A tooth preparation trajectory segmentation and sorting method based on comprehensive priority index

Abstract

This invention discloses a method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index, belonging to the field of medical robot-assisted preparation technology. The method first imports the coordinate data of the knife contact points of the theoretical tooth preparation trajectory; calculates the complexity of each knife contact point, which integrates the normalized angular distance ratio and curvature; determines whether the length of the preparation region formed by adjacent knife contact points exceeds a set threshold, and automatically segments and interpolates unqualified regions to ensure that the length of each trajectory segment is uniform and stable; calculates the comprehensive priority index of each preparation region, which integrates the difference between region length and complexity; divides the regions into different priority groups according to the comprehensive priority, achieving cross-group sorting of "difficult first, easy later"; within the same priority group, optimizes the execution order based on the principle of minimum spatial distance. This invention effectively improves the accuracy, efficiency, and motion stability of tooth preparation through multi-index collaborative optimization and a two-layer sorting strategy, and is applicable to various tooth restoration scenarios.

Description

Technical Field

[0001] This invention relates to the field of dental restoration and medical robot-assisted preparation technology, specifically to a method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index. Background Technology

[0002] In traditional tooth preparation, dentists primarily rely on manual manipulation to cut and shape the tooth. However, due to the complexity of tooth morphology, the preparation trajectory often involves abrupt changes in curvature or sharp angles, making it difficult to maintain consistent cutting during manual operation. Complex three-dimensional preparation paths require repeated adjustments of angles and force, resulting in long operation times and high workload. Furthermore, the lack of systematic optimization of cutting force and trajectory execution order during manual preparation affects the fit of the restoration. With the rise of digital dentistry and robot-assisted surgery, researchers have proposed optimizing the preparation process using theoretical trajectory data and algorithmic planning. Existing methods often focus on single indicators, neglecting the coupling constraints between different indicators, leading to unreasonable path segmentation, excessive local segment lengths, and poor cutting stability. The execution order lacks scientific rigor, with frequent region switching, reducing overall efficiency. Insufficient comprehensive consideration makes it difficult to balance accuracy and efficiency. Therefore, there is an urgent need to propose a trajectory optimization method oriented towards multi-indicator constraints to achieve automation, rationalization, and efficiency in the tooth preparation process. Summary of the Invention

[0003] To address the above problems, this invention proposes a method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index. The method's specific implementation process is as follows:

[0004] Step 1: Import theoretical trajectory data for tooth preparation:

[0005] Input theoretical preliminary trajectory curve Information set of coordinate values ​​of each tool contact point in the base coordinate system , To prepare the coordinates of the i-th tool contact point in the theoretical trajectory in the base coordinate system, where, To prepare the theoretical trajectory, the x-axis coordinates of the i-th tool contact point in the base coordinate system are... To prepare the theoretical trajectory, the y-axis coordinates of the i-th tool contact point in the base coordinate system are... The coordinates of the i-th tool contact point in the base coordinate system are prepared for the theoretical trajectory. Axis coordinates;

[0006] Step 2: Calculate the complexity of the tool contact point:

[0007] a) Define the tool contact preparation complexity. Tool contact preparation complexity is a comprehensive quantitative description of the difficulty of preparation, expressed using symbols. The complexity of the tool contact is expressed as: ,in, Indicates the first Normalized angular distance ratio of each tool contact point; specified , Indicates the first The tool contact angle ratio is a quantitative description of the preparation complexity of a single tool contact; it specifies... , For the tool contact point acting on the pre-planned trajectory The preparatory angle at the location, The distance between two adjacent knife contact points, i.e., the distance between the knife contact points. and The length of the straight line segment between them. To determine the minimum value of the angle distance ratio of the pre-curved tool contact point, To determine the maximum value of the angle distance ratio of the pre-curved knife contact point; Indicates the preliminary curve. Normalized cutter contact curvature of each cutter contact point, specified , Indicates the preliminary curve. The curvature of each blade contact point To determine the minimum curvature of the pre-existing curve, This is the maximum value of the curvature of the pre-set curve;

[0008] b) Calculate the complexity of each tool contact and determine whether the complexity of all tool contacts has been calculated.

