CN116307142A - Single-rule layout method for combining irregular images - Google Patents
Single-rule layout method for combining irregular images Download PDFInfo
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Abstract
The invention provides a single-rule layout method for combining irregular images, which comprises the following steps: s1, inputting information of a target block and a raw material plate to obtain layout information; step S2, initializing the layout information according to the original data; s3, initializing an optimal result linked list; s4, calculating all vectors V0 and V1 meeting the conditions according to the irregular image; step S5, traversing all the vectors V0 and V1; and S6, outputting the optimal solution condition by carrying out combination calculation, and ending the flow. The single-rule layout method for combining irregular images can obtain a high-efficiency layout scheme, provides an effective guide for blanking production of enterprises, and enables the blanking cost of the products of the enterprises to be low, the layout effect to be good, the production efficiency to be high, and the application range to be wide.
Description
Technical Field
The invention relates to the technical field of irregular pattern layout, in particular to a single-rule layout method for combining irregular images.
Background
At present, the economy of China rapidly develops, the scale of enterprises is continuously enlarged, and the demand for resources is continuously increased. The stock layout is an important problem related to daily life of people, the quality of the stock layout is directly related to the utilization rate of raw materials, and if resources cannot be effectively utilized, waste and environmental pollution can be caused. China is a large production country, and has great demands on the production of various products every year. Many of these materials are cut, and if the utilization of these materials is improved by one percentage, the improvement will be greatly improved in the manufacturing industry.
In many manufacturing industries, it is often necessary to cut raw materials into different types of parts for manufacturing. Such as cutting of wooden boards and glass, this type of problem is known as two-dimensional layout optimization. Whereas in a type of part, the majority is an irregular pattern. In some industries, cutting can only be performed in a fixed rotation angle because of the presence of texture. Such as patterned wood cutting, apparel industry cutting, marble cutting, and the like. In addition, in large enterprises, the supply of some products is relatively large, and thus the number of demand bases for individual items is large. Therefore, on the basis of considering some factors in cutting raw materials, an effective arrangement of the required components on the raw materials is found, so that the cheek utilization rate of the plane area on the raw materials is high, and the materials are saved as much as possible.
The prior art mainly aims at the layout problem of the irregular graphic suite, and the main method is to convert the original problem into a simplified problem which only needs to process points and intervals by utilizing a discrete critical polygon, and then nest a plurality of random search algorithms based on biological intelligence to solve the optimal solution. However, solving the critical polygon is a complex process, and the calculation of each process results in a great increase in time, which is not suitable for the layout of large-scale irregular patterns. The other main method is to use an envelope rectangle to surround the original irregular polygon by a minimum rectangle, so that the original irregular polygon pattern is simplified into a rectangular pattern, and the current research on the rectangular pattern at home and abroad is perfected, so that the solving speed of the irregular polygon is greatly improved, and the method is more suitable for large-scale pattern production, but each envelope rectangle has larger waste, so that the utilization rate of the method is lower.
At present, the large enterprises have larger outlets for the suites of irregular products, and aiming at the problem, each irregular graph in the suites can be produced in a large scale, so that the strategy can greatly improve the utilization rate and reduce the time required for discharging. The single-specification layout strategy has little development at home and abroad at present, and most of the single-specification layout strategies are simple transverse arrays and longitudinal arrays, so that the layout time can be shortened, the single-specification layout strategy is better applied to large-scale irregular layout, and the utilization rate of the obtained layout result diagram is low.
Therefore, the irregular product has poor sample discharging effect, low raw material utilization rate, high cost, low production efficiency and small application range.
Disclosure of Invention
Aiming at the defects of the related technology, the invention provides a single-rule layout method for combining irregular images, which is used for solving the problems of poor layout effect, low raw material utilization rate, high cost and low production efficiency of the existing irregular products.
In order to solve the technical problems, the embodiment of the invention provides a single-rule layout method for combining irregular images, which comprises the following steps:
s1, inputting information of a target block and a raw material plate to obtain layout information;
step S2, initializing the layout information according to the original data;
s3, initializing an optimal result linked list;
s4, calculating all vectors V0 and V1 meeting the conditions according to the irregular image;
step S5, traversing all the vectors V0 and V1;
and S6, outputting the optimal solution condition by carrying out combination calculation, and ending the flow.
