CN102436217A - Method for reconstructing web processing drive geometry of slot characteristic of aircraft structure - Google Patents

Abstract

The invention discloses a method for automatically reconfiguring the driving geometry of groove feature webs of aircraft structural parts. The method firstly combines all side surfaces, sunken surfaces and corner surfaces of the groove features to calculate their boundaries; combines the web surface and its outer ring The bottom corner face, and its boundary is calculated, the above two boundaries are combined into a whole, and the edges that do not meet the requirements are eliminated. In the sketch environment, project the screened edge to the web surface, obtain the intersection point between the projected edge and the edge, and use the intersection point to break the intersecting edge. Based on all the points and edges after projection and breaking, construct the edge, The attribute edge point graph of points and edge and point information; then calculate all the minimum enclosing contours in the attribute edge point graph; finally get the effective minimum enclosing contour from all the minimum enclosing contours as the driving geometry of web processing. The invention effectively solves the problem that the web driving geometry is difficult to automatically extract, and improves the quality and efficiency of web automatic programming in numerical control process programming.

Description

Machining-driven geometry reconstruction method for slot feature webs of aircraft structural parts

technical field

The invention relates to a method for geometric reconstruction of web processing drive, in particular to a method for geometric reconstruction of web processing drive geometry of aircraft structural part grooves, belonging to CAD (Computer Aided Design)/CAPP (Computer Aided Process Design)/CAM (Computer Aided Manufacturing) technology field. the

Background technique

The structure of aircraft structural parts is complex, with many processing features, including a large number of free-form surfaces, intersecting features and special processing areas, making processing difficult. Large domestic aviation companies have invested tens of billions of dollars to purchase a large number of advanced CNC machine tools, but the effective utilization rate of the equipment is low. The main reason is the low efficiency and unstable quality of CNC programming. During the NC programming of aircraft structural parts, it is necessary to manually pick up a large number of geometries, set a large number of parameters and create a large number of auxiliary geometries. With the increase of integral parts, thin-walled parts and special material parts, the workload of NC programming has increased significantly, and the NC programming of aircraft structural parts has increasingly become one of the important bottlenecks affecting the aircraft development cycle. the

The automatic acquisition process of driving information is called machining feature reconstruction. The automatic reconstruction of driving geometry is the key and difficult point in the reconstruction of machining features. The driving geometry is implicit in the geometric information of the machining features, which needs to be processed and converted into a data form that can be directly used by the tool path generation algorithm. the

In the CAD model represented by B-rep (Boundary Representation), the topology of the surface is organized by points, edges, and rings. .The boundary of a surface is composed of rings. The rings are divided into inner rings and outer rings. There is only one outer ring, and there can be multiple inner rings. The outer ring forms the outer contour of the surface, and the inner ring forms the contour of the hole or island. The inner and outer rings are the direct drive geometry for the web machining tool path generation algorithm. the

The shape of the cavity of aircraft structural parts is complex and the sealing is different. The side wall of the cavity contains a large number of free-form surfaces and the opening and closing angles coexist. The outer ring of the web surface itself cannot be directly used as the offset basis of the equidistance line. Therefore, the outer ring must be corrected, including a large number of curve cutting and splicing calculations, so as to ensure that the tool will neither interfere with the side surface nor produce cutting residue during the cutting process. The current method is to select and cut the driving geometry of the web in a 3D environment, which has a large workload and is difficult to guarantee the correctness, especially in the process of automatic calculation, it is difficult to generate an effective closed driving geometry. the

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the existing CAD/CAM system in the structural part groove characteristic web processing driving geometry calculation method, and to provide a method for automatic reconstruction of the aircraft structural part groove characteristic web processing driving geometry. the

The method for automatically reconfiguring the driving geometry of the groove feature web of the aircraft structural part of the present invention comprises the following steps:

Step 1. Combine all sides, sunken faces and corner faces of a groove feature, marked as JOIN.1;

Step 2. According to the adjacency relationship between all faces in JOIN.1, calculate its boundary, marked as: BOUNDARY.1;

Step 3. Combine the web surface and the bottom corner surface of the outer ring of the web, marked as: JOIN.2;

Step 4. According to the adjacency relationship between all faces in JOIN.2, get its boundary, marked as: BOUNDARY.2;

