Shaft part feature recognition method

Abstract

A shaft part feature recognition method comprises the steps that after a part model is analyzed and stitched edges are removed, a face-edge relation is established, and thread lines are recognized and removed; creating an inner and outer ring set and a seed ring combination set to judge the concavity and convexity of the edge; and finally, constructing a feature matrix and an attribute adjacency graph, and performing parameter extraction on identified features. According to the method, the topological relation between the geometric features is constructed, more accurate feature recognition is carried out on the shaft parts, and the application range of feature recognition is expanded.

Description

Technical Field

[0001] The present invention relates to a technology in the field of computer-aided design, specifically a method for identifying the features of shaft parts applied in the fields of CAD / CAM, numerical control machining and three-dimensional visualization. Background Art

[0002] Shaft parts have complex structures and high precision requirements in mechanical manufacturing, and their geometric feature recognition faces challenges. Current methods mostly rely on 3D CAD models, which makes it difficult to accurately identify complex features such as multiple steps and threads. Although topological relationship analysis improves recognition, there are still problems when dealing with complex structures, especially in the recognition of stitched edges and the determination of face-edge association.

[0003] The existing part feature recognition technologies mainly include: ① Analyzing the three-dimensional model and identifying the feature types through deep learning algorithms. Its advantages lie in its efficient learning ability and strong generalization ability, but this method requires a large amount of sample data. At the same time, the implementation and tuning process of the algorithm is relatively complex, which increases the difficulty of application. ② Methods based on boundary matching and volume decomposition, but for the feature recognition methods of shaft parts, there are still problems such as insufficient attribute adjacency graph topology information, insufficient feature decomposition, and low feature recognition accuracy. Summary of the invention

[0004] In view of the problems of low recognition accuracy and low efficiency in the prior art when processing complex geometric shapes, the present invention proposes a method for identifying the features of shaft parts, which determines the existence of stitched edges through the normal vectors of the adjacent faces of the edges, and reduces the interference of redundant edges on the attribute adjacency graph by removing the stitched edges. The method for determining the concavity and convexity of the edges is optimized, and the concavity and convexity of the edges are determined by calculating the normal vectors based on the type of the edges and the type of the adjacent faces, thereby improving the accuracy of the concavity and convexity determination. And by constructing an attribute adjacency graph through customizing the attributes of nodes and edges, and optimizing the search steps of the VF2 algorithm, the accuracy of feature recognition is improved. By constructing the topological relationship between geometric features, more accurate feature recognition of shaft parts is performed, expanding the application scope of feature recognition.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a method for identifying features of shaft parts. After parsing a part model and removing stitching edges, a face-edge relationship is established, and thread lines are identified and removed; then, an inner and outer ring set and a seed ring set are created to determine the concavity and convexity of the edge; finally, a feature matrix and an attribute adjacency graph are constructed, and parameters of the identified features are extracted.

[0007] The analysis refers to: a comprehensive geometric and topological analysis of the three-dimensional model of the part, specifically including: traversing all model faces in the three-dimensional model and all model edges on the model faces one by one: recording the geometric properties of the model edges, mapping and recording their corresponding relationship with the model faces to which they belong.

[0008] The stitching edge refers to: when the part model is analyzed, two opposite edges within the surface parameter area can be mapped to the same edge. When the surface where the edge is located is a cylindrical surface or a conical surface, and the edge only exists in one surface, the edge is determined to be a stitching edge.

[0009] The construction of the face-edge relationship specifically includes:

[0010] Step 1: Traverse all model faces of the 3D model to create a face list, traverse all model edges in the model to create an edge list, and traverse all vertices in the model to create a vertex list;

[0011] Step 2: traverse the model face list, and each time you access an unvisited model face object, obtain all model edges contained in the face, find the corresponding position index of all edges contained in the face in the edge list, add them to the edge index list in the face object, and add the index of the face in the list to the face index list of the edge;

[0012] Step 3: traverse the model edge list. Whenever an unvisited model edge object is accessed, obtain the endpoint of the model edge, add it to the point list of the edge object, and add the index of the edge to the edge index list under the point object.