[0009] Specifically:

[0010] like Established, Order Jump to step two (a)).

[0011] like If this does not work, proceed to step three.

[0012] Step 3: Determine if the length of a single preparatory region exceeds the length threshold:

[0013] Define the length of the preparation area, the distance between adjacent tool contacts, using the symbol... The length of the preparatory region is expressed as: ;

[0014] a) Set the threshold for the length of the preparatory region to... ;

[0015] Determine whether the length of the preparation region exceeds the preparation length threshold.

[0016] Specifically:

[0017] like If successful, the length of the preparation area is qualified, and proceed to step three (b).

[0018] like If this is not the case, the length of the preparatory area is not up to standard, and the area needs to be further divided. Proceed to step 3b).

[0019] b) Determine whether the complexity range of all tool contacts has been evaluated.

[0020] Specifically:

[0021] like If true, it means that the lengths of all preparation areas have not yet been evaluated. Jump to step 3a);

[0022] like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step four.

[0023] Step 4: Divide and interpolate the length of the unqualified preparatory region:

[0024] a) Calculate the number of points that need to be inserted in a single unqualified preparatory region, expressed as: This ensures that the length of each segment after re-division does not exceed [a certain value]. Define interpolation parameters, which are the location parameters of interpolation points within a single non-compliant preparatory region, using symbols. The interpolation parameters are expressed as follows: ,in ; Calculate the coordinates of the interpolation points, which can be obtained from the formula. The calculation shows that m new preparatory regions are formed after the interpolation is completed;

[0025] b) Determine whether the interpolation of all tool contacts is complete.

[0026] Specifically:

[0027] like If true, it means that not all unqualified preparatory areas have been interpolated. Proceed to step four a);

[0028] like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step five;

[0029] Step 5: Calculation of Comprehensive Priority Indicators for the Preparatory Area:

[0030] Define a comprehensive priority index, which is a quantitative indicator of the preparatory priority for the preparatory area, using the symbol... The overall priority indicator is expressed as follows: ,in, This is the length weighting coefficient. The complexity weighting coefficient is defined as follows: The length normalization index is expressed as: ,in, The maximum value of the global reserve region length; the complexity normalization index is defined as follows: ,in, Let the difference in complexity between the two ends of the preparatory region of segment j be the value of the complexity of the knife contact points. These represent the global maximum and minimum complexity, respectively; calculate the comprehensive priority index for all preparatory regions;

[0031] Step 6: Determine if all preparation areas belong to the same priority group:

[0032] a) Determine whether the two reserve areas belong to the same priority group.

[0033] Specifically:

[0034] like If it is true, then it is considered and If they belong to the same priority group, proceed to step six (b).

[0035] like If it is not true, then it is considered and If they do not belong to the same priority group, proceed to step six (b).

[0036] b) Determine whether all preparatory areas have been evaluated.

[0037] Specifically:

[0038] like If it is established, it means that all the preparatory areas have not yet been evaluated, and therefore... Proceed to step six a);

[0039] like If the condition is not met, it means the assessment of the prepared area is complete, and proceed to step six (c).

[0040] c) Rearrange the different priority groups according to the comprehensive priority index from largest to smallest to obtain the group sequence. To obtain the execution order between groups;

[0041] Step 7: Optimize the intra-group preparation order based on distance:

[0042] When determining the processing order within the same priority group, a spatial distance factor is introduced for judgment: the endpoint of the previous preparatory area is used as the reference starting point, and the starting point of the next preparatory area is used as the target endpoint. Among the unprocessed areas, the area with the smallest spatial distance from the current position is selected as the priority processing object, until all areas in the priority group have been processed.

[0043] Specifically:

[0044] a) When executing priority group When the w-th preparation area is reached, the positional distance between the current preparation area and the unexecuted preparation areas in the same priority group is calculated, and the preparation area with the smallest positional distance in the group is selected as the next preparation area.

