An orthodontic retainer wire anchor point positioning method

Abstract

This application relates to a method for locating anchor points of orthodontic retainer wires, belonging to the field of orthodontics. The method includes: reading tooth data of adjacent tooth pairs for which wire structures need to be placed, and calculating global reference features; analyzing the global reference features to obtain the labial contact points of adjacent tooth pairs; constructing an orthogonal coordinate system; determining the saddle points where the wire crosses adjacent tooth pairs based on the orthogonal coordinate system, and calculating the first and second characteristic anchor points of the adjacent tooth pairs; setting a cross-sectional point set, and calculating the first vertex, bottom point, and second vertex of a U-shaped path based on the labial contact points of the canines and the cross-sectional point set to construct a U-shaped path; and constructing a three-dimensional coordinate point set for the wire anchor points. This application solves the problem of low anchor point positioning accuracy and efficiency during orthodontic retainer fabrication due to reliance on manual operation by technicians and the lack of standardized parameters.

Description

Technical Field

[0001] This application relates to the field of orthodontic technology, and in particular to a method for positioning the anchor points of orthodontic retainer wires. Background Technology

[0002] Malocclusion is one of the most common oral health problems in the field of orthodontics, and it is prevalent in people of all ages. This type of malocclusion not only affects patients' normal chewing and speech functions, but may also lead to secondary oral diseases such as food impaction and increased periodontal burden. Furthermore, it has long-term adverse effects on facial contours, aesthetics, and the patient's mental health and social interactions. Therefore, restoring normal tooth alignment and occlusion through orthodontic treatment has become an important clinical approach.

[0003] After active orthodontic treatment is completed and teeth are moved to their ideal alignment, the periodontal tissues and related supporting structures are still in a reconstruction and adaptation phase, exhibiting significant biomechanical instability. Without effective maintenance, teeth are highly susceptible to relapse to varying degrees under the combined effects of muscle force, occlusal force, and soft tissue tension. Therefore, long-term wear of orthodontic retainers is considered crucial for consolidating treatment outcomes and preventing tooth relapse; their structural precision, fit, and stability directly affect clinical retention results.

[0004] In existing retainer technology, the wire anchor points rely entirely on experienced technicians manually bending them on plaster models. Technicians must rely on experience to set the anchor points, determine the contact position of the wire with each front tooth, plan its path through the interdental spaces, and manually bend the wire into a specific U-shaped path. This process is not only time-consuming and labor-intensive, resulting in low production efficiency, but more importantly, its quality is highly dependent on the technician's individual skill level and condition. This makes it difficult to guarantee the precision and consistency of the final product, becoming a bottleneck restricting standardized and large-scale production. Summary of the Invention

[0005] This application provides a method for positioning the steel wire anchor points of orthodontic retainers, which can solve the problem of low positioning accuracy and low efficiency caused by the reliance on manual operation by technicians and the lack of standardized parameters during the manufacturing process of orthodontic retainers.

[0006] To achieve the above objectives, this application provides a method for positioning the anchor points of an orthodontic retainer wire, the method comprising the following steps: S1. Read the tooth data of the adjacent tooth pairs for which the wire structure needs to be arranged, and calculate the global reference features of the adjacent tooth pairs. S2. Analyze individual teeth of adjacent tooth pairs based on global reference features, and obtain the labial contact points of adjacent tooth pairs based on the normal direction of each sampling point of an individual tooth. S3. Construct an orthogonal coordinate system, which describes the local spatial relationship between adjacent tooth pairs; S4. Determine the saddle point where the wire passes through the adjacent tooth pair based on the orthogonal coordinate system, and calculate the first and second characteristic anchor points of the wire for the adjacent tooth pair. S5. Set the cross-section point set, calculate the first vertex, bottom point, and second vertex of the U-shaped path based on the labial contact point of the canine and the cross-section point set, and construct the U-shaped path based on the first vertex, bottom point, and second vertex of the U-shaped path; S6. Construct a three-dimensional coordinate point set of the wire anchor point based on the lip contact point, the first wire feature anchor point, the second wire feature anchor point, and the U-shaped path.

