CN101515168B - Method for generating ring-cutting roughing NC tool path of product triangular mesh model - Google Patents
Method for generating ring-cutting roughing NC tool path of product triangular mesh model Download PDFInfo
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- CN101515168B CN101515168B CN2009100202021A CN200910020202A CN101515168B CN 101515168 B CN101515168 B CN 101515168B CN 2009100202021 A CN2009100202021 A CN 2009100202021A CN 200910020202 A CN200910020202 A CN 200910020202A CN 101515168 B CN101515168 B CN 101515168B
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Abstract
The invention provides a method for generating a ring-cutting roughing NC tool path of a product triangular mesh model. The method is characterized in that an R<*> S-tree dynamic space index structure is used for organizing the topological neighbor relation of the product triangular mesh model; based on the dynamic space index structure, a Z-oriented enveloping surface of the product triangular mesh model is established fast; an R<*> S-tree is used for establishing the dynamic space index structure of the enveloping surface; based on the structure, the enveloping surface and a cutting plane are calculated intersection to obtain each contour loop; the directions of the contour loops are adjusted one by one to establish the topological relation of each contour loop for confirming a processing area; and isometric offset is carried out on the contour loops to obtain the ring-cutting roughing tool path. The embodiment proves that the algorithm can generate the ring-cutting roughing tool path of various product triangular mesh models, and the algorithm has strong adaptability.
Description
Technical field
The invention provides a kind of ring cutting roughing NC knife rail generating method of product triangle grid model, belong to the Computer-aided manufacturing field.
Background technology
In the product reverse-engineering, adopt equipment such as laser scanner to obtain the scattered point cloud data of product entity model surface usually, and these data are carried out triangulation generate triangle grid model, approach former solid model.Directly generate based on triangle grid model
Numerical control machining knife rail can be avoided the process of reconstruction of products C AD model and the cumulative errors of Model Reconstruction, thereby effectively improves product development efficiency and machining precision based on reverse-engineering.
The prior art literature search is found, Liu Lei etc. are at academic journal " HUST's journal " 1999,27 (2): in the scientific paper of delivering on the P10-12 " based on the layer cutting method digital control processing of profiling measurement data ", with profiling measurement data data subdivision is the triangle polyhedral model, ask friendship to obtain contour loop this triangle polyhedral model and cutting plane, determine machining area according to the topological relation between contour loop, the biasing contour loop generates ring cutting roughing NC cutter rail, the size of selected cutter in process, shape must be consistent with gauge head, seriously restricted its range of application, algorithm is poor for applicability.Liu Fen etc. are at academic journal " computer engineering and design " 2003,24 (11): in the scientific paper of delivering on the P119-12 " management of multiple entity cross section profile ring and the automatic extraction on border ", the stl file that is generated by entity is carried out layering, and obtain the contour loop of sealing, the employing binary tree is organized the topological relation between contour loop, determine machining area,, contour loop generates ring cutting roughing NC cutter rail by being setovered, this method only is applicable to solid model, can not generate correct processing cutter rail to nonocclusive triangle grid model.
In sum, method can not effectively extract its contour loop to general triangle grid model described in the existing document, and carry out corresponding topological relation and set up to realize the generation of ring cutting processing cutter track, generating ring cutting roughing NC cutter rail fast based on triangle grid model becomes the technical matters that those skilled in the art need to be resolved hurrily.
