Method for fast solving shortest tool length based on aabc octree

Abstract

The present application relates to a kind of method for quickly solving shortest tool length based on AABC octree, the method first obtains the three-dimensional point cloud data of the model to be detected and all tool poses, and the corresponding relationship of each three-dimensional point cloud and tool pose is established, then the axis-aligned bounding box of the model to be detected is generated, and multiple initial directed enclosing cubes are constructed based on axis-aligned bounding box, then each tool pose is combined with each initial directed enclosing cube as binary group respectively, and the axis-aligned tool length box of each initial directed enclosing cube is constructed, and all binary groups are effectively screened to determine effective binary group.Finally, based on the upper limit value of the effective axis-aligned tool length box corresponding to effective binary group is determined as the shortest tool length of the model to be detected if preset condition screening ends, otherwise, after the subdivision of octree subdivision method to enclosing cube, new binary group is reconstructed and screened.The method can effectively improve the efficiency of shortest tool length calculation.

Description

Technical Field

[0001] This invention relates to the field of CNC machining technology, and in particular to a method for quickly solving the shortest tool length based on an AABC octree. Background Technology

[0002] In CNC multi-axis machining, especially when machining components with complex curved surfaces such as aircraft blades, excessively long cutting tools can easily cause collisions between the tool holder or machine spindle and the workpiece or fixture. This can result in damage to the tool and workpiece, or even damage to the machine tool itself. Conversely, excessively short cutting tools may be unable to machine deep cavities, steep sidewalls, or other characteristic areas. Therefore, it is essential to use the shortest possible cutting tool within safe limits to minimize the risk of interference. The shortest tool length refers to the minimum length of the tool extending beyond the chuck while ensuring that the tool and its clamping system do not interfere with the workpiece, fixture, or other machine tool components throughout the machining path. Determining the shortest tool length is a crucial step in CNC programming and process planning, directly impacting the safety, efficiency, and quality of the machining process.

[0003] In existing technologies, two methods are commonly used to determine the shortest tool length. One method is to calculate the shortest tool length for each pose individually. However, a typical multi-axis machining program contains hundreds or even thousands of tool poses. If each pose is calculated, a large number of interference checks are required, resulting in a time-consuming and inefficient task of determining the shortest tool length. The other method relies on manual experience, selecting the tool pose located at the deepest part of the channel that is most likely to ultimately determine the shortest tool length for calculation. The initially obtained shortest tool length is then updated until all tool poses are free of interference. While this method is faster than calculating each pose individually, it heavily relies on manual experience and its computational efficiency remains low. Summary of the Invention

[0004] Therefore, it is necessary to provide a method for quickly solving the shortest tool length based on the AABC octree to address the above-mentioned technical problems, which can effectively improve the calculation efficiency of the shortest tool length.

[0005] This invention provides a method for quickly solving the shortest tool length based on an AABC octree, comprising the following steps: Acquire the 3D point cloud data of the model to be detected and all tool poses, and establish the correspondence between each 3D point cloud and tool pose; Generate the axis-aligned bounding box of the model to be detected, and construct multiple initial directed bounding cubes based on the axis-aligned bounding box. The initial directed bounding cube is the nth layer directed bounding cube corresponding to the axis-aligned bounding box. Each tool pose is combined with each initial directed bounding cube into a binary pair; Construct an axis-aligned knife-length box for each initial oriented enclosing cube; Valid pairs are determined by filtering all pairs based on the tool length boxes aligned with all axes. If the number of valid pairs is 1, and the number of valid checkpoints of the valid initial directed enclosing cube in the valid pairs is 1, then the upper limit of the valid axis-aligned tool length box corresponding to the valid pairs is taken as the shortest tool length of the model to be tested; otherwise, proceed to the next step. Using the octet subdivision method, each nth layer directed bounding cube is subdivided into eight (n+1)th layer directed bounding cubes. Each effective tool pose is combined with each (n+1)th layer directed bounding cube to form a new pair. Then, the (n+1)th layer directed bounding cube is used as a new initial directed bounding cube, and the steps of constructing the axis-aligned tool length box for each initial directed bounding cube are returned.