[0007] In this application, after obtaining the set of labial surface points of a single tooth, the geometric features are extracted and calculated through normal direction filtering, two-dimensional view plane projection, geometric center calculation, and reverse three-dimensional mapping to obtain the labial contact point of the single tooth. This greatly improves the calculation speed and cleverly avoids the calculation drift caused by scanning tiny concavities and convexities. In determining the interdental passage point, by constructing an orthogonal coordinate system, discretizing the contour saddle point detection, and solving for the saddle point of the curve, the problem is transformed into a mathematical model that can be discretized and searched for extreme values. This accurately calculates the safe path for the wire to pass through the gap to prevent mold penetration. In the construction of the U-shaped path, the size and position of the semicircular arc of the U-shaped path are automatically determined based on the first vertex, the bottom point, and the second vertex of the U-shaped path, realizing parameterized driven generation based on geometric key points. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0009] Figure 1 This is a flowchart of the orthodontic retainer wire anchor point positioning method according to the embodiments of this application; Figure 2 This is a flowchart of the orthodontic retainer wire anchor point positioning method according to the embodiments of this application; Figure 3 The locations of the various key anchor points provided according to the embodiments of this application; Figure 4 A front view of the orthodontic retainer wire provided according to an embodiment of this application; Figure 5 This is a schematic diagram illustrating the construction of the labial contact point of a single tooth according to an embodiment of this application; Figure 6 This is a schematic diagram illustrating the construction of a local coordinate system according to an embodiment of this application; Figure 7 This is a schematic diagram of the interdental slice point cloud and the generated safety height provided according to the embodiments of this application; Figure 8 This is a schematic diagram of a U-shaped path steel wire model provided according to an embodiment of this application; Figure 9 This is a schematic diagram showing the positions of each point on the U-shaped path provided in the embodiments of this application in an orthogonal coordinate system. Detailed Implementation

[0010] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] like Figure 1 and Figure 2 This application provides a method for locating anchor points on orthodontic retainer wires. The core objective is to automatically and accurately calculate the three-dimensional coordinates of all key functional anchor points along the retainer wire path from the digital segmentation data of the patient's teeth using a complete spatial calculation algorithm, without manual intervention. Figure 3 and Figure 4 These key anchor points mainly include: the labial contact point of each anterior teeth (central incisors, lateral incisors, and canines, a point that ensures the wire can pass smoothly through the complex space between adjacent canines and first molars, also known as the saddle point; and the apex of the U-shaped path that provides specific mechanical properties. Figure 3 The yellow dot is the center point of the entire tooth model. Figure 3 The green dots represent the labial contact points of each tooth in the anterior region. Figure 3 The red dot represents the saddle point. Figure 3 The blue dot represents the vertex of the U-shaped curve.

[0012] The method for positioning the orthodontic retainer wire anchor points includes the following steps: S1. Read the tooth data of the adjacent tooth pairs for which the wire structure needs to be arranged, and calculate the global reference features of the adjacent tooth pairs. S2. Analyze individual teeth of adjacent tooth pairs based on global reference features, and obtain the labial contact points of adjacent tooth pairs based on the normal direction of each sampling point of an individual tooth. S3. Construct an orthogonal coordinate system, which describes the local spatial relationship between adjacent tooth pairs; S4. Based on the orthogonal coordinate system, determine the saddle point 101 where the wire passes through the adjacent tooth pair, and calculate the first wire characteristic anchor point 102 and the second wire characteristic anchor point 103 of the adjacent tooth pair. S5. Set the cross-section point set. Calculate the first vertex 105, the bottom point 106, and the second vertex 107 of the U-shaped path based on the labial contact point 104 of the canine and the cross-section point set. Construct the U-shaped path based on the first vertex 105, the bottom point 106, and the second vertex 107 of the U-shaped path. S6. Construct a three-dimensional coordinate point set of the wire anchor point based on the lip contact point, the first wire feature anchor point 102, the second wire feature anchor point 103, and the U-shaped path.

[0013] Optionally, S1 further includes the following steps: Read the tooth model data of adjacent tooth pairs, the tooth model data including the three-dimensional vertex coordinate data of the tooth model and the tooth identification file; The global center point of the tooth model is calculated, and the global reference features of adjacent tooth pairs are calculated based on a pre-defined directional bounding box algorithm. Figure 3 The purple border indicates the tooth-oriented bounding box.

[0014] Furthermore, the adjacent tooth pair consists of anterior teeth and the first molar, and the anterior teeth consist of the central incisors, lateral incisors, and canines; the global reference features include the center point of each tooth in the adjacent tooth pair and the tooth orientation bounding box.