Summary of the invention
The object of the present invention is to provide a kind of ring cutting roughing NC knife rail generating method that can overcome above-mentioned defective, adaptable product triangle grid model:
A kind of ring cutting roughing NC knife rail generating method of product triangle grid model, it is characterized in that steps in sequence is: 1) improve the dynamic space index structure R*S-tree that the R*-tree obtains being suitable for the storage products triangle grid model, set up the dynamic space index structure of product triangle grid model based on this structure, improve method that R*-tree dynamic space index data structure obtains the R*S-tree specifically: with tri patch and index node MBR is that minimum area-encasing rectangle unification is expressed as four-dimensional some object (x, y, z, r), x wherein, y, z is the MBR centre coordinate, r is a MBR circumsphere radius value, by the cluster sub-clustering of tri patch set, make up product triangle grid model dynamic space index structure; 2) set up the Z of triangle grid model fast to enveloping surface based on the dynamic space index structure of product triangle grid model; 3) adopt the R*S-tree to set up the dynamic space index structure of enveloping surface, with the plane, roughing layer place perpendicular to the Z axle is the cutting plane, position relation according to cutting plane and each layer of triangle grid model space index structure node, successively search each the layer index node that intersects with the cutting plane, finally obtain the data node that intersects with the cutting plane, and then obtain and the crossing tri patch in cutting plane, with tri patch and cutting plane ask hand over obtain the intersection section after, adopt tracing that the intersection section is sorted and obtain contour loop, and adjust the contour loop direction one by one; 4) vow the hoop of adjusting contour loop according to the method for tri patch that contour loop cuts, make material to be removed all be positioned at the left side of contour loop, set up nested machining cell according to the hoop of each contour loop and the relation of inclusion between them, organize the topological relation between each contour loop to determine each machining area; 5) contour loop is equidistantly setovered generate ring cutting roughing NC cutter rail.
For realizing goal of the invention, the ring cutting roughing NC knife rail generating method of described a kind of product triangle grid model, step
2) in, in cartesian coordinate system, calculate the axial area-encasing rectangle Box of triangle grid model at xOy face inner projection, evenly outwards biasing of each limit with Box, offset or dish d is tool radius, process redundancy and machining tolerance sum, Box after the biasing is divided into The Mesh Point Battle, and mesh spacing is mismachining tolerance ε; Adopt the cutter location of each the net point correspondence in the sciagraphy computing grid, and handle in two kinds of situation: (1) cutter location exists, with the Z of cutter location to the height of height as this net point; (2) cutter location does not exist, and with the height of model bottom level as this net point, connects the enveloping surface that each net point obtains triangle grid model successively.
For realizing goal of the invention, the ring cutting roughing NC knife rail generating method of described a kind of product triangle grid model, step 2) in, the process that sciagraphy calculates cutter location is specifically: with the net point is drive point, with Z to be cutter shaft to, with cutter from eminence along by drive point and cutter shaft when the axis of determining falls, if contact, then rigidly connect the cutter location that the position of cutter when touching is this drive point correspondence with triangle grid model.
For realizing goal of the invention, the ring cutting roughing NC knife rail generating method of described a kind of product triangle grid model, in the step 4), the process of setting up of nested machining cell is specifically: each nested machining cell is by a counterclockwise contour loop, the sequence L_s of the clockwise wide ring that this counterclockwise contour loop directly comprises and the sequence L_c of the sub nested machining cell that this counterclockwise contour loop directly comprises constitute, earlier set up the nested machining cell cell of initialization for each counterclockwise contour loop, this machining cell cell only comprises a Boundary Loop of being determined by counterclockwise contour loop, set up the nested machining cell sequence of first floor L, be initially sky, make current sequence S equal the nested machining cell sequence of first floor L, the nested machining cell of the current initialization that is inserted into is cell_insert, and then the construction step of the nest relation between each Boundary Loop ring is as follows: (1): detect the relation of inclusion between the Boundary Loop of each nested machining cell among the Boundary Loop be inserted into the nested machining cell cell_insert of initialization and the current sequence S; (2): do not comprised by the Boundary Loop of any nested machining cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, directly add among the current sequence S, carry out (5) being inserted into the nested machining cell cell_insert of initialization; (3): comprise nested machining cell cell_1, cell_2 among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization ..., cell_n Boundary Loop, with nested machining cell cell_1, cell_2 ..., the sub nested machining cell that directly comprises as cell_insert of cell_n sequence L_c, and in current sequence S the deletion nested machining cell cell_1, cell_2 ..., cell_n, carry out (5); (4): comprised by the Boundary Loop of nested machining cell cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, make that current sequence S is the sequence L_c of the sub nested machining cell that directly comprises of nested machining cell cell, carry out (1); (5): nested machining cell exists if next is inserted into initialization, make that current sequence S is the nested machining cell sequence of first floor L, be inserted into the nested machining cell cell_insert of initialization and be inserted into nested machining cell for next, carry out (1), otherwise the nest relation between each Boundary Loop ring makes up and finishes, and carries out (6); (6): the nested machining cell of depth-first traversal, each up time needle ring is added in the machining cell that Boundary Loop directly comprises it, finish the foundation of the nested machining cell sequence of the contour loop that obtains, clockwise wide ring that is directly comprised by its Boundary Loop and Boundary Loop thereof of the corresponding hand of each machining cell of setting up after finishing is determined machining area.