[0013] The seed ring, ie the boundary of the characteristic partition, includes a single-sided seed ring and a multi-sided seed ring, wherein: the single-sided seed ring is distributed inside a single surface, and the multi-sided seed ring is distributed at the boundaries of multiple surfaces and is adjacent to multiple surfaces.

[0014] The creating of the inner ring set specifically includes:

[0015] Step a, traverse all topological faces in the part model, and for each visited face, extract the outer ring on the face;

[0016] Step b, adding the outer ring extracted from each topological surface to the outer ring set used to identify the external connection relationship between each surface and its adjacent surfaces;

[0017] Step c: further traverse all the loops in the part: each time a loop is visited, first determine whether the loop belongs to the outer loop set. If the loop does not belong to the outer loop set, then treat it as an inner loop and further determine whether it is a seed loop.

[0018] When the ring is located on a conical surface or other non-planar structure, its geometric shape and positional relationship are analyzed, and the small-diameter circular ring on the conical surface is also treated as a seed ring.

[0019] Preferably, for the thread feature, when extracting the seed ring, the starting point and the ending point of the thread are analyzed, and the seed ring with a specific pitch and thread direction is identified.

[0020] The convexity of the edge refers to determining whether the edge is a convex edge or a concave edge based on the geometric relationship between the two faces connected by the edge. Specifically, when the angle formed by the two faces intersecting at the edge is less than 180 degrees, the edge is a concave edge, otherwise it is a convex edge.

[0021] Preferably, for determining the convexity of an arc edge, the curvature direction of the arc needs to be considered: by calculating the tangent vector at the midpoint of the arc and combining the direction of the normal vector and the inner and outer ring properties of the edge to make a judgment; when the cross product of the normal vector is consistent with the tangent vector of the arc, it is a convex edge, otherwise it is a concave edge. Technical Effects The present invention optimizes the edge concavity judgment method, and judges the concavity of the edge by calculating the normal vector based on the type of edge and the type of adjacent surface. By customizing the attributes of nodes and edges, an attribute adjacency graph is constructed. This graph structure can effectively capture the complex relationship between the edge and its adjacent surfaces, thereby providing richer information for subsequent feature recognition. At the same time, the search step of the VF2 algorithm is optimized to adapt to this new graph structure. This optimization will be achieved by reducing redundant calculations and increasing matching speed; compared with the prior art, the present invention can more effectively analyze the geometric features of the edge, which can not only improve the accuracy of the edge concavity judgment, but also enhance the efficiency of the overall feature recognition. The accuracy and response time of feature recognition are significantly improved through optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the present invention;

[0023] Figure 2 A schematic diagram of a sewing edge in an embodiment;

[0024] Figure 3 Schematic diagram for calculating edge concavity;

[0025] Figure 4 This is a schematic diagram of the seed ring;

[0026] Figure 5 To obtain the flow chart of inner and outer loop sets;

[0027] Figure 6 Edge concavity and convexity judgment flow chart;

[0028] Figure 7 It is a characteristic diagram of shaft parts;

[0029] In the figure: (a) is a straight rod, (b) is a first step, (c) is a second step, (d) is a third step, (e) is a chamfer, (f) is a back cutter groove, (g) is a thread line, (h) is a V-shaped groove, (i) is a hexagonal hole at the shaft end, (j) is a wrench groove, (k) is a keyway, (l) is a retaining ring groove, and (m) is a shaft end hole;

[0030] Figure 8 is the attribute adjacency graph;

[0031] In the figure: (a) is a straight rod, (b) is a first step, (c) is a second step, (d) is a third step, (e) is a chamfer, (f) is a back cutter groove, (g) is a thread line, (h) is a V-shaped groove, (i) is a hexagonal hole at the shaft end, (j) is a wrench groove, (k) is a keyway, (l) is a retaining ring groove, and (m) is a shaft end hole;

[0032] Fig. 9 It is a schematic diagram of the effect of the embodiment;

[0033] In the figure: (a) and (b) are feature display diagrams of the three-dimensional model of the embodiment, (c) is the attribute adjacency diagram of the three-dimensional model, and (d) is the bounding box of the identification feature; DETAILED DESCRIPTION

[0034] like Figures 2 to 6 As shown, a method for identifying the feature of shaft parts involved in this embodiment includes: establishing a face edge set, identifying stitched edges, determining concavity and convexity, extracting seed rings, identifying features, and extracting feature parameters, wherein: the concavity and convexity determination is connected with the seed ring extraction and transmits the concavity and convexity of the edge and accurately identifies the feature boundary, and the seed ring extraction part transmits the result to the feature recognition part to help accurately locate the feature boundary and feature area to ensure the accuracy of feature recognition. The feature recognition unit is the core step of the method, and the identified features are further transmitted to the feature parameter extraction step for extracting the geometric parameters of the features.