Preferably, the step S5 further includes the steps of:
step S51, if all the vectors V0 and V1 are not traversed, calculating the maximum utilization result under the condition of the current vectors V0 and V1;
step S52, judging whether the result is better than the optimal solution, if so, executing step S53; if not, returning to the step S5;
and step S53, reassigning the optimal solution, and returning to execute the step S5.
Preferably, in the step S6, the method further includes the steps of:
step S7, if the combination calculation is not carried out on all the vectors V0 and V1 which are traversed, 180-degree combination is carried out on the original irregular graph;
s8, removing illegal irregular patterns;
and S9, calculating all the vectors V0 and V1 meeting the conditions according to the combined irregular graph, and returning to the step S5.
Preferably, in the step S4, a calculation formula of the vector V0 is as follows;
presetting two line segments as l respectively 1 、l 2 The coordinates of the end points of the two line segments are respectively (x) 1 ,y 1 )(x 2 ,y 2 ) And (x) 3 ,y 3 )(x 4 ,y 4 ) The method comprises the steps of carrying out a first treatment on the surface of the Thus, two linear equations can be obtained;
y-y 1 ＝(y 2 -y 1 )(x-x 1 )/(x 2 -x 1 )；
y-y 3 ＝(y 4 -y 3 )(x-x 3 )/(x 4 -x 3 )；
let x and y be equal, the following can be obtained:
x＝((x 2 -x 1 )(x 3 -x 4 )(y 3 -y 1 )-x 3 (x 2 -x 1 )(y 3 -y 4 )+x 1 (y 2 -y 1 )(x 3 -x 4 ))/((y 2 -y 1 )(x 3 -x 4 )-(x 2 -x 1 )(y 3 -y 4 ))；
y＝((y 2 -y 1 )(y 3 -y 4 )(x 3 -x 1 )-y 3 (y 2 -y 1 )(x 3 -x 4 )+y 1 (x 2 -x 1 )(y 3 -y 4 ))/((x 2 -x 1 )(y 3 -y 4 )-(y 2 -y 1 )(x 3 -x 4 ))；
x≥max(x 1 ,x 3 )，x≤min(x 2 ,x 4 )；
y≥max(y 1 ,y 3 )，y≤min(y 2 ,y 4 )；
packaging the above formula into a function can be f (l 1 ,l 2 ) The output result of the function is an intersection point coordinate, if the two lines are parallel, the end point value of the overlapped part is returned, and the irregular graph is placed at one corner of the raw material plate;
setting P (x, y) as intersection point set, drawing a horizontal line segment L penetrating through the raw material plate by taking the rightmost upper corner point of the irregular graph, obtaining critical polygon by taking the right upper corner of the irregular graph as basic point, and placing the line segment into the line segment set L NFP Recording the number M of all the line segments to obtain the following formula;
l i ∈L NFP ；
the P (x, y) is the intersection point set of the critical polygon and the line segment L, and two points exist; and traversing the point set from left to right in sequence, judging whether the point set is legal, and taking the first legal point, namely the right upper corner point of the irregular graph after translation, so as to obtain the translated vector V0.
Preferably, in the step S4, a calculation formula of the vector V1 is as follows;
regenerating the graph after horizontal displacement into a corresponding critical polygonThe method comprises the steps of carrying out a first treatment on the surface of the Putting the newly obtained line segments of the critical polygon into a set L' NFP Then there is a set of intersection points P' (x, y) of two critical polygons;
l i ∈L NFP ；
l j ∈L′ NFP ；
by using the formula, the intersection point of two critical polygons is calculated, and when the third irregular pattern is positioned on the intersection point of two different critical polygons, namely, the third irregular pattern intersects with the first two irregular patterns, under the legal condition, a plurality of groups of vectors V1 are obtained.
Compared with the related art, the invention obtains the stock layout information by inputting the information of the target block and the raw material plate; initializing the layout information according to the original data; initializing an optimal result linked list; calculating all the vectors V0 and V1 meeting the conditions according to the irregular image; traversing all the vectors V0 and V1; and outputting the optimal solution condition by carrying out combination calculation, and ending the flow. Therefore, the layout method based on the combined single-specification graph can obtain a high-efficiency layout scheme through the algorithm, and provides an effective guide for the blanking production of enterprises, so that the blanking cost of the products of the enterprises is low, the layout effect is good, the production efficiency is high, and the application range is wide.