[0006] In one embodiment, the correspondence between each 3D point cloud and the tool pose is as follows: In the formula, T Indicates the unit cutter axis, p Represents any point cloud of the model to be detected. Indicates the tip of the tool. q r and q h This represents any point cloud of the model to be detected with respect to the tool position pose. The x and y coordinates of the points after rotation and collapse mapping.

[0007] In one embodiment, multiple initial directed bounding cubes are constructed based on axis-aligned bounding boxes. Specifically, the shortest side of the axis-aligned bounding box is selected as the side length of the cube's directed bounding cube, and the other side lengths of the axis-aligned bounding box are divided into multiples of the shortest side length to construct initial directed bounding cubes. The initial directed bounding cubes completely surround the axis-aligned bounding box.

[0008] In one embodiment, each tool pose is combined with each initial directed bounding cube into a binary tuple, including the following steps: Determine the circumsphere of each initial directed bounding cube, and rotate and collapse the circumsphere to map it to a Cartesian coordinate system to obtain multiple axis-aligned bounding rectangles; Each tool pose is combined with the bounding rectangle aligned to each axis to obtain a tuple.

[0009] In one embodiment, the axis-aligned tool length box for each initial directed bounding cube is constructed by: calculating the tool lengths of the top-left and bottom-right corners of the axis-aligned bounding rectangle corresponding to each initial directed bounding cube, and determining the axis-aligned tool length box based on the coordinates of the top-left and bottom-right corners in the Cartesian coordinate system and the tool lengths.

[0010] In one embodiment, the effective binary pair is determined by filtering all pairs based on all axis-aligned tool length boxes as follows: in the Cartesian coordinate system, axis-aligned tool length boxes with the maximum ordinate value greater than the minimum shortest tool length value are selected as effective axis-aligned tool length boxes, and the binary pairs containing the effective axis-aligned tool length boxes corresponding to the initial oriented enclosing cube are selected as effective binary pairs.

[0011] The beneficial effects of this invention are: (1) This invention filters the binary pairs formed by the combination of the tool pose and the directed enclosing cube of the model to be detected by constructing an axis-aligned tool length box. After multiple iterations, a final valid binary pair can be selected. By determining the upper limit of the valid axis-aligned tool length box corresponding to the final valid binary pair, the shortest tool length of the model to be detected can be obtained. In the whole iteration process, a large number of inspection areas and tool poses that are not related to the final shortest tool length can be quickly eliminated in the early stage. The computational resources are concentrated on a few valid tool poses, which greatly shortens the computation time of the shortest tool length and improves the computational efficiency of the shortest tool length. (2) In the iterative calculation process, the present invention subdivides the nth layer of the previous iteration into eight n+1th layer directed enclosing cubes by the octet subdivision method. The generated directed enclosing cubes infinitely approximate the real geometry of the model by continuously increasing the number of subdivision layers. This not only reduces the efficiency of interference calculation but also improves the calculation accuracy of the shortest tool length. (3) By using a circumscribed sphere of the cube for conservative approximation, the present invention transforms the complex 3D boundary mapping problem into a simple sphere center coordinate transformation and two-dimensional rectangle processing, avoiding the numerical difficulty of directly calculating the intersection of complex curves. This not only greatly simplifies the calculation, but also improves the numerical stability of the screening process. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the method for quickly solving the shortest tool length based on an AABC octree provided in this embodiment of the invention. Figure 2 This is a schematic diagram of the multi-tapered THS model corresponding to the model to be detected provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the rotational collapse mapping of a certain model to be tested in the Cartesian coordinate system of a multi-tapered THS model. Figure 3(a) is a schematic diagram of the shortest tool length for a collapsed model of a certain model to be tested. Figure 3 (b) is Figure 3 (a) The check surface of the collapsed model relative to the 10th tool position ( Figure 3 (a) Schematic diagram of the region after rotation and collapse mapping (dark red line); Figure 4 A schematic diagram of AABB and AABC provided for embodiments of the present invention; Figure 5 A schematic diagram of the outer enclosing sphere of the conservative rotational mapping cube of AABC provided in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the rotational collapse mapping of the outer enclosing sphere of the AABC conservative rotational mapping cube to the Cartesian coordinate system, as provided in an embodiment of the present invention. Figure 7 This is a schematic diagram of the rotational mapping region of the circumscribed sphere of AABC provided in an embodiment of the present invention. Figure 7 (a) is a schematic diagram of the complete circle after the circumscribed sphere collapses and is mapped. Figure 7 (b) is a schematic diagram of the great circle arc after the circumscribed sphere collapses and is mapped; Figure 8 A schematic diagram of AATB provided for an embodiment of the present invention; Figure 9 This is a schematic diagram illustrating multiple effective AATB screening methods provided in an embodiment of the present invention. Figure 9 (a) is a schematic diagram of the mapping of a binary tuple to the Cartesian coordinate system. Figure 9 (b) is a schematic diagram showing the positional relationship of the axis-aligned tool length boxes of all initial AATBs in the Cartesian coordinate system. Figure 9 (c) is a schematic diagram of the remaining valid AATBs after validity screening; Figure 10 This is a schematic diagram of an open bladed disk model and tool feed provided in an embodiment of the present invention; Figure 11 The effective AABC and effective tool pose obtained by filtering with different iteration numbers are provided in the embodiments of the present invention; Figure 12 This is a schematic diagram illustrating the change of the effective checkpoint sequence number with the number of screening generations provided in this embodiment of the invention; Figure 13 This is a schematic diagram illustrating the change of the effective tool position number with the number of screening generations provided in this embodiment of the invention; Figure 14 This is a schematic diagram illustrating the result of rapidly obtaining the shortest tool length with a small number of iterations using the method of the present invention, as provided in an embodiment of the present invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0014] In one embodiment, such as Figure 1 As shown, the method for quickly solving the shortest tool length based on the AABC octree in this embodiment includes the following steps: S11. Obtain the 3D point cloud data of the model to be detected and all tool poses, and establish the correspondence between each 3D point cloud and tool pose.