[0045] b) Determine the priority group Has the sorting of the s preparatory regions in the data been completed?

[0046] Specifically as follows:

[0047] like If established, then the priority group The sorting was not completed, so Proceed to step seven a);

[0048] like If not, then the priority group Once the sorting is complete, proceed to step seven (c).

[0049] c) Determine whether all s priority groups have been sorted.

[0050] Specifically as follows:

[0051] like If true, then the sorting of the s priority groups is incomplete. Let Proceed to step seven a);

[0052] like If the condition is not met, then the sorting of all s priority groups is completed, and the sorting of the preparatory area is finished.

[0053] The beneficial effects of this invention are as follows:

[0054] 1. This invention breaks through the limitations of relying on a single index in traditional tooth preparation trajectory optimization. It innovatively incorporates multiple factors such as trajectory length, tool contact complexity, and spatial distribution into a unified framework for collaborative optimization. By establishing a comprehensive priority quantitative index with length and complexity as weighting factors, the system can accurately evaluate and rank each preparation area. This method fully considers the coupling effect between different indices, avoiding the problem of unreasonable trajectories caused by one-sided optimization. For example, overemphasizing complexity may ignore the risk of length exceeding the limit, or optimizing only the length may not be able to cope with the challenges of geometrically abrupt regions. This multi-index collaborative optimization mechanism makes the trajectory planning process more comprehensive and scientific, and can adapt to complex and ever-changing tooth morphology and clinical needs, providing a solid theoretical basis and algorithmic support for high-precision tooth preparation.

[0055] 2. This invention addresses the problems of unstable cutting and decreased accuracy caused by excessive length of local segments in traditional trajectories by proposing an intelligent segmentation and interpolation method based on length thresholds. The system automatically detects preparatory areas where the distance between adjacent tool contact points exceeds a set threshold, and accurately calculates the number and coordinates of points to be inserted according to the interpolation formula, ensuring that the length of each segmented trajectory meets the constraints. This process not only eliminates motion discontinuity and vibration caused by uneven trajectory dispersion, but also significantly improves the fitting accuracy and cutting smoothness of the trajectory in geometrically complex parts by increasing the density of tool contact points in key areas. In addition, this method effectively avoids problems such as uneven tool load and material removal rate fluctuations caused by excessively long single-segment trajectories, thereby ensuring the stable operation and forming quality of the entire preparatory process. It is especially suitable for scenarios such as edge line preparatory and cavity forming with extremely high precision requirements.

[0056] 3. This invention proposes a two-layer optimization sorting strategy based on comprehensive priority and shortest spatial distance between groups, achieving global optimization of trajectory execution order. At the macro level, the system divides the preparation area into different priority groups according to the comprehensive priority index, ensuring that high-complexity and high-risk areas are processed first, which conforms to the intelligent machining principle of starting with the difficult and then moving to the easy. At the micro level, spatial distance factors are introduced within the same priority group, and the execution order within the group is determined according to the nearest neighbor principle, which greatly reduces the idle movement and trajectory jumps of the robotic arm between different areas. This two-layer optimization mechanism effectively shortens the total tool path length and total preparation time, reduces system energy consumption and mechanical wear, and further improves the smoothness of robot motion and trajectory tracking accuracy by reducing frequent starts, stops and direction switching, thus achieving a dual improvement in efficiency and quality overall.

[0057] 4. Compared with the invention patent "A Robot Tooth Preparation Trajectory Control Method Based on Dual Compensation of Tilt Vector and Curvature Vector" filed on the same day by the inventor, although both methods are used for robot tooth preparation trajectory control and optimization with high precision requirements, the method mentioned in "A Robot Tooth Preparation Trajectory Control Method Based on Dual Compensation of Tilt Vector and Curvature Vector" is based on the premise that dynamic factors in the actual cutting process lead to the accumulation of trajectory deviation and lack of trend prediction. Therefore, the trajectory features are extracted by calculating the tilt vector and curvature vector of the actual tool contact point, and then the actual tool contact point is compensated for convergence and trend with dual forward-looking compensation. This method is based on the complexity of tooth morphology and the existence of multi-index coupling constraints, which leads to the lack of scientific execution order. Therefore, the preparation area is divided by calculating the complexity of the tool contact point and the length of the preparation area, and then the execution order of the area is determined according to the comprehensive priority index. The two methods are applied to different categories of control dimensions and operation stages when optimizing robot tooth preparation trajectories. Therefore, the proposed method and the other method compensate for each other, thereby improving a series of methods for intelligent control and optimization of robot automated tooth preparation trajectories. Attached Figure Description