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The present invention will be described in detail with reference to the accompanying drawings. The foregoing and other aspects of the invention will become more apparent and more readily appreciated from the following detailed description taken in conjunction with the accompanying drawings. In the accompanying drawings:
FIG. 1 is a flow chart of a single-rule layout method for combining irregular images according to the present invention;
FIG. 2 is a schematic diagram of an array process of a single gauge irregular pattern of the present invention;
FIG. 3 is a schematic diagram of two irregular pattern critical polygons according to the present invention;
FIG. 4 is a schematic diagram of boundary conditions in an image array combined in accordance with the present invention;
FIG. 5 is a schematic diagram of an illegal combination of the present invention;
FIG. 6 is a schematic diagram of a legal combination of the present invention;
FIG. 7 is an overall flow chart of a single-rule layout method for combining irregular images according to the present invention;
FIG. 8 is a schematic diagram of the irregular pattern lower left corner placement initialization of the present invention;
FIG. 9a is a schematic view of placement point case 1 of FIG. 8;
FIG. 9b is a schematic view of placement point case 2 of FIG. 8;
FIG. 10 is a schematic diagram of irregular pattern placement initialization after translation in accordance with the present invention;
FIG. 11a is a schematic view of the placement point case 1 of FIG. 10;
FIG. 11b is a schematic view of placement point case 2 of FIG. 10;
FIG. 12 is a schematic diagram of the result of the case graph operation of the present invention;
FIG. 13 is a schematic diagram of an alternative irregular pattern layout 1 according to the present invention;
FIG. 14 is a schematic diagram of an alternative irregular pattern layout 2 according to the present invention;
FIG. 15 is a schematic diagram of an alternative irregular pattern layout 3 according to the present invention.
Detailed Description
The following describes in detail the embodiments of the present invention with reference to the drawings.
The detailed description/examples set forth herein are specific embodiments of the invention and are intended to be illustrative and exemplary of the concepts of the invention and are not to be construed as limiting the scope of the invention. In addition to the embodiments described herein, those skilled in the art will be able to adopt other obvious solutions based on the disclosure of the claims and specification of the present application, including those adopting any obvious substitutions and modifications to the embodiments described herein, all within the scope of the present invention.
Example 1
Referring to fig. 1-15, the present invention provides a single-rule layout method for combining irregular images, comprising the following steps:
and S1, inputting information of the target block and the raw material plate to obtain layout information.
The information can be specification data, patterns, colors, materials and the like of the target block and the raw material plate, and the stock layout information is obtained by the information of the target block and the raw material plate, so that stock layout is convenient, and the production efficiency is improved.
And step S2, initializing the layout information according to the original data. The original data may be the original data, or the set original data. And initializing the layout information according to the original data to obtain initialization data.
And S3, initializing an optimal result linked list. The optimal result linked list is obtained by initializing the initialized data, the linked list is a discontinuous and non-sequential storage structure on a physical storage unit, and the logic sequence of the data elements is realized by the pointer link sequence in the linked list. The linked list is made up of a series of nodes (each element in the linked list is called a node) that can be dynamically generated at runtime. Each node comprises two parts: one is a data field storing a data element and the other is a pointer field storing the address of the next node. The operation is complicated compared to the linear table sequential structure. Since it is not necessary to store in order, the linked list can reach the complexity of O (1) at the time of insertion much faster than another linear table order table, but the time of O (n) is needed to find a node or access a node of a specific number, and the corresponding time complexity of the linear table and the order table are O (log) and O (1), respectively.
And S4, calculating all vectors V0 and V1 meeting the conditions according to the irregular image.
And S5, traversing all the vectors V0 and V1.
And S6, outputting the optimal solution condition by carrying out combination calculation, and ending the flow.
Specifically, the invention obtains the stock layout information by inputting the information of the target block and the raw material plate; initializing the layout information according to the original data; initializing an optimal result linked list; calculating all the vectors V0 and V1 meeting the conditions according to the irregular image; traversing all the vectors V0 and V1; and outputting the optimal solution condition by carrying out combination calculation, and ending the flow. Therefore, the layout method based on the combined single-specification graph can obtain a high-efficiency layout scheme through the algorithm, and provides an effective guide for the blanking production of enterprises, so that the blanking cost of the products of the enterprises is low, the layout effect is good, the production efficiency is high, and the application range is wide.