Step 5. Combine all edges in BOUNDARY.1 and BOUNDARY.2 into a whole, marked as: JOIN.3;

Step 6. Filter the edges in JOIN.3 and eliminate unnecessary edges;

Step 7. In the sketch environment, project the edge in the filtered JOIN.3 to the web surface, obtain the intersection point between the projected edge and the edge, and use the intersection point to break the intersecting edge. The processed result is marked as SKETCH. 1;

Step 8. Based on all points and edges after projection and interruption, construct an attribute edge-point graph containing edge, point, and edge-to-point information;

Step 9, calculate all minimum enclosing contours in the attribute edge point graph;

Step 10. Obtain an effective minimum enclosing contour from all the minimum enclosing contours, which is the driving geometry for the final web contour machining. the

The specific steps of step 2 are: ① take out the faces in JOIN.1 one by one in order; ② extract the outer ring boundary of the face; ③ take out the edges in the outer ring boundary one by one in order; ④ judge whether the edge belongs to JOIN. For the outer ring edges of other faces in 1, if yes, return to step ③; otherwise, this edge belongs to the boundary of JOIN.1, and it is included in BOUNDARY.1. the

The method for screening the edges of JOIN.3 is: ① remove the same edges in JOIN.3; ② remove the straight edges perpendicular to the web surface. the

The specific steps of said step 7 are: 1. Project the obtained three-dimensional edge to the web plane to obtain projection curves such as plane straight lines, plane conic curves or plane spline curves; For the overlapped curves, find the overlapped part and keep only one; ③ Then find all the intersection points between the curves, break the corresponding curve into two curves at each intersection point, and finally get a network of curves. the

The realization method of the above process in CAD/CAM software: create a sketch based on the web plane, and project JOIN.3 as a whole to the sketch, so that the edge lines in JOIN.3 can be projected to the web surface, intersecting points, interruption and other operations can be realized ;

The concrete steps of described step 8 are: 1. define the point class MyVertex, member variables include the mathematical representation of the point, the topological representation of the point and the topological edge column connected with the point; 2. define the edge class MyEdge, the member variables include the topological representation of the edge, The feature representation of the edge, the opening and closing attribute identification of the edge, the starting point, and the ending point; ③ Create a list of the MyVertex class and mark it as: MYVERTEX_LIST, and create a list of the MyEdge class and mark it as: MYEDGE_LIST; ④ Take out the SKETCH one by one in order. 1 edge; ⑤ create a MyEdge class object, fill in the current edge attributes into the corresponding member variables, and list the object in MYEDGE_LIST; ⑥ take out the starting point of the current edge, and mark it as STARTPOINT. Determine whether STARTPOINT is a member of MYVERTEX_LIST, if so, skip to step ⑦, otherwise create a MyVertex object, fill in the attributes of STARTPOINT into the corresponding member and list the object in MYVERTEX_LIST; ⑦Take out the current edge End point, marked ENDPOINT. Determine whether ENDPOINT is a member of MYVERTEX_LIST, if not, create an object of MyVertex class, fill in the attributes of ENDPOINT into the corresponding member variable, and list the object in MYVERTEX_LIST. the

The concrete steps of described step 9 are:

①Choose a section of curve l _i in the attribute edge-point graph, take a vertex M _i (x ₀ , y ₀ , z ₀ ) of l _i as the current node, and mark the combination of the current curve and the current node, denoted as ( l _i , M _i );

与当前结点M_i连接的其他线段的切矢 

② Take the point M _i of the combination (l _i , M _i ) as the starting point of the curve segment, assuming that the tangent vector of the curve l _i at point M _i is

Tangent vectors of other line segments connected to the current node M _i

定义 

的旋转方向为 

那么 绕点M_i，以 

为起始方向旋转，在 

矢量中，与其重合的矢量相对应的第一条边即为当前最小包围轮廓线的下一条边，记为l_i1，取l_i1的另外一个顶点，记为M_i1，此时判断l_i1是否与l_i相同，如果不同则判断(l_i1，M_i1)是否已经标记，若没有标记，则将(l_i1，M_i1)赋值给(l_i，M_i)转入步骤②。  ③Record the outer normal direction of the web as

definition

The direction of rotation is

So Around the point M _i , take

is the starting direction of rotation, at

In the vector, the first edge corresponding to the coincident vector is the next edge of the current minimum enclosing contour line, which is denoted as l _i1 , and the other vertex of l _i1 is denoted as M _i1 , at this time, judge whether l _i1 is Same as l _i , if different, judge whether (l _i1 , M _i1 ) has been marked, if not, assign (l _i1 , M _i1 ) to (l _i , M _i ) and go to step ②.

