent reconstruction steps; when And without concave angles, it is judged to be a triangular-like shape; when Furthermore, the presence of concave angles indicates that it is a concave polygon. It is determined to be a concave angle.

9. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, Step 6 specifically involves: 1) If part A is determined to be a rectangle, proceed directly to steps 3 and 4 to reconstruct it into the corresponding minimum bounding rectangle. ; 2) If part A It is a polygon containing defects such as holes, where This represents the outermost vertices of part A, recorded in clockwise order. The innermost vertex represents the inner hole, recorded counter-clockwise; first, determine the area of ​​the inner hole. The shortest diagonal inside the hole Or the shortest adjacent side inside the hole The calculation method is as follows: ,in , Let represent the coordinates of any two distinct vertices within the inner hole, and ; Specific aperture area small parts Select according to area from largest to smallest, that is To select parts Longest diagonal and longest adjacent edge Not exceeding the shortest diagonal of the inner hole with the shortest adjacent edge Here are the constraints, where Select the candidate part and fill it into the inner hole of part A for reconstruction. The centroid of the candidate part is aligned with the centroid of part A as the placement method. Reconstruct the candidate part and part A into a rectangular part with the following constraints: 3) If part B is judged to be a defect-free concave polygon, first process the part in step 3 to form a convex hull set, and use the smallest bounding rectangle as its reconstructed rectangular part to solve the effective area ratio of the convex hull set. 4) If part B If the shape is determined to be a triangle, first consider reconstructing it with other parts of the same type (B) to form a new minimum bounding rectangle. If no part B of the same type exists, then it is compared with other types of triangles, such as part C. Reconstruct the structure and calculate the longest diagonal of part B. and longest adjacent edge Calculate the longest diagonal of part C. and longest adjacent edge And record the lines containing these four line segments. , , , The longest sides of parts B and C are respectively and and determine and The line in question is and Fix part B, according to and The parallel directions and the line connecting the centers of mass of the two parts are perpendicular to each other. and To place parts B and C according to the principle, the required distance between parts B and C after placement is... satisfy: ; in Represents the coordinates of all points in part B. Represents the coordinates of all points in part C. Let each represent a point in part B and part C respectively. This means finding the shortest distance between part B and part C. Determine the internal diagonal or adjacent sides of the part. Then, the placement of parts B and C in the two groups can be confirmed; based on this, part B remains stationary, so that... By flipping part C along the axis of symmetry, we can determine the other two placement methods. Find the minimum bounding rectangle of these four placement methods. The rectangle with the smallest area is the optimal reconstruction layout BC between part B and part C. Traverse other triangular rectangular parts to find the optimal reconstruction layout between each part and part B. Use the optimal reconstruction layout with the smallest area as the optimal reconstruction layout between part B and another part. After completing the above steps, the optimal reconstruction method between each part is obtained. The minimum bounding rectangle corresponding to the reconstructed part vertex information is then calculated as a whole, transforming the problem into a solution. The layout method for rectangular components with different heights and widths, each rectangular component can be represented as follows: , , The designation indicating the rectangular component. These represent the width, height, and effective area ratio of the rectangular component, respectively.

10. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, The sorting method in step 7 is as follows: place the rectangular pieces involved in the layout upright, ensuring that all rectangular pieces have a height greater than or equal to their width. Sort the rectangular pieces from largest to smallest according to their area. Based on the previous sorting, sort the rectangular pieces from largest to smallest according to their height and label them.

11. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, The dynamic layout strategy in step 8 is implemented as follows: The rectangular components are laid out sequentially according to the order in step 7. Each time a rectangular component is laid out, it is placed upright at the leftmost and bottommost position of the board, and the coordinates of the bottom right vertex of the rectangular component are recorded. and top left vertex Calculate the remaining width between this coordinate and the rightmost boundary of the board. Determine the next rectangular piece Is the width less than or equal to the remaining width? If so, then the second rectangular piece Place it according to its lower left vertex at the lower right coordinate. The position of the rectangular component is determined and placed within the board; otherwise, the second rectangular component is not placed first, and a rectangular component with a width less than or equal to the remaining width is found in the sequence to be arranged. ,Will Place it in the remaining space of this layer, if there is no suitable space. Then do not place them; at this point, the arrangement of the first layer is temporarily finished, and the height of the rectangular pieces in each layer decreases from left to right; Create a new layer to place the rectangular pieces that weren't placed earlier. Calculate the top left vertex With the remaining height of the highest point of the board, if If the height is less than or equal to the remaining height, then Start by inserting the board from the top right corner, moving it left and down until... No further movement is allowed; then determine the highest horizontal position of the new layer. The coordinates of the bottom right vertex are used to wait for the next rectangular component to be placed; if If the height is greater than the remaining height, then consider [doing something]. Rotate 90 degrees before placing; if If both the height and width are greater than the remaining height, then... Place the board directly from the top right corner downwards, or rotate it 90° before placing it. Move it close to the right side of the board and as low as possible, then ignore it. Whether or not it can be placed, it will move on to the next rectangle to be arranged. The smallest outer rectangle of the part will be laid out one by one until all rectangles are arranged.

12. The reconstruction optimization method for two-dimensional irregular parts according to claim 1, characterized in that, The utilization rate formula in step 9 is: ,in Indicates the number of parts.

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