[0035] like Figure 1 As shown, this embodiment is based on the above-mentioned shaft part feature recognition method. This embodiment is implemented using Python language and the Python interface Python OCC of the open source 3D CAD model Open Cascade, which specifically includes:

[0036] Step 1: Read the 3D model of the part in STEP format, parse the data in the STEP file through Python OCC, and load the parsed file content containing geometric information into the TopoDS_Shape object.

[0037] Step 2: Identify the stitching edge, including:

[0038] 2.1 Create a seam_edge list to store the seam edges.

[0039] 2.2 In the process of traversing the edges of the three-dimensional model, each time a model edge is accessed, the angle between the two faces connected by each edge is calculated. Specifically, the midpoint p0 of the model edge is obtained, and two normal vectors v1 and v2 belonging to the faces connected by the model edge at point p0 are constructed through this point, and the angle between the two faces is calculated through the normal vectors.

[0040] 2.3 When the angle is equal to 180 degrees or 0 degrees and the types of the two adjacent faces are the same, the edge is determined to be a seam edge and added to seam_edge.

[0041] Step 3: Establish a set of face edges and their relationships, including:

[0042] 3.1 Create a dictionary for storing the mapping from model edges to model faces;

[0043] 3.2 Traverse all model edges of the model and determine whether the edge is in the stitched edge geometry. Add the model edges that have not been visited and are not in the stitched edge geometry to the list, and add the index value of the edge in the list as the key to the dictionary;

[0044] 3.3 Traverse all model faces of the model, add the model faces that have not been visited to the model face list, and obtain the index value of the face in the model face list, and obtain the edges contained in the face, and add the index value of the face to the value of the corresponding key.

[0045] The described traversal of all edges of the model uses the Python OCC utility class tool to extract the topological elements in the three-dimensional geometric model from the Topo DS_Shape object, extracting the various components of faces, edges, and vertices. This class extracts various topological elements from the internal structure of the Shape object by traversing the internal structure of the Shape object, and each identified element is added to the result list, which usually contains all independent elements.

[0046] Step 4: Find the seed ring: perform ring traversal on the 3D model. Whenever an unvisited ring is accessed, add it to the ring set. Traverse each model face in the face list and extract the outer ring, and add it to the outer ring set. Traverse and determine whether each ring in the ring set is in the outer ring set. If not, add it to the inner ring set. At the same time, traverse the outer ring set. If the ring belongs to the minor diameter ring of the cone surface, add it to the seed ring set, and all the rings in the inner ring are added to the seed ring set.

[0047] Step 5 determines the convexity and concavity of the edge, including:

[0048] 5.1 Determination of the concavity of a straight edge: When the edge e formed by the intersection of two adjacent faces F1 and F2 is a straight edge, the angle formed by the tangent planes of the two adjacent faces at the intersection e is α. When 0<α<π, e is a concave edge, and when π<α<2π, e is a convex edge. When the angle α=π, the concavity of the edge is determined by the way α approaches π, and α→π - When , it is judged as a convex edge, α→π + The concave and convexity of the straight line edge e is related to the direction of the outer normal vector of the intersecting plane and the straight line edge e.

[0049] like Figure 3 As shown in (a), let the outer normal vectors of the adjacent faces F1 and F2 of the straight edge e be n1 and n2. According to the right-hand screw rule, the plane with the same direction as the straight edge e is taken as the reference plane. In the figure, F2 is taken as the reference plane, and the edges in F2 form a closed loop, and the direction of the outer loop satisfies the counterclockwise rotation around the normal vector of the surface.

[0050] The direction of the straight edge vector ne is consistent with the direction of the F2 loop. Take vector n = ne × n1, and let the angle between n and n2 be θ. When |θ|<90°, the edge is a concave edge, and when |θ|>90°, the edge is a convex edge.