④ Take another vertex of l _i as the current node M _i ′(x ₀ ′, y ₀ ′, z ₀ ′), judge whether (l _i , M _i ′) has been marked, if not, set (l _i , M _i ′) assign value to (l _i , M _i ) and go to step ②.

⑤ Get all the minimum enclosing contours in the sketch. the

矢量中，与 

第一个相重合的矢量的具体步骤是：  Judgment said

in vector, with

The specific steps for the first coincident vector are:

相交于点 

与 矢量相交于点  $L_n=M_i+{\stackrel{\→}{r}}_n.$ ①, Make a circle with M _i as the center and a radius of 1. the circle with

intersect at point

and vector intersects at point $L_{\mathrm{no}}=m_i+{\stackrel{\&Right\; Arrow;}{r}}_{\mathrm{no}}.$

② Construct n vectors starting from L ₀ $\stackrel{\&Right\; Arrow;}{V_1}=L_1-L_0=\stackrel{\&Right\; Arrow;}{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000100030910000021.png,HDA0000100030910000054.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}-\stackrel{\&Right\; Arrow;}{r_0},$ $\stackrel{\&Right\; Arrow;}{{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA0000100030910000055.png,HDA0000100030910000061.png"\; state="\{\{state\}\}">V</figure-callout>}}_2}=L_2-L_0=\stackrel{\&Right\; Arrow;}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000100030910000055.png,HDA0000100030910000061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}-\stackrel{\&Right\; Arrow;}{r_0},...,$ $\stackrel{\&Right\; Arrow;}{V_{\mathrm{no}}}=L_{\mathrm{no}}-L_0=\stackrel{\&Right\; Arrow;}{r_{\mathrm{no}}}-\stackrel{\&Right\; Arrow;}{r_0}.$

与 

向量之间的夹角，最小夹角对应的矢量即为与 第一个相重合的矢量。  ③ Then calculate separately

and

The angle between the vectors, the vector corresponding to the minimum angle is the The first coincident vector.

The concrete steps of described step 10 are:

① All the minimum enclosing contours obtained can be expressed as: LOOP0, LOOP1, ..., LOOPn;

②Exclude the minimum enclosing contour LOOPi (0≤i≤n) with the largest area, and the remaining minimum enclosing contours can be expressed as: LOOP0, LOOP1, ... LOOPi-1, LOOPi+1, ..., LOOPn;

③ Traverse the remaining minimum enclosing contours, calculate the center point of the current minimum enclosing contour, and make a straight line perpendicular to the web surface through the center point. If the straight line does not intersect JOIN.1, the current minimum enclosing contour is the effective minimum enclosing contour. the

The method of the present invention has high efficiency, the generated web processing and driving geometry has high quality, and the auxiliary geometry generated in the calculation process is less, saving storage space, and effectively solving the cumbersome calculation of the characteristic web processing and driving geometry of aircraft structural parts, which is difficult to automate Generate problems that drive geometry efficiently. the

Description of drawings

Fig. 1. flow chart of the method for generating the driving geometry of the groove feature web of the aircraft structural part of the present invention;

Figure 2. Algorithm flow chart for binding surface boundaries;

Figure 3. Curved columns of mesh. Among them, the number 1-11 represents the number of the curve column; LOOP1-LOOP6 represents the minimum enclosing contour;

Figure 4. Definition of attribute edge point graph class;

Figure 5. The construction flow chart of the attribute edge point graph;

为l_i在M_i处的单位切向量；  Figure 6. Tangent vectors of nodes on line segments. Where M _i is the current node of the current curve l _i ,

is the unit tangent vector of l _i at M _i ;

为当前曲线l₀在当前结点M_i处的单位切向量， 

为与M_i相连的曲线l_n在M_i处的单位切向量， 

为 

的旋转方向；  Figure 7. Schematic diagram of vector coincidence judgment. in

is the unit tangent vector of the current curve l ₀ at the current node _Mi ,

is the unit tangent vector of the curve l _n connected to M _i at M _i ,

for

direction of rotation;