[0015] Optionally, S2 further includes the following steps, such as Figure 5 : Based on global reference features, the individual teeth of adjacent tooth pairs are analyzed, and a direction vector is set. The direction vector starts from the overall center point of the tooth model and ends at the center point of the individual tooth to obtain the labial direction of the individual tooth. Figure 5 The red dot represents the center point of a single tooth. Figure 5 The red ray indicates the labial direction of a single tooth; For each sampling point of a single tooth, the normal direction is calculated, and the labial surface point set of the single tooth is obtained by filtering. Figure 5 The blue dot set is the dot set of the labial surface of a single tooth; The labial surface point set of a single tooth is projected onto a preset two-dimensional plane, and the geometric center of the labial surface point set of a single tooth is calculated in the two-dimensional plane. Figure 5 The right border is a two-dimensional plane. Figure 5 The green dot represents the geometric center of the set of points on the labial surface of a single tooth. Figure 5 The black border represents a two-dimensional view plane. Figure 5 The green border represents the geometric boundary of the lip side in this two-dimensional view plane; The geometric center of the labial surface point set of a single tooth is reverse-mapped to the labial surface point set of a single tooth, and the labial contact point of a single tooth is calculated.

[0016] It should be noted that the labial contact point is a point actually recorded in the tooth model, but the labial center point is a geometric location, not a point that actually exists in the tooth model.

[0017] Furthermore, the set of labial surface points is the set of points where the angle between the normal direction of the center point of a single tooth and the labial direction of the single tooth is less than a first threshold; the two-dimensional plane takes the labial direction of the single tooth as its normal vector; and the labial contact point is the point in the set of labial surface points of a single tooth that is closest to the labial center point.

[0018] Optionally, S3 further includes the following steps, such as... Figure 6 As shown: The center points of the first and second teeth of adjacent tooth pairs are calculated based on global reference features, and the midpoint of the line connecting the center points of the first and second teeth is taken as the origin of the orthogonal coordinate system. The average direction of the labial direction vector of adjacent tooth pairs is calculated based on the labial direction of a single tooth, and the average direction is normalized and set as the Y-axis of an orthogonal coordinate system. Figure 6 The red ray represents the Y-axis of the orthogonal coordinate system; Set the preset global vertical direction to the Z-axis of the orthogonal coordinate system; Figure 6 The blue ray represents the Z-axis of the orthogonal coordinate system; Calculate the cross product of the Y-axis and Z-axis to obtain the X-axis; fine-tune the Y-axis by calculating the cross product of the X-axis and Z-axis until the three coordinate axes are orthogonal to each other, thus completing the construction of the orthogonal coordinate system. Figure 6 The green dots represent the points through which the wire passes after the center point of the wire has been offset. Figure 6 The green ray represents the X-axis of an orthogonal coordinate system. Figure 6 The purple line is the center line of the steel wire.

[0019] Furthermore, the orthogonal coordinate system describes the local spatial relationship of adjacent tooth pairs; the adjacent tooth pairs require the arrangement of complex wire structures; the Y-axis of the orthogonal coordinate system represents the labial-lingual direction; the Z-axis represents the gingival-maxillary direction; and the X-axis represents the mesiodistal direction.

[0020] Optionally, S4 further includes the following steps, such as Figure 6 and 7 As shown: Based on the orthogonal coordinate system, the saddle point 101 where the wire passes through the adjacent tooth pair is determined. The saddle point 101 where the wire passes through the adjacent tooth pair is the optimal spatial position when the wire passes through the contact area between the canine and the first premolar. Thin slice data is selected on the X-axis of the orthogonal coordinate system. On the Y-axis of the orthogonal coordinate system, the thin slice data is discretized into a grid according to the preset sampling step size to obtain the discretized thin slice data. Figure 5 The blue dot set represents thin-layer slice data; Traverse the discretized thin slice data and search for the maximum coordinate value of adjacent tooth pairs in the Z-axis direction to construct the first height profile curve and the second height profile curve; the first height profile curve and the second height profile curve represent the height profile curves of the edge morphology of the mesial teeth and the distal teeth, respectively. The first height profile curve and the second height profile curve are compared point by point. At each Y-axis sampling point, the smaller value of the height values ​​of adjacent tooth pairs is taken, and a theoretical safe passage envelope is generated based on the smaller value. The theoretical safe passage envelope represents the highest placeable position of the steel wire without interference (mold penetration). On the theoretically safe passage envelope, the optimal passing coordinates of the steel wire centerline are found according to a preset extreme value search algorithm; the optimal passing coordinates are the global Z-axis maximum value point of the theoretically safe passage envelope; Figure 6 Red dot and Figure 7 The red dot represents the optimal passing coordinates, which is the highest point of the "valley" between the two tooth ridges; The safety gap offset is calculated based on the mesial and distal width data of adjacent tooth pairs. The optimal passing coordinate of the steel wire centerline is bidirectionally offset along the X-axis to generate the first steel wire feature anchor point 102 and the second steel wire feature anchor point 103. Figure 6 The two green dots are the first steel wire feature anchor point 102 and the second steel wire feature anchor point 103. The point closer to the lip side (i.e., the Y-axis coordinate is larger in the local coordinate) is the first steel wire feature anchor point 102, and the point farther away from the lip side (i.e., the Y-axis coordinate is smaller in the local coordinate) is the second steel wire feature anchor point 103. According to the preset inverse transformation matrix, the first steel wire feature anchor point 102 and the second steel wire feature anchor point 103 are transformed into global three-dimensional coordinate output.