Wherein the irregular panel discharge includes an uncombined array, a combined array, an illegitimate combined array, and the like.
Specifically, the uncombined array is summarized as: firstly, an irregular pattern is placed at the leftmost lower corner of a raw material plate, and then an array in the x or y direction is carried out, wherein the x direction is taken as an example; after the array, a second pattern is obtained as shown in FIG. 2 (A). The third pattern is then again arrayed on the basis just before so that the third image is in contact with the first two patterns, as in fig. 2 (B). Two vectors V0 and V1 can be drawn with the lower left corner of the irregular pattern as a base point, as shown in fig. 2 (C). And (3) carrying out regular array by the directions of the two vectors until the raw material plate can not be placed with any irregular pattern, and stopping the array. Of course, the third pattern may be placed in various ways, only one of which is shown in the drawings, and will not be described here.
Overview of combinatorial arrays: and rotating the original irregular polygon by 180 degrees to obtain the irregular polygon in a new direction. Then, the critical polygon of the newly generated irregular polygon with respect to the original irregular polygon is calculated by taking the rightmost upper corner point as a base point, as shown in fig. 3. And taking the vertex of each critical polygon and the bisection point (the bisection point is the midpoint in the figure) on each edge as the placement point of the new object block, thereby obtaining a combined graph, and as shown in fig. 3, the combined graph is generated when the midpoint of the critical polygon edge 1 is placed. The new combined pattern can be regarded as a brand new irregular pattern, and the array is performed by utilizing the outline method in the uncombined array. However, in the combined graphic array, some boundaries are noted, as shown in fig. 4, where the left half is still inside the raw material board, and the right half is outside the raw material board, and is out of range, but the combined graphic cannot be calculated entirely, and only half of the combined graphic can be calculated. Therefore, the combined graph needs to be split, and the available parts of each block are calculated.
Illegal combined overview: some illegal combinations can occur in the combination process, and if calculation is performed by using an illegal graph, an output result is wrong. An illegal pattern is shown in fig. 5. In a strict sense, the combined pattern is not a single irregular polygon, and this pattern may cause errors in the combined layout algorithm. As shown in fig. 6, although the middle of the combined graph is hollow, the outer contour is an irregular polygon in a strict sense, so that subsequent calculation can be performed.
In this embodiment, as shown in fig. 7, the step S5 further includes the following steps:
step S51, if all the vectors V0 and V1 are not traversed, calculating the maximum utilization result under the condition of the current vectors V0 and V1;
step S52, judging whether the result is better than the optimal solution, if so, executing step S53; if not, returning to the step S5;
and step S53, reassigning the optimal solution, and returning to execute the step S5.
In this embodiment, as shown in fig. 7, the step S6 further includes the following steps:
step S7, if the combination calculation is not carried out on all the vectors V0 and V1 which are traversed, 180-degree combination is carried out on the original irregular graph;
s8, removing illegal irregular patterns;
and S9, calculating all the vectors V0 and V1 meeting the conditions according to the combined irregular graph, and returning to the step S5.
Specifically, (1) the size information of the target block and the raw material plate is first inputted by an algorithm, and the rotatable angle of the target block is initialized.
(2) And creating an irregular layout optimal solution set for storing the corresponding optimal solution.
(3) First, according to the description of the non-combined whole column, the situation that the image accords with the corresponding placement method when the image is not combined is calculated, and all the V0 and V1 vectors which accord with the conditions are obtained. And then carrying out full-arrangement calculation on V0 and V1 in each case, namely, fully arranging the raw material plates of the whole layout by the array, calculating the current solution, updating the optimal solution if the solution is better than the optimal solution, and continuing calculation if the solution is not better than the optimal solution, until all V1 and V0 meeting the conditions under the condition of no combination are calculated.
(4) The original irregular polygon is rotated 180 degrees, then the graph of the critical polygon is calculated by utilizing the algorithm of the critical polygon, each vertex of the critical polygon and a plurality of equal dividing points of each edge are used as placement points of the rotated irregular graph, and various combined irregular polygons are formed by the original irregular polygon. In these multiple variants, illegal combinations of irregular polygons are excluded based on the number of contacts to the variants of two irregularities. And then taking the combined irregular polygon as a brand new irregular polygon to perform V1 and V0. During the discharging process, the calculated V1 and V0 must pay attention to the boundary condition, the combined graph is disassembled, and the part where the graph is placed is wasted.