[0015] In this embodiment, the tool pose is obtained from the machining program sheet. The 3D point cloud and the tool pose correspond in the two-dimensional orthogonal Cartesian coordinate system of the multi-tapered THS (tool holding system) model of the model to be detected.

[0016] like Figure 2 As shown, the specific method for establishing the multi-tapered THS model corresponding to the model to be tested includes: using the tip of the knife as the reference point. P ct With the origin of the coordinate system, the radius of the complete tool holding system (THS) is... r Shaft, axial height is h Establish a two-dimensional orthogonal Cartesian coordinate system. In this coordinate system, the profile of the tool clamping system can be characterized by a monotonically increasing taper segment. Clearly, the h-coordinate of the tool clamping system profile is a function of the tool length L; therefore, the tool clamping system profile can be denoted as... , Specifically, it is represented as follows: the coordinate distribution of the endpoints of each component line segment of THS is as follows. ,in , , , According to the above distribution, It is divided into k segments. The coordinate range of the k-th segment's contour is (R... k R k+1 The height difference is (Special, Additionally, within this segment, non-parallel h The portion of the shaft's profile is the effective part that limits the tool length, and its taper is... ,in , , Therefore, it is available Definition of the first k Profile of a segmented tool clamping system. For a known tool clamping system... , and All are constants, except for the tool length L, which is a variable. Therefore, the general model of a multi-tapered tool clamping system can be characterized as follows: .

[0017] Combination Figure 3 It can be seen that the correspondence between each 3D point cloud and the tool pose is as follows: In the formula, T Indicates the unit cutter axis, p Represents any point cloud of the model to be detected. Indicates the tip of the tool. q r and q h This represents any point cloud of the model to be detected with respect to the tool position pose. The x and y coordinates of the points after rotation and collapse mapping.

[0018] S12. Generate the axis-aligned bounding box of the model to be detected, and construct multiple initial directed bounding cubes based on the axis-aligned bounding box. The initial directed bounding cube is the nth layer directed bounding cube corresponding to the axis-aligned bounding box.

[0019] like Figure 4 As shown, in this embodiment, the main axis directions of the axis-aligned bounding box of the model to be detected are respectively , , The center of the AABB (axis-aligned bounding box) of the model to be detected is AABB along , , The side lengths in the directions are respectively , , The specific method of its establishment is well known to those in the field and will not be elaborated here.