Fig. 8. Groove used in the embodiment;

Figure 9.Join.1, which represents the combination of all sides, sunken faces and corner faces of the groove feature;

Figure 10.Join.2, representing the combination of the web face and the bottom corner face of the groove feature;

Figure 11. The sketch after projection of Join.3 to the web surface, the numbers 1-5 indicate the intersection parts in the sketch;

Figure 12. The enlarged view at "1" in Figure 11;

Fig. 13. The result diagram of the realization of the method of the present invention, Guidel is the effective minimum enclosing contour, and Bottom is the web surface;

Detailed ways

The present invention will be further described below in conjunction with the embodiments and accompanying drawings. The C++ language is used to realize the automatic geometry reconstruction method driven by the groove feature web of aircraft structural parts. The CAD/CAM software platform used is CATIA, and the development platform is CAA, the secondary development platform of CATIA. The specific steps of implementation are as follows:

Step 1. Execute the "Join" command to join all the sides, sunken faces and corner faces of a groove feature, as shown in Figure 9, to get the "Join.1" feature;

Step 2. Execute the "Boundary" command to calculate the boundary of "Join.1" and obtain the feature of "Boundary.1";

Step 3. Execute the "Join" command to join the web surface and the bottom corner surface of the outer ring of the web, as shown in Figure 10, to obtain the "Join.2" feature;

Step 4. Execute the "Boundary" command to calculate the boundary of "Join.2" and obtain the feature of "Boundary.2";

Step 5. Execute the "Join" command to combine "Boundary.1" and "Boundary.2" into a whole to get the "Join.3" feature;

Step 6. In the sketch environment, project "Join.3" to the web surface, as shown in Figure 11, and get the feature of "Sketch after joining.3 projected to the web surface". In CATIA, after projecting the sketch, the system All intersecting curves have been automatically interrupted;

Step 7. Construct an attribute edge-point graph containing edge, point, and edge-to-point information. The specific steps are: ①Define the point class MyVertex, and the member variables include the mathematical representation of the point, the topological representation of the point, and the topological edge columns connected to the point; ②Define the edge class MyEdge, and the member variables include the topological representation of the edge, the characteristic representation of the edge, Edge opening and closing attribute identification, starting point, and ending point; ③ Create a list of MyVertex class, marked as: MYVERTEX_LIST, create a new list of MyEdge class, marked as: MYEDGE_LIST; ④ Take out the edges in SKETCH.1 one by one in order; ⑤Create an object of MyEdge class, fill in the attributes of the current edge into the corresponding member variables, and list the object in MYEDGE_LIST; ⑥Take out the starting point of the current edge, and mark it as STARTPOINT. Determine whether STARTPOINT is a member of MYVERTEX_LIST, if so, skip to step ⑦, otherwise create a MyVertex class object, fill in the attributes of STARTPOINT into the corresponding member and list the object in MYVERTEX_LIST; ⑦Take out the current edge End point, marked ENDPOINT. Determine whether ENDPOINT is a member of MYVERTEX_LIST, if not, create an object of MyVertex class, fill in the attributes of ENDPOINT into the corresponding member variable, and list the object in MYVERTEX_LIST. the

Step 8. Calculate all minimum enclosing contours in the attribute edge-point graph. The enlarged view of "1" in Figure 11 is shown in Figure 12, and "2" to "5" are similar to "1";

The nodes in Fig. 12 include ABCDEFGHIJ, wherein the minimum enclosing contours are ABCD and DGA, etc., and the steps to obtain the minimum enclosing contour ABCD are as follows. the

Traverse the curves in the attribute edge-point graph, assuming that the current curve is AD, take a vertex A of AD as the current node, mark the combination of the current curve and the current node, and record it as (AD, D);

In the combination (AD, D), D is the starting point, and the tangent vectors of the curve segments DA, DG, DE, and DC are made, and the units are denoted as

那么定义 

的旋转方向为 

绕点D，以 

为起始方向旋转，在 

矢量中，与其重合的矢量相对应的第一条边为DC，即为当前最小包围轮廓线的下一条边，此时判断DC是否与当前曲线AD相同，如果不同则判断(DC，C)是否已经标记，若没有标记，则将(DC，C)转入步骤②；  Denote the outward normal direction of the web surface as

then define

The direction of rotation is

Around point D, with

is the starting direction of rotation, at

In the vector, the first side corresponding to the coincident vector is DC, which is the next side of the current minimum enclosing contour line. At this time, judge whether DC is the same as the current curve AD, and if it is different, judge whether (DC, C) is Already marked, if not marked, then transfer (DC, C) to step ②;