[0051] 5.2 Determination of the concave-convexity of the arc edge: Figure 3 As shown in (b), let the cylindrical surface be F1, the plane be F2, and the external normal vectors of F1 and F2 be n1 and n2 respectively. When the arc edge e is an outer loop, take the midpoint p of the arc edge, ne is the tangent vector of the arc edge e at point p, and its direction is consistent with the direction of the loop. Let vector n = ne × n2, and the angle between n and n1 be θ. When |θ|<90°, the edge is a concave edge, and when |θ|>90°, the edge is a convex edge. When the arc edge e is an inner loop, the tangent vector ne′ at point p is in the opposite direction to ne, n′=ne′×n2′, and the subsequent judgment method is the same as before.

[0052] Step 6: Feature recognition, including:

[0053] 6.1 Based on the extracted topological structure and defined attributes, construct the feature matrix and attribute adjacency graph of the 3D model, including:

[0054] Construction of feature matrix:

[0055] ①Construct an n-order 0 matrix, where n is the number of faces in the three-dimensional model.

[0056] ② Through the face-edge relationship, determine whether there is a common edge between each two faces, and the attributes of the common edge. If there is, add the attributes corresponding to the common edge at the corresponding (i, j) and (j, i) in the matrix. Among them, i and j represent the index values ​​of the two faces with common edges in the face set.

[0057] Construction of attribute adjacency graph:

[0058] ①Construct nodes, create a node for each face in the model, and attach the geometric and topological properties of the node to the node.

[0059] ② Perform edge construction and create an edge in the graph and its attributes for each edge connecting two faces in the model.

[0060] The attributes of the edge include the topological relationship between the two faces, such as the convexity and concavity of the edge and the connection type.

[0061] ③ Connect adjacent face nodes in the graph to indicate their actual connection in the three-dimensional model. Each pair of adjacent faces is connected by an edge.

[0062] 6.2 Build feature library: Establish a feature library, construct the attribute adjacency graph of the shaft part features that need to be identified, and put the geometric features and their attribute adjacency graphs into the feature library. These features are usually abstracted and simplified standard geometric shapes, which are used to match and identify similar features in the actual part model.

[0063] 6.3 Use the VF2 algorithm for subgraph matching: Use the GraphMatcher method in networkx to check whether the two passed graphs match in a topology-first manner to ensure that the two graph structures remain consistent. Once a possible identical structure is found, check the node and edge attributes to see if the matching conditions are met.

[0064] The VF2 algorithm sets the part attribute adjacency graph as the target graph G p , set the attribute adjacency graph of the feature to be identified to G t , initialize the mapping: M p and M t , used to record the matched nodes in the current pattern graph and the target graph. Start matching the nodes in the two graphs and check the consistency of the edges connecting the nodes. If a matching node is found, add it to the matching set and continue matching the next node. Until the pattern graph G is found t All nodes are connected to G p If the nodes in match, it is determined that the part has this feature.

[0065] Step 7 Parameter extraction: Extract the identified features and establish a bounding box for them. The established bounding box will completely surround the features as tightly as possible, and at the same time, extract parameters from the bounding box. Depending on the type of feature, the type of extracted parameters is also different. In this embodiment, the width of the bounding box of the wrench slot will be extracted, and the length and width of the bounding box of the hole will be extracted for diameter measurement, and the height is used for hole depth measurement.

[0066] After specific practical experiments, the above method was used to identify a three-dimensional model of a carbide punch part with shaft end hole and keyway features, and the specific features contained therein could be identified, as well as the parameters of each feature could be extracted.

