CN107609704A - Two-dimensional silhouette Nesting based on profile principal component analysis feature extraction - Google Patents
Two-dimensional silhouette Nesting based on profile principal component analysis feature extraction Download PDFInfo
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Abstract
The invention discloses a kind of two-dimensional silhouette Nesting based on profile principal component analysis feature extraction, this method first carries out stock layout mother metal profile discrete, then to stock layout mother metal profile reading process and principal component analysis is carried out, obtains first principal component and Second principal component, that mother metal treats stock layout area；Then all convex features of stock layout profile are treated in extraction, then carry out Principle component extraction and expression to these convex features of profile with PCA；Then it is all principal components are unitization, and accordingly assign characteristic value ratio to principal component weight, obtain the principal component for reflecting the convex feature of actual profile；Then calculate respectively and treat stock layout region and treat the convex feature first principal component of stock layout profile, the ratio of Second principal component, select to be used as layout project similar in first principal component ratio and Second principal component, ratio, be finally completed the stock layout of two-dimensional silhouette.Inventive algorithm is realized simple, it is not necessary to which the indexing rotation of conventional method, which is abutted against, can find out corresponding optimal layout project, and stock layout is accurate, and filling rate is high, stock layout efficiency high.
Description
Technical Field
The invention relates to a contour layout method, in particular to a two-dimensional contour layout method based on contour principal component analysis feature extraction.
Background
The problem of stock layout is widely present in many industries of modern economic society, such as mechanical manufacturing, print packaging, apparel, leather, glass, wood processing, construction, microelectronics, etc. The problem is mainly generated as a result of the development of modern processing and manufacturing industries and the promotion of market economy competition. The problem of solving can be solved, the utilization rate of materials can be improved, so that the production cost of enterprises is reduced, the competitiveness of the enterprises is improved, and the research and layout problem has important application value.
In practical engineering application, the core aim of the stock layout problem is to seek a reasonable part stock layout scheme on the basis of meeting process conditions, and improve the utilization rate of materials as much as possible so as to achieve the aims of saving materials and reducing cost.
The layout problem can be divided into a one-dimensional layout problem (also linear), a two-dimensional layout problem and a three-dimensional filling and boxing problem, wherein the one-dimensional and two-dimensional layout problems are mainly involved in a wide range of aspects. The research focus of the prior stock layout problem is focused on the aspect of two-dimensional stock layout, and the two-dimensional stock layout problem is the most widely researched stock layout problem.
Common two-dimensional contour layout methods are mainly classified into three categories: a rectangle fitting based approach, an image pixel based representation and a critical polygon based NFP layout approach.
1) Method based on rectangle fitting
In the early stage of researching the layout of the irregular parts, in order to simplify the complexity of the irregular parts in the layout process, many researchers firstly find out the minimum envelope rectangle of a single or a combination of a plurality of irregular parts, and then carry out optimized layout on the envelope rectangle by using a rectangular layout algorithm. The envelope of a single part is easy to solve, but the solution of a plurality of part combinations is somewhat complex, and the method has low precision, low material utilization rate and low practicability and is rarely adopted at present.
2) Image pixel based representation
The representation method based on image pixels is to make each part be represented by a bitmap dot matrix, and the representation method is not limited by the shape of the outline of the graph and is particularly suitable for parts with irregular shapes. Inspection of the overlap of parts in this way is relatively simple and fast. However, the process of converting the vector diagram into the bitmap by the algorithm also brings extra overhead on the algorithm, the position of the part cannot be accurately represented due to the accuracy problem of pixel determination, and the positioning accuracy of the algorithm is limited by the resolution division of the pixels of the image; the complexity of algorithm operation is in direct proportion to the square of the image resolution, the higher the accuracy of the image is, the greater the complexity of layout is, and the longer the operation time is.
3) NFP layout method based on critical polygon
The method based on the critical polygon is an algorithm based on calculation and solution of a trajectory line.
The method can effectively perform stock layout on irregular parts, but the algorithm needs to calculate the track formed by the parts around the outline of the plate, the algorithm for constructing the critical polygon is complex, particularly the part polygon of the concave polygon is solved, the calculated amount is quite large, the stock layout efficiency is limited, and the development of the stock layout algorithm is hindered.