The present invention compared with prior art has following three advantages:
(1) adopts sciagraphy to calculate the grid point height of enveloping surface, guaranteed that there is not interference in the cutter rail of follow-up generation;
(2) obtain each contour loop by setting up enveloping surface, avoided the influence of original triangle grid model intermediate gap, overlapping and hole, algorithm adaptability is strong;
(3) organize the relation of inclusion between each contour loop to determine machining area by setting up machining cell, quick and precisely realized obtaining of each machining area.
Description of drawings
Fig. 1 is a program flow diagram of the present invention;
Fig. 2 is each layer index node MBR illustraton of model of dynamic space index structure of automobile engine cover triangle grid model in the embodiment of the invention one;
Fig. 3 is the acquisition process synoptic diagram that enveloping surface of the present invention is set up net point in the process;
Fig. 4 is that cutter location calculates synoptic diagram among the present invention;
Fig. 5 is the enveloping surface that the present invention sets up;
Fig. 6 is a contour loop acquisition process synoptic diagram of the present invention;
Fig. 7 is a circular cutter rail generator program process flow diagram of the present invention;
Fig. 8 is that contour loop annular of the present invention is adjusted synoptic diagram;
Fig. 9 is the data structure and concrete application the thereof of nested machining cell among the present invention;
Figure 10 is the single layer of rings cutting knife rail that generates in the embodiment of the invention one;
Figure 11 is the ring cutting roughing NC cutter rail and the simulated effect thereof of the embodiment of the invention one;
Figure 12 is cutter rail and the simulated effect thereof that people's face portion triangle grid model generates in the embodiment of the invention two.
Embodiment
The invention will be further described below in conjunction with drawings and Examples:
Fig. 1 is the realization flow figure of the ring cutting roughing NC cutter rail generator program of triangle grid model of the present invention.Dynamic space index structure construction procedures 1 is responsible for reading in the triangle grid model data, and set up the dynamic space index structure for it, call the foundation that enveloping surface creation facilities program (CFP) 2 realizes enveloping surface based on this space index structure, calling program 1 is set up the dynamic space index structure for enveloping surface, call the dynamic space index structure that contour loop obtains program 3 depth-first traversal enveloping surfaces, cutting plane and enveloping surface are asked friendship fast, antinode sorts and obtains contour loop, call each contour loop that 4 pairs of circular cutter rail generator programs obtain and adjust and set up nested machining cell and determine machining area, the biasing contour loop generates ring cutting processing cutter rail.
Embodiment one: to generate ring cutting roughing NC cutter rail as the triangle grid model of Fig. 2 shown in a).
Fig. 2 is that the present invention calls each layer of dynamic space index structure node MBR illustraton of model that 1 pair of automobile engine cover triangle grid model of dynamic space index structure construction procedures is set up.The used triangle grid model tri patch of example quantity is 14325, the indexing parameter m=8, the M=20 that are adopted, again insert nodal point number R=6, wherein, Fig. 2 a) has shown automobile engine cover triangle grid model, Fig. 2 b) shown dynamic space index structure root node MBR, Fig. 2 c) shown second layer node MBR, Fig. 2 d) shown three-layered node point MBR leaf node MBR, Fig. 2 e) shown leaf node MBR, Fig. 2 f) shown data node MBR.This experiment shows, adopts the dynamic space index structure can accurately realize the space clustering division of triangle grid model data.