[0058] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0059] Figure 1 This is a method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index;

[0060] Figure 2 This is a schematic diagram of an implementation example 1 of a tooth preparation trajectory segmentation and sorting method based on a comprehensive priority index;

[0061] Figure 3 This is a schematic diagram of an implementation example 2 of a tooth preparation trajectory segmentation and sorting method based on a comprehensive priority index;

[0062] Figure 4 Prepare an experimental platform for the dental structure;

[0063] Figure 5 The preliminary results are presented for a tooth preparation trajectory segmentation and sorting method based on a comprehensive priority index.

[0064] Figure 6 Surface roughness after the tooth preparation and sorting method is implemented; Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention patent clearer, the invention patent is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of this invention patent. Furthermore, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of this invention patent.

[0066] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown, this specific embodiment adopts the following technical solution: a method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index, the specific implementation process of which is as follows:

[0067] Step 1: Import theoretical trajectory data for tooth preparation:

[0068] Input theoretical preliminary trajectory curve Information set of coordinate values ​​of each tool contact point in the base coordinate system , To prepare the coordinates of the i-th tool contact point in the theoretical trajectory in the base coordinate system, where, To prepare the theoretical trajectory, the x-axis coordinates of the i-th tool contact point in the base coordinate system are... To prepare the theoretical trajectory, the y-axis coordinates of the i-th tool contact point in the base coordinate system are... The coordinates of the i-th tool contact point in the base coordinate system are prepared for the theoretical trajectory. Axis coordinates;

[0069] Step 2: Calculate the complexity of the tool contact point:

[0070] a) Define the tool contact preparation complexity. Tool contact preparation complexity is a comprehensive quantitative description of the difficulty of preparation, expressed using symbols. The complexity of the tool contact is expressed as: ,in, Indicates the first Normalized angular distance ratio of each tool contact point; specified , Indicates the first The tool contact angle ratio is a quantitative description of the preparation complexity of a single tool contact; it specifies... , For the tool contact point acting on the pre-planned trajectory The preparatory angle at the location, The distance between two adjacent knife contact points, i.e., the distance between the knife contact points. and The length of the straight line segment between them. To determine the minimum value of the angle distance ratio of the pre-curved tool contact point, To determine the maximum value of the angle distance ratio of the pre-curved knife contact point; Indicates the preliminary curve. Normalized cutter contact curvature of each cutter contact point, specified , Indicates the preliminary curve. The curvature of each blade contact point To determine the minimum curvature of the pre-existing curve, This is the maximum value of the curvature of the pre-set curve;

[0071] b) Calculate the complexity of each tool contact and determine whether the complexity of all tool contacts has been calculated.

[0072] Specifically:

[0073] like Established, Order Jump to step two (a)).

[0074] like If this does not work, proceed to step three.

[0075] Step 3: Determine if the length of a single preparatory region exceeds the length threshold:

[0076] Define the length of the preparation area, the distance between adjacent tool contacts, using the symbol... The length of the preparatory region is expressed as: ;

[0077] a) Set the threshold for the length of the preparatory region to... ;

[0078] Determine whether the length of the preparation region exceeds the preparation length threshold.

[0079] Specifically:

[0080] like If successful, the length of the preparation area is qualified, and proceed to step three (b).

[0081] like If this is not the case, the length of the preparatory area is not up to standard, and the area needs to be further divided. Proceed to step 3b).