[0067] like Figure 7 As shown, the features of the shaft parts involved in this embodiment include: straight rod shape, a basic shape of shaft parts, usually a simple cylinder, but may include specific surface treatments or geometric features to meet specific design requirements. Straight rod shape: a basic shape of shaft parts, usually a simple cylinder, but may include specific surface treatments or geometric features to meet specific design requirements. Steps (primary, secondary, tertiary), transition areas between parts of different diameters in shaft parts, usually used for segmented installation or segmented transmission. These steps usually require precise processing and positioning. Chamfers, small-angle cutting treatments performed on the edge of the shaft or the corner of the step, are used to reduce stress concentration, facilitate installation, and improve the durability of parts. Chamfers usually have fixed angle requirements. The tool retractor, also known as the chip retractor or groove, is usually located at the end of the thread or on the cylindrical surface to provide a tool retracting space to avoid damaging the thread or surface when processing the end. Threads, parts used for connection or fixing, include external threads and internal threads. Threads usually have strict precision requirements. Keyway, a groove feature on shaft parts, is used to install keys to transmit torque. This feature requires high-precision machining and positioning. Center hole: Located at both ends of the shaft, it is usually used for positioning and support during manufacturing and assembly. The machining accuracy of the center hole directly affects the coaxiality of the shaft. Tapered step. Hexagonal hole, usually used to cooperate with hexagonal tools for easy assembly or disassembly. The machining of hexagonal holes requires high precision to ensure a tight fit with the tool. V-groove, usually used for positioning or guiding. In shaft parts, V-groove can be used for specific assembly requirements or for accurate positioning in the process. Set screw groove is a groove machined on the surface of the shaft, used to install set screws to ensure that the assembled parts are fixed on the shaft and prevent rotation. Wrench groove: A plane or groove usually machined at the end or middle of the shaft, used for fixing or adjusting with a wrench. This feature is common in shaft parts that need to be frequently disassembled and assembled. Circlip grooves are similar to retaining ring grooves, but are used to install circlips (elastic rings). Circlip grooves usually have precise depth and width requirements to ensure the correct installation and function of the circlips. Cam avoidance grooves are used to avoid or accommodate the movement path of the cam to avoid interference. This groove feature is very common in complex mechanical systems. Wrench grooves are usually flat surfaces or grooves machined at the end or middle of the shaft, which are used for fixing or adjusting with a wrench. This feature is common in shaft parts that need to be frequently disassembled and assembled.

[0068] The bounding box is a minimum rectangular parallelepiped that contains the features to be extracted and has any direction relative to the coordinate axis. The bounding box surrounds the object as tightly as possible, so that the data to be measured is more accurate.

[0069] The subgraph matching is to find a subset in a larger target graph that is isomorphic to the pattern graph. Specifically, subgraph matching is to find a node-to-node mapping so that all nodes and edges in the pattern graph can be matched with a portion of nodes and edges in the target graph.

[0070] like Figure 7 As shown, the corresponding Figure 8 The attribute adjacency graph of the features in the figure, and the corresponding parameter list extracted includes: straight rod: length, diameter;

[0071] First step: diameter, length;

[0072] Second step: diameter, length;

[0073] Three steps: diameter, length;

[0074] Chamfer: major diameter, minor diameter;

[0075] Undercut groove: arc diameter and axial distance;

[0076] Thread line: major and minor diameters, direction of rotation, and pitch of the thread;

[0077] V-groove: groove diameter;

[0078] Hexagonal hole at the shaft end: hole depth, hexagonal side length;

[0079] Wrench slot: slot width;

[0080] Keyway: length, width, depth;

[0081] Circlip groove: groove diameter, groove width;

[0082] Shaft end hole: hole diameter, hole depth;

[0083] The above features were successfully identified and parameters were successfully extracted. The following are two identification experiment results:

[0084] Identify the keyway-hole type punch, accurately identify its wrench slot and pore features, and obtain its parameter list. The results are shown in Table 1: Unit: mm

[0085] Identify the step type of the positioning pin, accurately identify its step and hole features, and obtain its parameter list. The results are shown in Table 2: Unit: mm

[0086] like Fig. 9 As shown, the specific technical information disclosed is: the attribute adjacency graph of the part model and the bounding box model made for the feature, and the feature type and feature parameters are identified at the same time.

[0087] Compared with the existing technology, this method ensures the accuracy of feature recognition by identifying and removing stitched edges. The algorithm can effectively distinguish between actual edges and stitched edges, avoiding recognition errors caused by stitched edges. By constructing the topological relationship of face edges, the accurate description of part geometric features is achieved. By defining new face, edge, and point classes and constructing the corresponding relationship between them according to the structure of the actual parts, the accurate extraction and determination of complex structural features are ensured by extracting the model seed ring. On the basis of the traditional convexity determination method, the convexity of the edge in the shaft part is determined by the adjacent face normal vector analysis method, and the convexity of the edge is discussed according to the type of edge and the type of adjacent face, thereby improving the accuracy of feature recognition. By constructing a bounding box to obtain various parameters of the feature, and performing subgraph matching on the attribute adjacency graph of the identified part and the feature adjacency graph in the feature library to determine whether the part has the feature.