The cyclic process of step ② and step ③ can be combined (CB, B), (BA, A) and (AD, D) sequentially. At this time, the curve in (AD, D) is the same as the current curve AD, and it can be judged that the currently obtained The minimum enclosing contours of are AD, DC, CB and BA, namely ABCD. the

Step 9, cyclically adopt the method in step 8 to obtain all the minimum enclosing contours, and delete the contour with the largest area. Traverse each minimum enclosing contour to get its center point, and then make a straight line perpendicular to the web surface through the center point, if it does not intersect with the "Join.1" feature, then the minimum enclosing contour is the result of feature reconstruction, that is, valid The minimum enclosing contour, the resulting web driving geometry and the resulting web machining toolpath are shown in Fig. 13. the

Claims (8)

1. A method for automatically reconfiguring the geometry of an aircraft structural part groove feature web machining drive, characterized in that it comprises the following steps: Step 1. Combine all sides, sunken faces and corner faces of a groove feature, marked as JOIN.1; Step 2. According to the adjacency relationship between all faces in JOIN.1, extract its boundary, marked as: BOUNDARY.1; Step 3. Combine the web surface and the bottom corner surface of the outer ring of the web, mark it as: JOIN2; Step 4. According to the adjacency relationship between all faces in JOIN.2, extract its boundary, marked as: BOUNDARY.2; Step 5. Combine all edges in BOUNDARY.1 and BOUNDARY.2 into a whole, marked as: JOIN.3; Step 6. Filter the edges in JOIN.3 and eliminate unnecessary edges; Step 7. In the sketch environment, project the edge in the filtered JOIN.3 to the web surface, obtain the intersection point between the projected edge and the edge, and use the intersection point to break the intersecting edge. The processed result is marked as SKETCH. 1; Step 8. Based on all points and edges after projection and interruption, construct an attribute edge-point graph containing edge, point, and edge-to-point information; Step 9, calculate all the minimum enclosing contours in the attribute edge point graph, and the minimum enclosing contours are defined as a group of plane curves that are connected end to end and do not intersect with each other; Step 10. Obtain an effective minimum enclosing contour from all the minimum enclosing contours, which is the driving geometry for the final web contour machining. 2. The method for automatically reconstructing the geometry of a groove feature web of an aircraft structure as claimed in claim 1, wherein the specific steps of the step 2 are: ① Take out the JOIN.1 one by one in order ② Extract the outer ring boundary of the face; ③ Take out the edges in the outer ring boundary one by one in order; ④ Determine whether the edge belongs to the outer ring edge of other faces in JOIN.1, if so, return to step ③, otherwise, the Sidelines belong to the border of JOIN.1, which includes it in BOUNDARY.1. 3. A method for automatic geometry reconstruction driven by machining of groove feature webs of aircraft structural parts as claimed in claim 1, characterized in that, the method for screening the edges of JOIN.3 is: ① Eliminate JOIN.3 The same edge; ② Remove the straight edge perpendicular to the web surface. 4. The method for automatically reconstructing the geometry of a grooved feature web of an aircraft structure as claimed in claim 1, wherein the specific steps of step 7 are: Projection to get the projected curve; ②For the completely overlapping curves, only keep one, for the partially overlapping curves, find the overlapping part and keep only one; ③Find all the intersection points between the curves, and at each intersection point the corresponding The curve breaks into two curves, resulting in a grid-like column of curves. 5. A method for automatic geometry reconstruction driven by machining of groove feature webs of aircraft structural parts as claimed in claim 1, characterized in that, the specific steps of step 8 are: ① define the point class MyVertex, and the member variables include point The mathematical representation of the point, the topological representation of the point, and the topological edge column connected to the point; ②Define the edge class MyEdge, and the member variables include the topological representation of the edge, the feature representation of the edge, the opening and closing attribute identification of the edge, the starting point, and the ending point;③ Create a new list of MyVertex class, marked as: MYVERTEX_LIST, create a new list of MyEdge class, marked as: MYEDGE_LIST; ④ Take out the edges in SKETCH.1 one by one in order; ⑤ Create an object of MyEdge class, fill in the attributes of the current edge Enter the corresponding member variable, and list the object in MYEDGE_LIST; ⑥Take out the starting point of the current edge and mark it as STARTPOINT; judge whether STARTPOINT is a member in MYVERTEX_LIST, if so, skip to step ⑦, otherwise create a new MyVertex class object, fill in the attribute of STARTPOINT into the corresponding member and list the object in MYVERTEX_LIST; ⑦Take out the end point of the current edge and mark it as ENDPOINT; judge whether ENDPOINT is a member in MYVERTEX_LIST, if not, create a new MyVertex For the object of the class, fill in the attribute of ENDPOINT in the corresponding member variable, and list the object in MYVERTEX_LIST. 6. The method for automatically reconstructing the geometry of a groove feature web of an aircraft structural part according to claim 1, wherein the specific steps of the step 9 are: ①Choose a section of curve l _i in the attribute edge-point graph, take a vertex M _i (x ₀ , y ₀ , z ₀ ) of l _i as the current node, and mark the combination of the current curve and the current node, denoted as ( l _i , M _i ); ② Take the point M _i of the combination (l _i , M _i ) as the starting point of the curve segment, assuming that the tangent vector of the curve l _i at the point M _i is