The implementation procedure of enveloping surface creation facilities program (CFP) 2: in cartesian coordinate system, calculate the bounding box Box of triangle grid model on the xOy face, each limit of outside biasing Box, offset or dish d is tool radius, process redundancy and machining tolerance sum, value is 7.0, Box is divided into The Mesh Point Battle, and mesh spacing is mismachining tolerance ε, and value is 1.0.To being tool axis, with the cutter location of each the net point correspondence in the sciagraphy computing grid, and handle in two kinds of situation: 1) cutter location exists with Z, with Z to the height of height as this net point; 2) cutter location does not exist, with the height of model bottom level as this net point.If Box has 216 * 174 net points, p
(i, j)Be arranged in the capable j row of grid model i, wherein 1≤i≤216,1≤j≤174.Connect p successively
(i, j)p
(i, j+1), p
(i, j+1)p
(i+1, j), p
(i+1, j)p
(i, j)And p
(i+1, j)p
(i, j+1), p
(i, j+1)p
(i+1, j+1), p
(i+1, j+1)p
(i+1, j), the enveloping surface of grid model is set up in 1≤i≤216,1≤j≤174 wherein.As Fig. 3 is Box and the border biasing synoptic diagram thereof of triangle grid model on the xOy face a), as Fig. 3 b) be Box grid dividing synoptic diagram; Calculate the cutter location synoptic diagram as Fig. 4 sciagraphy, cutter from eminence when the Z axle falls, as contact cutter location height when contacting with the position relation calculating of triangular plate with triangle grid model according to cutter solid surface; As Fig. 5 is the enveloping surface of being set up.
Fig. 6 is contour loop acquisition process synoptic diagram among the present invention.Fig. 6 a), Fig. 6 b) each layer index node that intersects with the cutting plane for inquiring, Fig. 6 c) the data node that intersects with the cutting plane for inquiring, Fig. 6 d) contour loop that generates after sorted for the intersection point tri patch that intersects with the cutting plane for inquiring, Fig. 6 e).
Fig. 7 is a circular cutter rail generator program process flow diagram of the present invention.The contour loop hoop is adjusted program 5 and is responsible for adjusting each contour loop hoop, is always machining area to guarantee the contour loop left side; Nested machining cell creation facilities program (CFP) 6 makes up the topological relation between each contour loop by setting up the storage organization of contour loop, determines machining area; Each contour loop is setovered and is realized the generation of ring cutting roughing NC cutter rail in 7 pairs of same machining areas of profile biasing program.
Fig. 8 adjusts synoptic diagram for contour loop annular of the present invention.Obtain a single hop intersection section place tri patch on the contour loop, with the method for this tri patch vow on the n projection cutting plane vector n ', obtain the direction vector v of intersection section according to the trend of contour loop, as vector n ' then this ring trend meets rule on the right side of direction vector v, handle otherwise contour loop is carried out inverted order, make the contour loop left side be always machining area after the adjustment.
Fig. 9 is the data structure and concrete application the thereof of the nested machining cell of the present invention.Each nested machining cell is by a counterclockwise contour loop, the sequence L_s of the clockwise wide ring that counterclockwise contour loop directly comprises and the sequence L_c of the sub nested machining cell that counterclockwise contour loop directly comprises constitute, as Fig. 9 is the synoptic diagram of nested machining cell data structure a), earlier set up the nested machining cell cell of initialization for each counterclockwise contour loop, this machining cell cell only comprises a Boundary Loop of being determined by counterclockwise contour loop, set up the nested machining cell sequence of first floor L, be initially sky, make current sequence S equal the nested machining cell sequence of first floor L, the nested machining cell of the current initialization that is inserted into is cell_insert, and then the construction step of the nest relation between each Boundary Loop ring is as follows: (1): detect the relation of inclusion between the Boundary Loop of each nested machining cell among the Boundary Loop be inserted into the nested machining cell cell_insert of initialization and the current sequence S; (2): do not comprised by the Boundary Loop of any nested machining cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, directly add among the current sequence S, carry out (5) being inserted into the nested machining cell cell_insert of initialization; (3): comprise nested machining cell cell_1, cell_2 among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization ..., cell_n Boundary Loop, with nested machining cell cell_1, cell_2 ..., the sub nested machining cell that directly comprises as cell_insert of cell_n sequence L_c, and in current sequence S the deletion nested machining cell cell_1, cell_2 ..., cell_n, carry out (5); (4): comprised by the Boundary Loop of nested machining cell cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, make that current sequence S is the sequence L_c of the sub nested machining cell that directly comprises of nested machining cell cell, carry out (1); (5): nested machining cell exists if next is inserted into initialization, make that current sequence S is the nested machining cell sequence of first floor L, be inserted into the nested machining cell cell_insert of initialization and be inserted into nested machining cell for next, carry out (1), otherwise the nest relation between each Boundary Loop ring makes up and finishes, and carries out (6); (6): the nested machining cell of depth-first traversal, each up time needle ring is added in the machining cell that Boundary Loop directly comprises it, finish the structure of the nested machining cell sequence of the contour loop that obtains.After foundation finished, each machining cell was determined machining area corresponding to a clockwise wide ring that is directly comprised by its Boundary Loop and Boundary Loop thereof.As Fig. 9 b) in the inverse time needle ring 1., 4., the up time needle ring 2., nested machining cell 3. such as Fig. 9 c), the machining area of determining is A and B.