[0020] The multiple nth layer AABBs (directed bounding cubes) corresponding to the axis-aligned bounding box perfectly enclose the model to be detected. Specifically, multiple initial directed bounding cubes are constructed based on the axis-aligned bounding box. Specifically, the shortest side of the axis-aligned bounding box is selected as the side length of the cube-shaped directed bounding cube. The other side lengths of the axis-aligned bounding box are divided into multiples of the shortest side length to construct the initial directed bounding cubes. The initial directed bounding cubes completely enclose the axis-aligned bounding box.

[0021] In this embodiment, the number is recorded as... The side length of layer AABC is The following calculation formula is: In the formula, This is the minimum side length set to prevent the initial AABC scale from being too small, such as 0.1.

[0022] S13. Combine each tool pose with each initial directed bounding cube to form a binary pair.

[0023] Specifically, each tool pose is combined with each initial directed bounding cube into a binary pair, including the following steps: S131. Determine the circumsphere of each initial directed bounding cube, and rotate and collapse the circumsphere to map it to the Cartesian coordinate system to obtain multiple axis-aligned bounding rectangles.

[0024] In 3D space, when AABC rotates and folds relative to the tool pose, all 12 linear edges are mapped to quadratic hyperbolas (the mapped image is a line segment only when the edge is coplanar with or perpendicular to the tool pose), such as... Figure 5 The 12 red curves are shown in the image. Figure 6 As shown in the light red area, these hyperbolas form the boundaries of the true 2D region of the collapsed AABC. Figure 5 and Figure 6 The red outline represents the bounding box of the shape, and the blue circle represents the boundary circle of the box. However, accurately calculating the hyperbola of the mapping is quite tedious. More importantly, further comparing the positional relationships between multiple complex boundaries involves complex intersection operations. All of this requires significant computational resources. To reduce the computational burden, we adopt a conservative strategy: using its circumsphere instead of AABC.

[0025] Specifically, this embodiment uses radius The circumscribed sphere of AABC is conservatively used to replace AABC for rotational collapse mapping relative to the tool position. The mapped 2D region is a circle with the same radius as the sphere. Furthermore, an axis-aligned bounding rectangle of the mapped circle is used instead of the mapped circle to quickly determine the conservative tool length range. Using this strategy, only the mapped coordinates of the sphere center are needed to quickly obtain the slightly "enlarged" collapsed mapping region, greatly reducing the amount of computation, and the accuracy of tool length approximation is not significantly affected compared to the loss of AABC mapping.

[0026] In fact, as Figure 7 As shown, the circumscribed sphere may collapse into a complete circle (see...). Figure 7 (a) or great arc (see Figure 7 (b)). Therefore, AABC regarding the tool position The mapped region, i.e., the circumscribing square of the mapped circle. for: .

[0027] This embodiment uses a conservative approximation with a circumscribed sphere surrounding the cube, transforming the complex 3D boundary mapping problem into a simple sphere center coordinate transformation and two-dimensional rectangle processing. This avoids the difficulty of directly calculating the numerical values ​​of complex curve intersections and effectively simplifies the calculation.

[0028] S132. Combine each tool pose with the bounding rectangle of each axis to obtain a tuple.

[0029] For the combined binary pair, the number of AABC pairs is: The number of tool poses is Together constitute A binary tuple (AABC, tool orientation).

[0030] It should be noted that if the effective binary pair screening has already been performed, due to the previous... After the second screening, some AABC pairs and some tool orientations could not form a valid binary pair, therefore satisfying... .

[0031] S14. Construct an axis-aligned knife-length box for each initial oriented bounding cube.

[0032] AATB (Axis-Aligned Tool Box) is established in Cartesian coordinates, specifically, as shown below. Figure 8 As shown, the axis-aligned tool length box for each initial directed bounding cube is constructed as follows: calculate the tool lengths of the top-left and bottom-right corners of the axis-aligned bounding rectangle corresponding to each initial directed bounding cube, and determine the axis-aligned tool length box based on the coordinates of the top-left and bottom-right corners in the Cartesian coordinate system and the tool lengths.

[0033] The tool length range of AATB can be determined by the tool lengths determined by the four corner points and the left and right extreme points of the boundary point, ultimately yielding the region of AATB in Cartesian coordinates. .

[0034] S15. Based on all axis-aligned tool length boxes, perform validity screening on all pairs to determine valid pairs.