In addition to the above three main methods, there is also an optimization algorithm used in combination with the intelligent algorithm, the intelligent optimization idea using the intelligent algorithm only generates different layout sequences, and the optimization effect largely depends on the basic layout algorithm, but the geometric features of the contour are not considered in the existing method, which results in the waste of the geometric feature resources of the contour to be laid, the layout efficiency is low, and the effect is not good.
Disclosure of Invention
The method aims to overcome the defects of the existing stock layout method and further improve the stock layout quality. The invention provides a two-dimensional contour layout method based on contour principal component analysis feature extraction, which has no requirement on the shape of a layout parent material and can be used for solving the layout problem of irregular contours on rectangular, circular and irregular parent materials.
In addition, the method can give a larger weight to the main characteristics of the profile characteristics in the aspect of characteristic extraction, and further extract the profile characteristics more completely.
In order to solve the technical problems, the invention is realized by the following technical scheme:
a two-dimensional contour layout method based on contour principal component analysis feature extraction comprises the following steps:
step 1: dispersing the outline of a to-be-arranged area of the arranged parent metal into scattered points;
and 2, step: reading discrete points of a to-be-arranged region of the arranged parent material, wherein the discrete points form an initial sample space, and carrying out vectorization processing on the discrete points to obtain a new sample space;
and step 3: performing principal component analysis on a new sample space of the region to be sampled by using a principal component analysis method, and extracting and expressing principal components, namely feature vectors, of the region to be sampled;
and 4, step 4: reading the outline of the part to be subjected to layout, identifying all convex features, namely convex polygons, of the outline of the part to be subjected to layout, and numbering the extracted convex features clockwise;
and 5: selecting the convex features processed in the step 4 to be represented by an initial sample space, and then carrying out vectorization processing on the initial sample space of the convex features to obtain a new sample space for analyzing the convex features;
step 6: carrying out principal component analysis on the new sample space of the convex features by using a principal component analysis method, and extracting and expressing principal components of the convex features, namely feature vectors;
and 7: unitizing all extracted principal components, and weighting corresponding characteristic values to the principal components;
and 8: repeating the step 5 to the step 7, and calculating and storing the ratio of the first principal components of all the convex features of the outline of the part to be laid to the first principal components of the area to be laid;
and step 9: comparing the ratio, and selecting a plurality of convex features with the ratio close to 1;
step 10: comparing the ratio of the second principal component of the convex features screened in the step 9 to the second principal component of the area to be stock layout, and selecting the convex features with the ratio closest to 1 as a final stock layout scheme;
step 11: calculating an included angle between the first principal component of the selected convex features and the first principal component of the to-be-stock-layout area;
step 12: rotating the selected convex features by the included angle between the first principal component of the convex features calculated in the step 11 and the first principal component of the to-be-laid area, so that the directions of the first principal components of the two parts are overlapped, and obtaining a new laying attitude of the selected convex features;
step 13: taking the outline centroid of the part to be stock layout as a reference point, and carrying out translational inarching along the vector direction by using the stock layout attitude selected in the step 12 to obtain a new stock layout attitude;
step 14: repeating the step 2 to the step 13, and carrying out layout on all the contours to be subjected to layout;
step 15: the sample arrangement is finished.
When the geometric characteristics of the outline are considered, the proportion of different parts of the characteristics in the outline is considered, the extracted characteristics can play a good noise reduction role compared with a layout method based on outline skeleton lines, and the influence of insignificant small characteristics on layout is ignored while the characteristics are relatively completely expressed.
According to the method, after the convex features are expressed by the principal components, the principal component feature vectors are used for completing contour matching, so that the solution of the stock layout posture is simplified, and the problem tends to be simplified.
The invention has the advantages of simple algorithm realization, high filling rate of stock layout and high stock layout efficiency, and only needs to carry out rotation matching of the area to be stock layout and the feature vector extracted from the contour to be stock layout after extraction due to the consideration of the geometric features of the contour, thereby obviously reducing the rotation times and the abutting calculation and obtaining the final stock layout result by a high-efficiency and accurate-purpose method.