[0088] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for identifying features of shaft parts, characterized in that: After parsing the part model and removing the stitching edges, the face-edge relationship is established, and the thread lines are identified and removed. Then, the inner and outer ring sets and the seed ring collection are created to determine the convexity of the edges. Finally, the feature matrix and attribute adjacency graph are constructed and parameters of the identified features are extracted.

2. The method for identifying features of shaft parts according to claim 1, characterized in that: The analysis refers to: a comprehensive geometric and topological analysis of the three-dimensional model of the part, specifically including: traversing all model faces in the three-dimensional model and all model edges on the model faces one by one: recording the geometric properties of the model edges, mapping and recording their corresponding relationship with the model faces to which they belong.

3. The method for identifying features of shaft parts according to claim 1, characterized in that: The stitching edge refers to: when the part model is parsed, two opposite edges within the surface parameter area are mapped to the same edge. When the surface where the edge is located is a cylindrical surface or a conical surface, and the edge only exists in one surface, the edge is determined to be a stitching edge.

4. The method for identifying features of shaft parts according to claim 1, characterized in that: The construction of the face-edge relationship specifically includes: Step 1: Traverse all model faces of the 3D model to create a face list, traverse all model edges in the model to create an edge list, and traverse all vertices in the model to create a vertex list; Step 2: traverse the model face list, and each time you access an unvisited model face object, obtain all model edges contained in the face, find the corresponding position index of all edges contained in the face in the edge list, add them to the edge index list in the face object, and add the index of the face in the list to the face index list of the edge; Step 3: traverse the model edge list. Whenever an unvisited model edge object is accessed, obtain the endpoint of the model edge, add it to the point list of the edge object, and add the index of the edge to the edge index list under the point object.

5. The method for identifying features of shaft parts according to claim 1, characterized in that: The seed ring, ie the boundary of the characteristic partition, includes a single-sided seed ring and a multi-sided seed ring, wherein: the single-sided seed ring is distributed inside a single surface, and the multi-sided seed ring is distributed at the boundaries of multiple surfaces and is adjacent to multiple surfaces.

6. The method for identifying features of shaft parts according to claim 1, characterized in that: The creating of the inner ring set specifically includes: Step a, traverse all topological faces in the part model, and for each visited face, extract the outer ring on the face; Step b, adding the outer ring extracted from each topological surface to the outer ring set used to identify the external connection relationship between each surface and its adjacent surfaces; Step c: further traverse all the loops in the part: each time a loop is accessed, first determine whether the loop belongs to the outer loop set; if the loop does not belong to the outer loop set, treat it as an inner loop and further determine whether it is a seed loop.

7. The method for identifying features of shaft parts according to claim 6, characterized in that: When the ring is located on a conical surface or other non-planar structure, its geometric shape and positional relationship are analyzed, and the small-diameter circular ring on the conical surface is also treated as a seed ring.

8. The method for identifying features of shaft parts according to claim 6, characterized in that: For thread features, when extracting seed rings, the start and end points of the threads are analyzed, and seed rings with specific pitches and thread directions are identified.

9. The method for identifying features of shaft parts according to claim 1, characterized in that: The convexity of the edge refers to determining whether the edge is a convex edge or a concave edge based on the geometric relationship between the two faces connected by the edge. Specifically, when the angle formed by the two faces intersecting at the edge is less than 180 degrees, the edge is a concave edge, otherwise it is a convex edge.

10. The method for identifying features of shaft parts according to claim 9, characterized in that: To determine the convexity of an arc edge, the curvature of the arc must be considered: the tangent vector is calculated at the midpoint of the arc, and the judgment is made based on the direction of the normal vector and the inner and outer ring properties of the edge. When the cross product of the normal vector is consistent with the tangent vector of the arc, it is a convex edge, otherwise it is a concave edge.

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