Figure 10 is the single layer of rings cutting knife rail that generates in the embodiment of the invention one.With the border of enveloping surface be the blank border to ask hand over suitable the pointer ring that obtains to add Boundary Loop (inverse time needle ring) and set up nested machining cell and determine machining area after, each interior contour loop of biasing machining cell obtains individual layer ring cutting roughing NC cutter rail.
Figure 11 is the ring cutting roughing NC cutter rail and the simulated effect thereof of the embodiment of the invention one, and wherein Figure 11 is a ring cutting roughing NC cutter rail a), Figure 11 b) be a) the cutting simulation effect of middle cutter rail of Figure 11;
Embodiment two: to as Figure 12 a) people's face portion triangle grid model generate ring cutting roughing NC cutter rail, method is the same, the ring cutting roughing NC cutter rail of generation is as Figure 12 b) shown in, the cutting simulation effect is as Figure 12 b) shown in;
The ring cutting roughing NC knife rail generating method of other product triangle grid models is the same.
Claims (4)
1. the ring cutting roughing NC knife rail generating method of a product triangle grid model, it is characterized in that steps in sequence is: 1) improve the dynamic space index structure R*S-tree that the R*-tree obtains being suitable for the storage products triangle grid model, set up the dynamic space index structure of product triangle grid model based on this structure, improve method that R*-tree dynamic space index data structure obtains the R*S-tree specifically: with tri patch and index node MBR is that minimum area-encasing rectangle unification is expressed as four-dimensional some object (x, y, z, r), x wherein, y, z is the MBR centre coordinate, r is a MBR circumsphere radius value, by the cluster sub-clustering of tri patch set, make up product triangle grid model dynamic space index structure; 2) set up the Z of triangle grid model fast to enveloping surface based on the dynamic space index structure of product triangle grid model; 3) adopt the R*S-tree to set up the dynamic space index structure of enveloping surface, with the plane, roughing layer place perpendicular to the Z axle is the cutting plane, position relation according to cutting plane and each layer of triangle grid model space index structure node, successively search each the layer index node that intersects with the cutting plane, finally obtain the data node that intersects with the cutting plane, and then obtain and the crossing tri patch in cutting plane, with tri patch and cutting plane ask hand over obtain the intersection section after, adopt tracing that the intersection section is sorted and obtain contour loop, and adjust the contour loop direction one by one; 4) vow the hoop of adjusting contour loop according to the method for tri patch that contour loop cuts, make material to be removed all be positioned at the left side of contour loop, set up nested machining cell according to the hoop of each contour loop and the relation of inclusion between them, organize the topological relation between each contour loop to determine each machining area; 5) contour loop is equidistantly setovered generate ring cutting roughing NC cutter rail.
2. the ring cutting roughing NC knife rail generating method of product triangle grid model as claimed in claim 1, it is characterized in that: step 2) in, in cartesian coordinate system, calculate the axial area-encasing rectangle Box of triangle grid model at xOy face inner projection, evenly outwards biasing of each limit with Box, offset or dish d is tool radius, process redundancy and machining tolerance sum, Box after the biasing is divided into The Mesh Point Battle, and mesh spacing is mismachining tolerance ε; Adopt the cutter location of each the net point correspondence in the sciagraphy computing grid, and handle in two kinds of situation: (1) cutter location exists, with the Z of cutter location to the height of height as this net point; (2) cutter location does not exist, and with the height of model bottom level as this net point, connects the enveloping surface that each net point obtains triangle grid model successively.
3. the ring cutting roughing NC knife rail generating method of product triangle grid model as claimed in claim 2, it is characterized in that: step 2) in, the process that sciagraphy calculates cutter location is specifically: with the net point is drive point, with Z to be cutter shaft to, with cutter from eminence along by drive point and cutter shaft when the axis of determining falls, if contact, then rigidly connect the cutter location that the position of cutter when touching is this drive point correspondence with triangle grid model.