The invention relates to a two-dimensional contour layout method based on principal component analysis feature extraction, which mainly solves the layout problem of irregular shapes, extracts the layout contour and uses the principal component analysis feature extraction, simplifies the layout method by utilizing the information of the contour feature represented by the principal component, increases the effect of the main contour of convex features, reduces the influence of minor contour factors, fully utilizes the principal component of the convex features, integrates the factors, and realizes the layout of the two-dimensional contour by utilizing the principal component of the layout contour.
At present, all patents related to stock layout simplify stock layout outlines by using rectangular outlines, and the condition of low stock layout filling rate is inevitable.
Drawings
FIG. 1 is a flow chart of the stock layout method of the present invention;
FIG. 2 is a result diagram of vectorization processing of a to-be-laid region;
FIG. 3 is a main component analysis extraction diagram of a region to be sampled;
FIG. 4 is a drawing for extracting and expressing convex features of a contour to be laid out;
FIG. 5 is a diagram of the analysis result of the principal components of each convex feature of the contour to be sampled;
FIG. 6 is a graph of principal component results after unitization and weighting;
FIG. 7 is a graph of the included angle of the convex features of the layout plan and the first principal component of the area to be laid;
FIG. 8 is a rotated result view of the male feature;
fig. 9 is a graph of the results of the abutment.
Detailed Description
The invention will be further described with reference to the following figures and specific examples:
the invention relates to a two-dimensional contour layout method based on contour principal component analysis feature extraction, and FIG. 1 is a flow chart of the layout method, and the specific implementation steps are as follows:
step 1: and dispersing the profile of the to-be-arranged area of the arranged base material into scattered points.
Step 2: reading discrete points of a to-be-arranged region of the arranged parent material, forming an initial sample space by the discrete points, and carrying out vectorization processing on the discrete points to obtain a new sample space. Fig. 2 is a diagram showing the result of vectorization processing of a to-be-laid region, wherein 3 in fig. 2 represents a contour of a laid part, which encloses a to-be-laid region as shown in 4;
the specific implementation process of the step is as follows:
indicating { P (pitch length) in a counterclockwise direction for vertexes of discrete points of to-be-arranged region of arranged base metal i H, i =1,2,3 \ 8230n; the coordinate is (x) i ，y i ) Expressing P in the form of a vector i (x i ，y i ) Obtaining an initial sample space of a to-be-arranged area of the arranged parent material, wherein the sample space is closely related to a coordinate system;
the normalization and weighting treatment:
selecting discrete point starting end point P of to-be-arranged area of arranged parent metal 0 Then, vectorizing the discrete points along the counterclockwise direction from the starting end point, that is, connecting the discrete points in turn according to the counterclockwise direction, and obtaining (n-1) vectors X after processing i And a new sample space is constructed using the lengths of the vectors as weights for the vectors.
And step 3: and (3) performing principal component analysis on the new sample space of the region to be subjected to stock layout by using a principal component analysis method, and extracting and expressing principal components of the region to be subjected to stock layout, namely the feature vectors. As shown in fig. 3, vectors 1,2 are the first and second principal components of the area to be laid; the steps are completed by a computer, and the specific implementation process is as follows:
the method comprises the steps of carrying out vectorization processing on an initial sample space of a to-be-arranged region of a arranged mother material to obtain a new sample space for main component analysis, and the vectorization processing is represented as follows:
whereinIs a length weighted column vector with dimension 2, n is the number of vectors of the new sample space;
secondly, calculating the average column vector of the n length weighted column vectors
X i Weighting the ith length column vector;
calculating the difference value between each length weighted column vector and the average column vector to obtain a difference value vector
D i ＝X i -X' (2)
Fourth configuration covariance matrix C = (C) ij ) 2×2 ：
C＝D*D T (3)
Wherein, D = (D) 1 ,D 2 ,D 3 ……D n )＝(d ij ) 2×n ；
And fifthly, performing characteristic decomposition on the covariance matrix obtained in the step four.
Because the obtained covariance matrix C is a real symmetric matrix, the covariance matrix C can be subjected to singular value decomposition by using a Jacobi SVD method, i.e., singular value decomposition, to obtain two eigenvalues lambda k (k =1,2) and λ k >, 0 and two feature vectors xi corresponding to the two k (k =1,2), features corresponding to relatively large feature valuesThe vector is its first principal component and the other is the second principal component.