(5) And after the calculation is finished, outputting the optimal emission condition, namely the optimal solution condition. Therefore, the layout method based on the combined single-specification graph can obtain a high-efficiency layout scheme through the algorithm, and provides an effective guide for the blanking production of enterprises, so that the blanking cost of the products of the enterprises is low, the layout effect is good, the production efficiency is high, and the application range is wide.
In this embodiment, in the step S4, the calculation formula of the vector V0 is as follows;
presetting two line segments as l respectively 1 、l 2 Two line segmentsThe coordinates of the end points are (x) 1 ,y 1 )(x 2 ,y 2 ) And (x) 3 ,y 3 )(x 4 ,y 4 ) The method comprises the steps of carrying out a first treatment on the surface of the Thus, two linear equations can be obtained;
y-y 1 ＝(y 2 -y 1 )(x-x 1 )/(x 2 -x 1 )；
y-y 3 ＝(y 4 -y 3 )(x-x 3 )/(x 4 -x 3 )；
let x and y be equal, the following can be obtained:
x＝((x 2 -x 1 )(x 3 -x 4 )(y 3 -y 1 )-x 3 (x 2 -x 1 )(y 3 -y 4 )+x 1 (y 2 -y 1 )(x 3 -x 4 ))/((y 2 -y 1 )(x 3 -x 4 )-(x 2 -x 1 )(y 3 -y 4 ))；
y＝((y 2 -y 1 )(y 3 -y 4 )(x 3 -x 1 )-y 3 (y 2 -y 1 )(x 3 -x 4 )+y 1 (x 2 -x 1 )(y 3 -y 4 ))/((x 2 -x 1 )(y 3 -y 4 )-(y 2 -y 1 )(x 3 -x 4 ))；
x≥max(x 1 ,x 3 )，x≤min(x 2 ,x 4 )；
y≥max(y 1 ,y 3 )，y≤min(y 2 ,y 4 )；
packaging the above formula into a function can be f (l 1 ,l 2 ) The output result of the function is an intersection point coordinate, if the two lines are parallel, the end point value of the overlapped part is returned, and the irregular graph is placed at one corner of the raw material plate; the lower left corner of the blank plate is taken as an example. As shown in fig. 8.
Setting P (x, y) as the intersection point set, taking the rightmost upper corner point of the irregular pattern, drawing a horizontal line segment L penetrating the raw material plate, taking the right upper corner of the irregular pattern as the upper corner pointThe basic point obtains a critical polygon, and the line segments are put into a line segment set L NFP Recording the number M of all the line segments to obtain the following formula;
l i ∈L NFP ；
then P (x, y) is the intersection set of the critical polygon and the line segment L, as shown in fig. 8, with two points; then, traversing the point set from left to right in turn, judging whether the point set is legal, taking the first legal point, namely the right upper corner point of the irregular graph after translation, as shown in fig. 9a, and as shown in fig. 9b, obtaining the translated vector V0.
In this embodiment, in the step S4, the calculation formula of the vector V1 is as follows;
regenerating the graph after horizontal displacement into a corresponding critical polygon; as shown in FIG. 10, the newly obtained line segments of the critical polygon are put into the set L' NFP Then there is a set of intersection points P' (x, y) of two critical polygons;
l i ∈L NFP ；
l j ∈L′ NFP ；
by using the formula, the intersection point of two critical polygons is calculated, and when the third irregular pattern is positioned on the intersection point of two different critical polygons, namely, the third irregular pattern intersects with the first two irregular patterns, under the legal condition, a plurality of groups of vectors V1 are obtained. As shown in fig. 11a and 11 b.
In this embodiment, 4 degrees of freedom of rotation are taken as an example, and the above cases and some result graphs are output as shown in fig. 12 to 15. Therefore, the layout method based on the combined single-specification graph can obtain a high-efficiency layout scheme through the algorithm, and provides an effective guide for the blanking production of enterprises, so that the blanking cost of the products of the enterprises is low, the layout effect is good, the production efficiency is high, and the application range is wide.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any such modifications, equivalents, and improvements that fall within the spirit and principles of the present invention are intended to be covered by the following claims.