[0082] b) Determine whether the complexity range of all tool contacts has been evaluated.

[0083] Specifically:

[0084] like If true, it means that the lengths of all preparation areas have not yet been evaluated. Jump to step 3a);

[0085] like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step four.

[0086] Step 4: Divide and interpolate the length of the unqualified preparatory region:

[0087] a) Calculate the number of points that need to be inserted in a single unqualified preparatory region, expressed as: This ensures that the length of each segment after re-division does not exceed [a certain value]. Define interpolation parameters, which are the location parameters of interpolation points within a single non-compliant preparatory region, using symbols. The interpolation parameters are expressed as follows: ,in ; Calculate the coordinates of the interpolation points, which can be obtained from the formula. The calculation shows that m new preparatory regions are formed after the interpolation is completed;

[0088] b) Determine whether the interpolation of all tool contacts is complete.

[0089] Specifically:

[0090] like If true, it means that not all unqualified preparatory areas have been interpolated. Proceed to step four a);

[0091] like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step five;

[0092] Step 5: Calculation of Comprehensive Priority Indicators for the Preparatory Area:

[0093] Define a comprehensive priority index, which is a quantitative indicator of the preparatory priority for the preparatory area, using the symbol... The overall priority indicator is expressed as follows: ,in, This is the length weighting coefficient. The complexity weighting coefficient is defined as follows: The length normalization index is expressed as: ,in, The maximum value of the global reserve region length; the complexity normalization index is defined as follows: ,in, Let the difference in complexity between the two ends of the preparatory region of segment j be the value of the complexity of the knife contact points. These represent the global maximum and minimum complexity, respectively; calculate the comprehensive priority index for all preparatory regions;

[0094] Step 6: Determine if all preparation areas belong to the same priority group:

[0095] a) Determine whether the two reserve areas belong to the same priority group.

[0096] Specifically:

[0097] like If it is true, then it is considered and If they belong to the same priority group, proceed to step six (b).

[0098] like If it is not true, then it is considered and If they do not belong to the same priority group, proceed to step six (b).

[0099] b) Determine whether all preparatory areas have been evaluated.

[0100] Specifically:

[0101] like If it is established, it means that all the preparatory areas have not yet been evaluated, and therefore... Proceed to step six a);

[0102] like If the condition is not met, it means the assessment of the prepared area is complete, and proceed to step six (c).

[0103] c) Rearrange the different priority groups according to the comprehensive priority index from largest to smallest to obtain the group sequence. To obtain the execution order between groups;

[0104] Step 7: Optimize the intra-group preparation order based on distance:

[0105] When determining the processing order within the same priority group, a spatial distance factor is introduced for judgment: the endpoint of the previous preparatory area is used as the reference starting point, and the starting point of the next preparatory area is used as the target endpoint. Among the unprocessed areas, the area with the smallest spatial distance from the current position is selected as the priority processing object, until all areas in the priority group have been processed.

[0106] Specifically:

[0107] a) When executing priority group When the w-th preparation area is reached, the positional distance between the current preparation area and the unexecuted preparation areas in the same priority group is calculated, and the preparation area with the smallest positional distance in the group is selected as the next preparation area.

[0108] b) Determine the priority group Has the sorting of the s preparatory regions in the data been completed?

[0109] Specifically as follows:

[0110] like If established, then the priority group The sorting was not completed, so Proceed to step seven a);

[0111] like If not, then the priority group Once the sorting is complete, proceed to step seven (c).

[0112] c) Determine whether all s priority groups have been sorted.

[0113] Specifically as follows:

[0114] like If true, then the sorting of the s priority groups is incomplete. Let Proceed to step seven a);

[0115] like If this condition is not met, then the sorting of all s priority groups is complete, and the sorting of the preparatory region is finished.