4. the ring cutting roughing NC knife rail generating method of product triangle grid model as claimed in claim 1, it is characterized in that: in the step 4), the process of setting up of nested machining cell is specifically: each nested machining cell is by a counterclockwise contour loop, the sequence L_s of the clockwise wide ring that this counterclockwise contour loop directly comprises and the sequence L_c of the sub nested machining cell that this counterclockwise contour loop directly comprises constitute, earlier set up the nested machining cell cell of initialization for each counterclockwise contour loop, this machining cell cell only comprises a Boundary Loop of being determined by counterclockwise contour loop, set up the nested machining cell sequence of first floor L, be initially sky, make current sequence S equal the nested machining cell sequence of first floor L, the nested machining cell of the current initialization that is inserted into is cell_insert, and then the construction step of the nest relation between each Boundary Loop ring is as follows: (1): detect the relation of inclusion between the Boundary Loop of each nested machining cell among the Boundary Loop be inserted into the nested machining cell cell_insert of initialization and the current sequence S; (2): do not comprised by the Boundary Loop of any nested machining cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, directly add among the current sequence S, carry out (5) being inserted into the nested machining cell cell_insert of initialization; (3): comprise nested machining cell cell_1, cell_2 among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization ..., cell_n Boundary Loop, with nested machining cell cell_1, cell_2 ..., the sub nested machining cell that directly comprises as cell_insert of cell_n sequence L_c, and in current sequence S the deletion nested machining cell cell_1, cell_2 ..., cell_n, carry out (5); (4): comprised by the Boundary Loop of nested machining cell cell among the current sequence S if be inserted into the Boundary Loop of the nested machining cell cell_insert of initialization, make that current sequence S is the sequence Lc of the sub nested machining cell that directly comprises of nested machining cell cell, carry out (1); (5): nested machining cell exists if next is inserted into initialization, make that current sequence S is the nested machining cell sequence of first floor L, be inserted into the nested machining cell cell_insert of initialization and be inserted into nested machining cell for next, carry out (1), otherwise the nest relation between each Boundary Loop ring makes up and finishes, and carries out (6); (6): the nested machining cell of depth-first traversal, each up time needle ring is added in the machining cell that Boundary Loop directly comprises it, finish the foundation of the nested machining cell sequence of the contour loop that obtains, each machining cell of setting up after finishing is determined machining area corresponding to a clockwise wide ring that is directly comprised by its Boundary Loop and Boundary Loop thereof.
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| CN101738982B (en) * | 2009-12-10 | 2012-01-04 | 沈阳飞机工业（集团）有限公司 | Airplane complex construction member roughing unit automatic building method |
| CN101763048B (en) * | 2009-12-22 | 2012-01-04 | 沈阳飞机工业（集团）有限公司 | Method for selecting roughing tool for aircraft complex component based on Voronoi Mountain variation |
| CN101957609B (en) * | 2010-08-11 | 2012-12-19 | 北京数码大方科技有限公司 | C-axis code generation method and device for multiple-section characteristic processing |
| CN101937209B (en) * | 2010-08-13 | 2013-04-24 | 北京数码大方科技股份有限公司 | Method and device for performing multi-section characteristic processing and generating four-axis codes |
| CN103513607B (en) * | 2013-09-22 | 2016-02-10 | 沈阳飞机工业（集团）有限公司 | Based on 2.5 axle collar cutting knife rail generating methods of mathematical morphology |
| CN106325211B (en) * | 2016-11-16 | 2019-01-04 | 清华大学 | A kind of material removal algorithm based on STL model intersection ring |
| CN108268009B (en) * | 2016-12-29 | 2020-10-27 | 华中科技大学 | Method, device and system for determining knife contact |
| CN114115117B (en) * | 2022-01-24 | 2022-06-03 | 广州中望龙腾软件股份有限公司 | Tool path generation method and system with normal machining allowance |
| CN116740317B (en) * | 2023-08-14 | 2023-11-03 | 济南邦德激光股份有限公司 | Three-dimensional simulation visual display method and device for laser numerical control |
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