[0035] Specifically, the validity screening of all pairs based on all axis-aligned tool length boxes is as follows: in the Cartesian coordinate system, axis-aligned tool length boxes with the largest ordinate value greater than the minimum shortest tool length value are selected as valid axis-aligned tool length boxes, and pairs containing the initial directed enclosing cube corresponding to the valid axis-aligned tool length boxes are also selected as valid pairs.

[0036] Specifically, in this embodiment, let and Then it satisfies All AATBs are valid for determining the shortest tool length, and the corresponding tuples for AATBs are also valid; all AABCs and tool poses involved in all valid tuples are also considered valid.

[0037] For example, such as Figure 9 As shown, after this [number]th After the second screening, the range of the shortest blade length was narrowed down to... Within the range, that is .exist Figure 9 Find the minimum value of all AATB, which is the bottom edge of each rectangle, and set the value of the highest bottom edge of all rectangles as the minimum value of the shortest tool length. Then filter all rectangles whose top edge height is greater than the specified value. The AATB corresponding to a large fixed edge is a valid AATB.

[0038] S16. If the number of valid pairs is 1, and the number of valid check points of the valid initial directed enclosing cube in the valid pairs is 1, then the upper limit of the valid axis-aligned tool length box corresponding to the valid pairs is taken as the shortest tool length of the model to be tested; otherwise, proceed to the next step. S17. Using the octet subdivision method, subdivide each nth layer directed bounding cube into eight n+1th layer directed bounding cubes, and combine each effective tool pose with each n+1th layer directed bounding cube to form a new tuple. Then, use the n+1th layer directed bounding cube as a new initial directed bounding cube, and return to the step of constructing the axis-aligned tool length box for each initial directed bounding cube.

[0039] By employing the octet subdivision method to process the 3D space hierarchically, the computational efficiency of interference calculation is improved, and the workload is greatly reduced.

[0040] This embodiment presents a method for quickly solving the shortest tool length based on an AABC octree. It constructs an axis-aligned tool length box to filter pairs composed of tool pose and directed enclosing cubes of the model to be detected. After multiple iterations, a final valid pair is selected. By determining the upper limit of the valid axis-aligned tool length box corresponding to the final valid pair, the shortest tool length of the model to be detected can be obtained. Throughout the iteration process, a large number of inspection regions and tool poses unrelated to the final shortest tool length can be quickly eliminated in the early stages. This concentrates computational resources on a few valid tool poses, greatly shortening the calculation time for the shortest tool length and improving its computational efficiency.

[0041] In one specific embodiment, to verify the efficiency and accuracy of the method for quickly solving the shortest tool length based on the AABC octree of the present invention, this embodiment developed a prototype software system using C++ language based on the Unigraphics V18.0 and MATLAB 2017b software platforms and the Microsoft Visual Studio 2015 integrated development environment, and applied it to an open bladed disk, a typical complex flow channel component of an aero-engine. Figure 10 As shown, the blade is approximately 160 mm long. A BR2C2 tapered ball end mill (2 mm ball radius, 2° taper) is used for finishing the pressure surface of the blade on a five-axis machine tool. To improve machining efficiency and quality, the shortest possible tool length is required to enhance tool rigidity. The calculation accuracy for the shortest tool length is 0.01 mm. The tool axis follows a constraint law of constant lead angle (18°) and tilt angle (0°) along the toolpath. Five cyan toolpaths are shown near the blade root (the cutting path width is set to a value greater than usual for ease of display). Ignoring non-cutting motion, a total of 196 non-interference tool positions are involved in the shortest tool length calculation. Two inspection surfaces are considered in this example, each containing 27 × 34 = 918 control points. The step size is set to 0.01 mm when searching the envelope curve. A schematic diagram of the iteration results is shown below. Figure 11 , Figure 12 , Figure 13 As shown.

[0042] from Figure 11 , Figure 12 and Figure 13 As can be seen from the previous iterations, the number of effective checkpoints and corresponding effective tool poses is significantly reduced. Basically, the number of effective checkpoints and effective tool poses can be limited to a very small number through the first six iterations, which shows that the method of the present invention can greatly reduce the number of tool positions for calculating the shortest tool length.