And 4, step 4: the contour of the part to be laid out is read, all convex features, namely convex polygons, of the contour of the part to be laid out are identified, and the extracted convex features are numbered as a, b and c clockwise as shown in fig. 4.
And 5: and 4, selecting the convex features processed in the step 4 to represent by an initial sample space, and then carrying out vectorization processing on the initial sample space of the convex features to obtain a new sample space for analyzing the convex features. The specific implementation process of the step is as follows:
performing discretization on the selected convex features, and representing vertexes of generated discrete points in a counterclockwise direction { P i H =1,2,3 \ 8230n; the coordinates are (x) i ，y i ) Expressing P in the form of a vector i (x i ，y i ) Obtaining an initial sample space of the convex feature, wherein the sample space is also closely related to a coordinate system;
and carrying out normalization and weighting treatment.
Selecting the starting point P of the discrete point with convex characteristics 0 Then, vectorization processing is carried out on the convex feature discrete points along the counterclockwise direction from the starting end point, namely, (n-1) vectors X are obtained by connecting the discrete points in turn according to the counterclockwise direction and carrying out processing i And the length of these vectors is used as the weight of the vector to construct a new sample space.
Step 6: and performing principal component analysis on the new sample space of the convex features by using a principal component analysis method, and extracting and expressing principal components of the convex features, namely feature vectors. The principal component results for each convex feature are shown in FIG. 5, where: the main components of the characteristic a are a1 and a2; the main components of the b characteristic are b1 and b2 respectively; the main components of the c characteristic are c1 and c2.
The specific implementation process for extracting and expressing the main component of the convex features is as follows:
obtaining a new sample space for main component analysis by vectorization processing of the convex-feature initial sample space, wherein the new sample space is represented as follows:
whereinIs a length weighted column vector with dimension 2, n is the number of vectors in the new sample space;
secondly, calculating the average column vector of the n length weighted column vectors
X i Weighting the column vector for the ith length;
calculating the difference value between each length weighted column vector and the average column vector to obtain a difference value vector
D i ＝X i -X' (6)
Fourth configuration covariance matrix C = (C) ij ) 2×2 ：
C＝D*D T (7)
Wherein, D = (D) 1 ,D 2 ,D 3 ……D n )＝(d ij ) 2×n ；
And fifthly, performing characteristic decomposition on the covariance matrix obtained in the step four.
Because the obtained covariance matrix C is a real symmetric matrix, the covariance matrix C can be subjected to singular value decomposition by using a Jacobi SVD method, i.e., singular value decomposition, to obtain two eigenvalues lambda k (k =1,2) and λ k >, 0 and two feature vectors xi corresponding to the two k (k =1, 2), the eigenvector corresponding to the larger eigenvalue is the first principal component thereof, and the other eigenvector is the second principal component thereofThe second principal component.
And 7: all principal components extracted are unitized, and the corresponding feature values are weighted to the principal components. The principal components after the unitization and weighting processing are shown in fig. 6, and Y1 and Y2 represent the principal components after the processing of the to-be-laid region; a1', a2' represent the principal component of the a-convex feature after processing; b1 'and b2' represent main components of the b-convex features after being processed; c1', c2' represent the principal component after the c-convex feature has been processed.
The weighted principal component, which is also a weighted feature vector, is:
wherein λ is k Is a main component xi k The corresponding characteristic value.
And step 8: and (5) repeating the step (5) to the step (7), and calculating and storing the ratio of the first principal component of all the convex features of the outline of the part to be laid to the first principal component of the area to be laid.
Calculating the ratio of the first principal component of all convex features of the outline of the part to be subjected to stock layout to the first principal component of the area to be subjected to stock layout:
wherein: lambda [ alpha ] i1 Representing a characteristic value corresponding to the first principal component of the ith convex characteristic; lambda [ alpha ] 1 Characteristic values of a first principal component of the region to be laid out; select k i1 ，k i2 Several convex features close to 1.
And step 9: and comparing the ratios to select a plurality of convex features with the ratio close to 1.
Step 10: and 9, comparing the ratio of the second principal component of the convex feature screened in the step 9 to the second principal component of the area to be subjected to stock layout, and selecting the convex feature with the ratio closest to 1 as a final stock layout scheme.