[0116] Implementation Example 2: Based on step one, input the theoretical preliminary trajectory, including the coordinates of 8 tool contact points, as follows: , , , , , , , Proceed to step two and calculate the complexity of the 8 tool contacts using the formula: , , , , , , , According to step three, calculate the length of a single preparatory region and determine whether it exceeds the length threshold, then set the length threshold. The length is 1.25mm. Calculate all 7 preparatory regions. The 7th preparatory region exceeds the threshold, while the lengths of the other six regions are all less than the threshold. Proceed to step four to segment and interpolate the unqualified 7th preparatory region. The starting point of this region is... The destination is Length of the preparation area Calculate the number of points to be inserted according to the formula. The interpolation parameters are calculated as follows: The final calculated coordinates of the interpolation points are as follows: After segmentation, the length of the two new preparatory regions is 0.75mm, and all preparatory regions are now qualified. Proceed to step five to calculate the overall priority of all preparatory regions and arrange them in descending order. The result is: , , , , , , , Proceed to step six and use... The reserve area is divided according to the principle of being assigned to the same priority group, and a set priority level is established. The final grouping result is: Group 1 Group 2 Group 3 According to step seven, the nearest distance optimization rule within the group, starting from the current endpoint position, prioritizes the option with the smallest distance from the current position to the candidate segment start point. The result of the reordering within the group is: Group 1 [1,7], Group 2 [6,3], Group 3 [2,4,5,8], and the final determined execution order is: [1,7,6,3,2,4,5,8]. Before optimization, when executing the preliminary trajectory in the conventional spatial order, the area switching is frequent, the idle movement distance is long, the overall processing time is long, and the cutting force fluctuates violently. The comprehensive priority index and distance-based optimization of this invention are introduced. After optimization of the intra-group sorting, the tool's idle path was shortened by approximately 45%, and the overall preparation efficiency was improved by 35%. Simultaneously, due to a more rational and coherent cutting process, instability caused by excessively long local segments was effectively eliminated. This method successfully integrates multiple indicators such as trajectory complexity, length, and spatial distance, breaking through the limitations of previous single-indicator evaluations. By first sorting between groups based on comprehensive priority and then optimizing within groups based on spatial distance, scientific path segmentation under multi-indicator coupling constraints was achieved, ensuring both cutting stability and the matching degree of the prosthesis, while maximizing the overall surgical execution efficiency.