[0043] Furthermore, based on actual model examples, the experimental results obtained using this method after a relatively small number of iterations are as follows: Figure 14 As shown. From Figure 14 It can be seen that after 5 iterations, the number of effective checkpoints has decreased from 3007 to 23, and the number of effective tool positions has decreased from 196 to 15.

[0044] Statistics show that the total number of (AABC-toolposture) pairs involved in the tool length calculation is 7217, which is significantly less than the initial number of (check point, toolposture) pairs (3007 × 196 = 589372). The effective pairs account for (4 × 7217) / 589372 = 4.90% of the total number of (AABC-toolposture) pairs involved in the tool length calculation. Therefore, this method can significantly improve computational efficiency.

[0045] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for quickly solving the shortest tool length based on an AABC octree, characterized in that, Includes the following steps: Acquire the 3D point cloud data of the model to be detected and all tool poses, and establish the correspondence between each 3D point cloud and tool pose; Generate the axis-aligned bounding box of the model to be detected, and construct multiple initial directed bounding cubes based on the axis-aligned bounding box. The initial directed bounding cube is the nth layer directed bounding cube corresponding to the axis-aligned bounding box. Each tool pose is combined with each initial directed bounding cube into a binary pair; Construct an axis-aligned knife-length box for each initial oriented enclosing cube; Valid pairs are determined by filtering all pairs based on the tool length boxes aligned with all axes. If the number of valid pairs is 1, and the number of valid checkpoints of the valid initial directed enclosing cube in the valid pairs is 1, then the upper limit of the valid axis-aligned tool length box corresponding to the valid pairs is taken as the shortest tool length of the model to be tested; otherwise, proceed to the next step. The nth layer directed bounding cube is subdivided into eight (n+1)th layer directed bounding cubes using the octet subdivision method. Each effective tool pose is then combined with each (n+1)th layer directed bounding cube to form a new binary pair. The (n+1)th layer directed bounding cube is then used as a new initial directed bounding cube, and the process returns to the step of constructing the axis-aligned tool length box for each initial directed bounding cube.

2. The method for quickly solving the shortest tool length based on an AABC octree according to claim 1, characterized in that, The correspondence between each 3D point cloud and the tool pose is as follows: ， In the formula, T Indicates the unit cutter axis, p Represents any point cloud of the model to be detected. Indicates the tip of the tool. q r and q h This represents any point cloud of the model to be detected with respect to the tool position pose. The x and y coordinates of the points after rotation and collapse mapping.

3. The method for quickly solving the shortest tool length based on an AABC octree according to claim 1, characterized in that, The construction of multiple initial directed bounding cubes based on axis-aligned bounding boxes specifically involves: selecting the shortest side of the axis-aligned bounding box as the side length of the directed bounding cube, and splitting the other side lengths of the axis-aligned bounding box into integer multiples of the shortest side length to construct initial directed bounding cubes, wherein the initial directed bounding cubes completely enclose the axis-aligned bounding box.

4. The method for quickly solving the shortest tool length based on an AABC octree according to claim 3, characterized in that, The step of combining each tool pose with each initial directed bounding cube into a binary tuple includes the following steps: Determine the circumsphere of each initial directed bounding cube, and rotate and collapse the circumsphere to map it to a Cartesian coordinate system to obtain multiple axis-aligned bounding rectangles; Each tool pose is combined with the bounding rectangle aligned to each axis to obtain a tuple.

5. The method for quickly solving the shortest tool length based on an AABC octree according to claim 4, characterized in that, The construction of the axis-aligned tool length box for each initial directed bounding cube is as follows: calculate the tool lengths of the upper left and lower right corners of the axis-aligned bounding rectangle corresponding to each initial directed bounding cube, and determine the axis-aligned tool length box based on the coordinates of the upper left and lower right corners in the Cartesian coordinate system and the tool lengths.

6. The method for quickly solving the shortest tool length based on an AABC octree according to claim 5, characterized in that, The specific steps for determining valid pairs based on all axis-aligned tool length boxes are as follows: In the Cartesian coordinate system, axis-aligned tool length boxes with the largest ordinate value greater than the minimum shortest tool length value are selected as valid axis-aligned tool length boxes, and pairs containing valid axis-aligned tool length boxes corresponding to the initial oriented enclosing cube are also selected as valid pairs.

Images