The formula for calculating the ratio of the second principal component of the screened convex features to the second principal component of the to-be-laid area is as follows:
wherein: lambda i2 Representing a characteristic value corresponding to the ith convex characteristic second principal component; lambda 2 Characteristic values of the second principal component of the region to be laid out.
Step 11: calculating an included angle between the first principal component of the selected convex features and the first principal component of the to-be-laid area; the calculation steps are as follows:
setting the ith convex feature of the profile and the first principal component of the area to be sampled, namely the feature vector as alpha i ＝(a i1 ,b i1 ) T ，γ 1 ＝(a 12 ,b 12 ) T Then the included angle of the feature vector is calculated as follows:
α i *γ 1 ＝|α i ||γ 1 |cosθ i
FIG. 7 is a graph of included angles between convex features of a layout scheme and a first principal component of a region to be laid, as shown in FIG. 7; the ratio of the first and second principal components of the characteristic b to the principal component of the area to be laid is closest, and the included angle theta between the first principal component of the convex characteristic b and the first principal component of the area to be laid is selected and calculated 1 For the purpose of comparison and explanation, the angles of a and c are calculated as θ 2 ，θ 3 。
Step 12: rotating the selected convex features by the included angle between the first principal component of the convex features calculated in the step 11 and the first principal component of the to-be-stock-layout area, so that the directions of the first principal components of the two parts are overlapped to obtain a new stock-layout posture of the selected convex features; FIG. 8 is a diagram of the result of rotation of the principal components of each convex feature, as shown: in the figure: the method comprises the following steps of (1) matching a characteristic with a main component of a to-be-laid region, (2) matching an characteristic with a main component of the to-be-laid region, and (3) matching a characteristic with a main component of the to-be-laid region. As can be seen from the figure, the main component of the b feature is closest to the to-be-laid region, then the c feature, and the worst is the a feature, and the feature abutment result should be consistent with this.
Step 13: and (4) taking the outline centroid of the part to be stock layout as a reference point, and performing translational inarching along the vector direction by using the stock layout posture selected in the step (12) to obtain a stock layout result. As shown in fig. 9, fig. 9 is a graph of the abutment result, and the verification result: respectively butting the three determined stock layout postures, and respectively butting the stock layout postures along the direction of the first principal component by taking the hexagonal centroid of the profile to be stock layout as a reference point; the results of the abutment of different features are shown in (1), (2) and (3) of fig. 9, and the graphs show that the results are consistent with the principal component representation; and selecting the b characteristic as the layout posture for the approach joint.
Step 14: and (5) repeating the step 2 to the step 13, and performing layout on all the contours to be laid.
Step 15: the sample arrangement is finished.
Claims (1)
1. A two-dimensional contour layout method based on contour principal component analysis feature extraction is characterized by comprising the following steps: the method comprises the following steps:
step 1: dispersing the outline of a to-be-arranged area of the arranged parent metal into scattered points;
and 2, step: reading discrete points of a to-be-arranged region of the arranged parent material, wherein the discrete points form an initial sample space, and carrying out vectorization processing on the discrete points to obtain a new sample space; the specific implementation process of the step is as follows:
indicating { P (pitch length) in a counterclockwise direction for vertexes of discrete points of to-be-arranged region of arranged base metal i H =1,2,3 \ 8230n; the coordinates are (x) i ，y i ) Expressing P in the form of a vector i (x i ，y i ) Obtaining an initial sample space of a to-be-arranged area of the arranged parent material, wherein the sample space is closely related to a coordinate system;
the normalization and weighting treatment:
selecting discrete points of to-be-arranged area of arranged base materialStarting point P 0 Then, vectorizing the discrete points along the counterclockwise direction from the starting end point, that is, connecting the discrete points in turn according to the counterclockwise direction, and obtaining (n-1) vectors X after processing i And the length of these vectors is used as the weight of the vector to construct a new sample space;