Claims

1. A method for segmenting and sorting tooth preparation trajectories based on a comprehensive priority index, characterized in that: The specific implementation process of the method is as follows: Step 1: Import theoretical trajectory data for tooth preparation: Input theoretical preliminary trajectory curve Information set of coordinate values ​​of each tool contact point in the base coordinate system , To prepare the coordinates of the i-th tool contact point in the theoretical trajectory in the base coordinate system, where, To prepare the theoretical trajectory, the x-axis coordinates of the i-th tool contact point in the base coordinate system are... To prepare the theoretical trajectory, the y-axis coordinates of the i-th tool contact point in the base coordinate system are... The coordinates of the i-th tool contact point in the base coordinate system are prepared for the theoretical trajectory. Axis coordinates; Step 2: Calculate the complexity of the tool contact point: a) Define the tool contact preparation complexity. Tool contact preparation complexity is a comprehensive quantitative description of the difficulty of preparation, expressed using symbols. The complexity of the tool contact is expressed as: ,in, Indicates the first Normalized angular distance ratio of each tool contact point; specified , Indicates the first The tool contact angle ratio is a quantitative description of the preparation complexity of a single tool contact; it specifies... , For the tool contact point acting on the pre-planned trajectory The preparatory angle at the location, The distance between two adjacent knife contact points, i.e., the distance between the knife contact points. and The length of the straight line segment between them. To determine the minimum value of the angle distance ratio of the pre-curved tool contact point, To determine the maximum value of the angle distance ratio of the pre-curved knife contact point; Indicates the preliminary curve. Normalized cutter contact curvature of each cutter contact point, specified , Indicates the preliminary curve. The curvature of each blade contact point To determine the minimum curvature of the pre-existing curve, This is the maximum value of the curvature of the pre-set curve; b) Calculate the complexity of each tool contact and determine whether the complexity of all tool contacts has been calculated. Specifically: like Established, Order Jump to step two (a)). like If this does not work, proceed to step three. Step 3: Determine if the length of a single preparatory region exceeds the length threshold: Define the length of the preparation area, the distance between adjacent tool contacts, using the symbol... The length of the preparatory region is expressed as: ; a) Set the threshold for the length of the preparatory region to... ; Determine whether the length of the preparation region exceeds the preparation length threshold. Specifically: like If successful, the length of the preparation area is qualified, and proceed to step three (b). like If this is not the case, the length of the preparatory area is not up to standard, and the area needs to be further divided. Proceed to step 3b). b) Determine whether the complexity range of all tool contacts has been evaluated. Specifically: like If true, it means that the lengths of all preparation areas have not yet been evaluated. Jump to step 3a); like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step four. Step 4: Divide and interpolate the length of the unqualified preparatory region: a) Calculate the number of points that need to be inserted in a single unqualified preparatory region, expressed as: This ensures that the length of each segment after re-division does not exceed [a certain value]. Define interpolation parameters, which are the location parameters of interpolation points within a single non-compliant preparatory region, using symbols. The interpolation parameters are expressed as follows: ,in ; Calculate the coordinates of the interpolation points, which can be obtained from the formula. The calculation shows that m new preparatory regions are formed after the interpolation is completed; b) Determine whether the interpolation of all tool contacts is complete. Specifically: like If true, it means that not all unqualified preparatory areas have been interpolated. Proceed to step four a); like If the condition is not met, it means that the length assessment of the prepared area is complete, and proceed to step five; Step 5: Calculation of Comprehensive Priority Indicators for the Preparatory Area: Define a comprehensive priority index, which is a quantitative indicator of the preparatory priority for the preparatory area, using the symbol... The overall priority indicator is expressed as follows: ,in, This is the length weighting coefficient. The complexity weighting coefficient is defined as follows: The length normalization index is expressed as: ,in, The maximum value of the global reserve region length; the complexity normalization index is defined as follows: ,in, Let the difference in complexity between the two ends of the preparatory region of segment j be the value of the complexity of the knife contact points. These represent the global maximum and minimum complexity, respectively; calculate the comprehensive priority index for all preparatory regions; Step 6: Determine if all preparation areas belong to the same priority group: a) Determine whether the two reserve areas belong to the same priority group. Specifically: like If it is true, then it is considered and If they belong to the same priority group, proceed to step six (b). like If it is not true, then it is considered and If they do not belong to the same priority group, proceed to step six (b). b) Determine whether all preparatory areas have been evaluated. Specifically: like If it is established, it means that all the preparatory areas have not yet been evaluated, and therefore... Proceed to step six a); like If the condition is not met, it means the assessment of the prepared area is complete, and proceed to step six (c). c) Rearrange the different priority groups according to the comprehensive priority index from largest to smallest to obtain the group sequence. To obtain the execution order between groups; Step 7: Optimize the intra-group preparation order based on distance: When determining the processing order within the same priority group, a spatial distance factor is introduced for judgment: the endpoint of the previous preparatory area is used as the reference starting point, and the starting point of the next preparatory area is used as the target endpoint. Among the unprocessed areas, the area with the smallest spatial distance from the current position is selected as the priority processing object, until all areas in the priority group have been processed. Specifically: a) When executing priority group When the w-th preparation area is reached, the positional distance between the current preparation area and the unexecuted preparation areas in the same priority group is calculated, and the preparation area with the smallest positional distance in the group is selected as the next preparation area. b) Determine the priority group Has the sorting of the s preparatory regions in the data been completed? Specifically as follows: like If established, then the priority group The sorting was not completed, so Proceed to step seven a); like If not, then the priority group Once the sorting is complete, proceed to step seven (c). c) Determine whether all s priority groups have been sorted. Specifically as follows: like If true, then the sorting of the s priority groups is incomplete. Let Proceed to step seven a); like If the condition is not met, then the sorting of all s priority groups is completed, and the sorting of the preparatory area is finished.

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