Claims (5)
1. A method of single-rule layout for combining irregular images, comprising the steps of:
s1, inputting information of a target block and a raw material plate to obtain layout information;
step S2, initializing the layout information according to the original data;
s3, initializing an optimal result linked list;
s4, calculating all vectors V0 and V1 meeting the conditions according to the irregular image;
step S5, traversing all the vectors V0 and V1;
and S6, outputting the optimal solution condition by carrying out combination calculation, and ending the flow.
2. The method for single-rule layout of combined irregular images according to claim 1, wherein said step S5 further comprises the steps of:
step S51, if all the vectors V0 and V1 are not traversed, calculating the maximum utilization result under the condition of the current vectors V0 and V1;
step S52, judging whether the result is better than the optimal solution, if so, executing step S53; if not, returning to the step S5;
and step S53, reassigning the optimal solution, and returning to execute the step S5.
3. The method for single-rule layout of combined irregular images according to claim 1, further comprising the steps of:
step S7, if the combination calculation is not carried out on all the vectors V0 and V1 which are traversed, 180-degree combination is carried out on the original irregular graph;
s8, removing illegal irregular patterns;
and S9, calculating all the vectors V0 and V1 meeting the conditions according to the combined irregular graph, and returning to the step S5.
4. The method for single-rule layout for combining irregular images according to claim 1, wherein in the step S4, the calculation formula of the vector V0 is as follows;
presetting two line segments as l respectively 1 、l 2 The coordinates of the end points of the two line segments are respectively (x) 1 ,y 1 )(x 2 ,y 2 ) And (x) 3 ,y 3 )(x 4 ,y 4 ) The method comprises the steps of carrying out a first treatment on the surface of the Thus, two linear equations can be obtained;
y-y 1 ＝(y 2 -y 1 )(x-x 1 )/(x 2 -x 1 )；
y-y 3 ＝(y 4 -y 3 )(x-x 3 )/(x 4 -x 3 )；
let x and y be equal, the following can be obtained:
x＝((x 2 -x 1 )(x 3 -x 4 )(y 3 -y 1 )-x 3 (x 2 -x 1 )(y 3 -y 4 )+x 1 (y 2 -
y 1 )(x 3 -x 4 ))/((y 2 -y 1 )(x 3 -x 4 )-(x 2 -x 1 )(y 3 -y 4 ))；
y＝((y 2 -y 1 )(y 3 -y 4 )(x 3 -x 1 )-y 3 (y 2 -y 1 )(x 3 -x 4 )+y 1 (x 2 -
x 1 )(y 3 -y 4 ))/((x 2 -x 1 )(y 3 -y 4 )-(y 2 -y 1 )(x 3 -x 4 ))；
x≥max(x 1 ,x 3 )，x≤min(x 2 ,x 4 )；
y≥max(y 1 ,y 3 )，y≤min(y 2 ,y 4 )；
packaging the above formula into a function can be f (l 1 ,l 2 ) The output result of the function is an intersection point coordinate, if the two lines are parallel, the end point value of the overlapped part is returned, and the irregular graph is placed at one corner of the raw material plate;
setting P (x, y) as intersection point set, drawing a horizontal line segment L penetrating through the raw material plate by taking the rightmost upper corner point of the irregular graph, obtaining critical polygon by taking the right upper corner of the irregular graph as basic point, and placing the line segment into the line segment set L NFP Recording the number M of all the line segments to obtain the following formula;
l i ∈L NFP ；
the P (x, y) is the intersection point set of the critical polygon and the line segment L, and two points exist; and traversing the point set from left to right in sequence, judging whether the point set is legal, and taking the first legal point, namely the right upper corner point of the irregular graph after translation, so as to obtain the translated vector V0.
5. The method for single-rule layout for combined irregular images according to claim 4, wherein in step S4, the calculation formula of the vector V1 is as follows;
regenerating the graph after horizontal displacement into a corresponding critical polygon; putting the newly obtained line segments of the critical polygon into a set L' NFP Then there is a set of intersection points P' (x, y) of two critical polygons;
l i ∈L NFP ；
l j ∈L′ NFP ；
by using the formula, the intersection point of two critical polygons is calculated, and when the third irregular pattern is positioned on the intersection point of two different critical polygons, namely, the third irregular pattern intersects with the first two irregular patterns, under the legal condition, a plurality of groups of vectors V1 are obtained.
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