and step 3: performing principal component analysis on the new sample space of the to-be-sampled area by using a principal component analysis method, and extracting and expressing principal components of the to-be-sampled area, namely feature vectors; the step is completed by a computer, and the specific implementation process is as follows:
performing vectorization processing on an initial sample space of a to-be-arranged region of a arranged mother material to obtain a new sample space for main component analysis, wherein the vectorization processing is represented as:
whereinIs a length weighted column vector with dimension 2, n is the number of vectors in the new sample space;
secondly, calculating the average column vector of the n length-weighted column vectors
X i Weighting the ith length column vector;
calculating the difference value between each length weighted column vector and the average column vector to obtain a difference value vector
D i ＝X i -X′ (2)
Fourth configuration covariance matrix C = (C) ij ) 2×2 ：
C＝D*D T (3)
Wherein D = (D) 1 ，D 2 ，D 3 ……D n )＝(d ij ) 2×n ；
Fifthly, performing characteristic decomposition on the covariance matrix obtained from the fourth step;
because the obtained covariance matrix C is a real symmetric matrix, the covariance matrix C can be subjected to singular value decomposition by using a Jacobi SVD method, i.e., singular value decomposition, to obtain two eigenvalues lambda k (k =1,2) and λ k 0 and their corresponding two feature vectors ξ k (k =1, 2), the eigenvector corresponding to the larger eigenvalue is the first principal component thereof, and the other is the second principal component;
and 4, step 4: reading the outline of the part to be subjected to layout, identifying all convex features, namely convex polygons, of the outline of the part to be subjected to layout, and numbering the extracted convex features clockwise;
and 5: selecting the convex features processed in the step 4 to be represented by an initial sample space, and then carrying out vectorization processing on the initial sample space of the convex features to obtain a new sample space for analyzing the convex features; the specific implementation process of the step is as follows:
performing discretization on the selected convex features, and representing vertexes of generated discrete points in a counterclockwise direction { P i H =1,2,3 \ 8230n; the coordinates are (x) i ，y i ) Expressing P in the form of a vector i (x i ，y i ) Obtaining an initial sample space of the convex feature, wherein the sample space is also closely related to a coordinate system;
normalization and weighting processing are carried out;
selecting the starting point P of the convex feature discrete point 0 Then, vectorization processing is carried out on the convex feature discrete points along the counterclockwise direction from the starting end point, namely, (n-1) vectors X are obtained by connecting the discrete points in turn according to the counterclockwise direction and carrying out processing i And the length of these vectors is used as the weight of the vector to construct a new sample space;
and 6: performing principal component analysis on the new sample space of the convex features by using a principal component analysis method, and extracting and expressing principal components of the convex features, namely feature vectors; the specific implementation process for extracting and expressing the main component of the convex feature is as follows:
obtaining a new sample space for main component analysis by vectorization processing of the convex-feature initial sample space, wherein the new sample space is represented as follows:
whereinIs a length weighted column vector with dimension 2, n is the number of vectors in the new sample space;
secondly, calculating the average column vector of the n length weighted column vectors
X i Weighting the ith length column vector;
calculating the difference value between each length weighted column vector and the average column vector to obtain a difference value vector
D i ＝X i -X′ (6)
Fourth configuration covariance matrix C = (C) ij ) 2×2 ：
C＝D*D T (7)
Wherein, D = (D) 1 ，D 2 ，D 3 ……D n )＝(d ij ) 2×n ；
Carrying out characteristic decomposition on the covariance matrix obtained from the step four;
because the obtained covariance matrix C is a real symmetric matrix, the covariance matrix C can be subjected to singular value decomposition by using a Jacobi SVD method, namely singular value decomposition, to obtain two eigenvalues lambda k (k =1,2) and λ k > 0 and their corresponding two feature vectors ξ k (k =1, 2), the eigenvector corresponding to the larger eigenvalue is the first principal component thereof, and the other is the second principal component;
and 7: unitizing all extracted principal components, and weighting corresponding characteristic values to the principal components; the weighted principal component, which is also a weighted feature vector, is:
wherein λ is k Is a main component xi k Corresponding characteristic values;