Tangent vectors of other line segments connected to the current node M _i

③Record the outer normal direction of the web as definition The direction of rotation is So

Around the point M _i , take is the starting direction of rotation, at In the vector, the first edge corresponding to the coincident vector is the next edge of the current minimum enclosing contour line, which is denoted as l _i1 , and the other vertex of l _i1 is denoted as M _i1 , at this time, judge whether l _i1 is Same as l _i , if different, judge whether (l _i1 , M _i1 ) has been marked, if not, assign (l _i1 , M _i1 ) to (l _i , M _i ) and go to step ②; ④ Take another vertex of l _i as the current node M _i ′(x ₀ ′, y ₀ ′, z ₀ ′), judge whether (l _i , M _i ′) has been marked, if not, set (l _i , M _i ′) is assigned to (l _i , M _i ) and transferred to step ②; ⑤ Obtain all the minimum enclosing contours in the sketch; 7. The method for automatically reconfiguring the geometry of a grooved feature web of an aircraft structure as claimed in claim 6, characterized in that, judging the

in vector, with

The specific steps for the first coincident vector are: ① Take M _i as the center and make a circle with a radius of 1. The circle and

intersect at point

and

vector intersects at point $L_{\mathrm{no}}=m_i+\stackrel{\&Right\; Arrow;}{r_{\mathrm{no}}};$ ② Construct n vectors starting from L ₀ ${\stackrel{\&Right\; Arrow;}{V}}_1=L_1{-L}_0=\stackrel{\&Right\; Arrow;}{r_1}\stackrel{\&Right\; Arrow;}{-r_0},$ ${\stackrel{\&Right\; Arrow;}{V}}_2=L_1{-L}_0=\stackrel{\&Right\; Arrow;}{r_2}\stackrel{\&Right\; Arrow;}{-r_0},...,$ ${\stackrel{\&Right\; Arrow;}{V}}_{\mathrm{no}}=L_{\mathrm{no}}{-L}_0=\stackrel{\&Right\; Arrow;}{r_{\mathrm{no}}}\stackrel{\&Right\; Arrow;}{-r_0};$ ③ Then calculate separately

and

The angle between the vectors, the vector corresponding to the minimum angle is the the first coincident vector; 8. The method for automatically reconstructing geometry driven by machining of groove feature webs of aircraft structural parts as claimed in claim 1, characterized in that, the specific steps of step 10 are: ① All the minimum enclosing contours obtained can be expressed as: LOOP0, LOOP1, ..., LOOPn; ② Excluding the minimum enclosing contour LOOPi (0≤i≤n) with the largest area, the remaining minimum enclosing contours can be expressed as: LOOP0, LOOP1, ... LOOPi-1, LOOPi+1, ..., LOOPn; ③ Traverse the remaining minimum enclosing contours, calculate the center point of the current minimum enclosing contour, and make a straight line perpendicular to the web surface through the center point. If the straight line does not intersect JOIN.1, the current minimum enclosing contour is the effective minimum enclosing contour.

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