and 8: repeating the step 5 to the step 7, calculating and storing the ratio of the first principal components of all convex features of the outline of the part to be subjected to layout to the first principal component of the area to be subjected to layout; calculating the ratio of the first principal components of all convex features of the outline of the part to be stock layout to the first principal components of the area to be stock layout respectively:
wherein: lambda [ alpha ] i1 Representing a characteristic value corresponding to the first principal component of the ith convex characteristic; lambda 1 Characteristic values of a first principal component of the region to be laid out; selecting k i1 ，k i2 A number of convex features close to 1;
and step 9: comparing the ratio, and selecting a plurality of convex features with the ratio close to 1;
step 10: comparing the ratio of the second principal component of the convex features screened in the step 9 to the second principal component of the area to be stock layout, and selecting the convex features with the ratio closest to 1 as a final stock layout scheme;
the formula for calculating the ratio of the second principal component of the screened convex features to the second principal component of the to-be-laid area is as follows:
wherein: lambda [ alpha ] i2 Representing a characteristic value corresponding to the ith convex characteristic second principal component; lambda [ alpha ] 2 Characteristic values of a second principal component of the region to be laid out;
step 11: calculating an included angle between the first principal component of the selected convex features and the first principal component of the to-be-laid area; the calculation steps are as follows:
setting the ith convex feature of the profile and the first principal component of the area to be sampled, namely the feature vector as alpha i ＝(a i1 ，b i1 ) T ，γ 1 ＝(a 12 ，b 12 ) T Then, the included angle of the feature vector is calculated as follows:
α i *γ 1 ＝|α i ||γ 1 |cosθ i
step 12: rotating the selected convex features by the included angle between the first principal component of the convex features calculated in the step 11 and the first principal component of the to-be-laid area, so that the directions of the first principal components of the two parts are overlapped, and obtaining a new laying attitude of the selected convex features;
step 13: taking the outline centroid of the part to be stock layout as a reference point, and carrying out translational inarching along the vector direction by using the stock layout attitude selected in the step 12 to obtain a new stock layout attitude;
step 14: repeating the step 2 to the step 13, and performing layout on all contours to be subjected to layout;
step 15: the sample preparation is finished.
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|---|---|---|---|---|
| CN109685790A (en) * | 2018-12-24 | 2019-04-26 | 杭州澳星科技有限公司 | A kind of quick discharge algorithm of corium based on GPU operation |
| CN110286291A (en) * | 2019-07-15 | 2019-09-27 | 广东石油化工学院 | A kind of running state of transformer vibration sound detection method and system using principal component |
| CN110827260A (en) * | 2019-11-04 | 2020-02-21 | 燕山大学 | Cloth defect classification method based on LBP (local binary pattern) features and convolutional neural network |
| CN113704841A (en) * | 2021-08-31 | 2021-11-26 | 浙江大学 | Optimized stock layout method based on bias |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101650777A (en) * | 2009-09-07 | 2010-02-17 | 东南大学 | Corresponding three-dimensional face recognition method based on dense point |
| CN106926212A (en) * | 2017-04-28 | 2017-07-07 | 燕山大学 | Two-dimensional silhouette Nesting based on profile framework characteristic |
-
2017
- 2017-09-18 CN CN201710840521.1A patent/CN107609704B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101650777A (en) * | 2009-09-07 | 2010-02-17 | 东南大学 | Corresponding three-dimensional face recognition method based on dense point |
| CN106926212A (en) * | 2017-04-28 | 2017-07-07 | 燕山大学 | Two-dimensional silhouette Nesting based on profile framework characteristic |
Non-Patent Citations (1)
| Title |
|---|
| 郭保苏等: "复杂网格曲面高效加工编程关键技术研究", 《中国博士学位论文全文数据库 信息科技辑》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109685790A (en) * | 2018-12-24 | 2019-04-26 | 杭州澳星科技有限公司 | A kind of quick discharge algorithm of corium based on GPU operation |
| CN110286291A (en) * | 2019-07-15 | 2019-09-27 | 广东石油化工学院 | A kind of running state of transformer vibration sound detection method and system using principal component |
| CN110286291B (en) * | 2019-07-15 | 2021-04-06 | 广东石油化工学院 | Method and system for detecting vibration and sound of running state of transformer by using principal components |
| CN110827260A (en) * | 2019-11-04 | 2020-02-21 | 燕山大学 | Cloth defect classification method based on LBP (local binary pattern) features and convolutional neural network |
| CN110827260B (en) * | 2019-11-04 | 2023-04-21 | 燕山大学 | Cloth defect classification method based on LBP characteristics and convolutional neural network |
| CN113704841A (en) * | 2021-08-31 | 2021-11-26 | 浙江大学 | Optimized stock layout method based on bias |
| CN113704841B (en) * | 2021-08-31 | 2023-11-14 | 浙江大学 | Bias-based optimized layout method |
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