[0021] Optionally, S5 further includes the following steps, such as... Figure 8 and Figure 9 As shown: Set a cross-section point set, which includes all points in the canine model that have the same X-axis coordinate as the labial contact point 104 of the canine; set the point in the cross-section point set whose Y-axis coordinate is greater than 0 and whose Z-axis coordinate is the smallest as the first vertex 105 of the U-shaped path; Set the point whose Z-axis and Y-axis coordinates are the same as the first vertex 105 of the U-shaped path and whose X-axis coordinate is the same as the first steel wire feature anchor point 102 as the second vertex 107 of the U-shaped path; Set the line connecting the first vertex 105 and the second vertex 107 of the U-shaped path as the diameter of the semicircle and calculate its length L and radius R. The midpoint of the line connecting the first vertex 105 and the second vertex 107 of the U-shaped path is set as the center 201 of the semicircular arc; the size and position of the semicircular arc are determined by the coordinates of the center 201 and the radius R. Based on the coordinates of the center 201 of the semicircle and the radius R, the distance of the radius length R offset from the center 201 of the semicircle in the negative Z-axis direction is used to obtain the bottom point 106 of the U-shaped path. The bottom point 106 of the U-shaped path is the coordinate of the lowest vertex of the U-shaped path. Fine-tune the first vertex 105, the bottom point 106, and the second vertex 107 of the U-shaped path along the average normal direction and set a safety distance to avoid mold penetration. Calculate the distances between the first vertex 105, the bottom point 106, and the second vertex 107 of the U-shaped path and the tooth model and compare them with the safety distance. If they are less than the safety distance, repeat the above fine-tuning operation; if they are greater than the safety distance, it means there is no mold penetration, and stop the fine-tuning operation.

[0022] Furthermore, the three-dimensional coordinate point set of S6 is a JSON file.

[0023] The technical solution of this application has the following advantages or beneficial effects: 1. This application provides a method for positioning the anchor point of the orthodontic retainer wire based on point cloud normal analysis and two-dimensional projection mapping. After obtaining the point set of the labial surface of a single tooth, the geometric features are extracted and calculated by normal direction filtering, two-dimensional view plane projection, geometric center calculation and reverse three-dimensional mapping, which greatly improves the calculation speed and cleverly avoids the calculation drift caused by scanning small concavities and convexities. 2. This application uses an orthogonal coordinate system and discretization to construct the contour saddle point detection for the steel wire passing through the interdental gap. In determining the interdental passing point, by constructing an orthogonal coordinate system, discretizing the contour saddle point detection, and solving for the saddle point of the curve, the problem is transformed into a mathematical model that can be discretized and searched for extreme values. This accurately calculates the safe path for the steel wire to pass through the gap, thus preventing the steel wire from causing the mold to go through. 3. This application automatically generates U-shaped curve parameters based on known feature points and geometric constraints. In the construction of the U-shaped curve, the size and position of the semicircular arc of the U-shaped path are automatically determined according to the first vertex 105, the bottom point 106, and the second vertex 107 of the U-shaped path, realizing parameterized driven generation based on geometric key points.

[0024] In the several embodiments provided in this application, it should be understood that the disclosed methods and apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between devices or units, and may be electrical, mechanical, or other forms.

[0025] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can be physically included separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0026] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute some steps of the transmission and reception methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0027] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principles described in this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for positioning the anchor points of an orthodontic retainer wire, characterized in that, The method includes the following steps: S1. Read the tooth data of the adjacent tooth pairs for which the wire structure needs to be arranged, and calculate the global reference features of the adjacent tooth pairs. S2. Analyze individual teeth of adjacent tooth pairs based on global reference features, and obtain the labial contact points of adjacent tooth pairs based on the normal direction of each sampling point of an individual tooth. S3. Construct an orthogonal coordinate system, which describes the local spatial relationship between adjacent tooth pairs; S4. Based on the orthogonal coordinate system, determine the saddle point (101) where the wire passes through the adjacent tooth pair, and calculate the first characteristic anchor point (102) and the second characteristic anchor point (103) of the adjacent tooth pair. S5. Set the cross-section point set, calculate the first vertex (105), bottom point (106), and second vertex (107) of the U-shaped path based on the labial contact point (104) of the canine and the cross-section point set, and construct the U-shaped path based on the first vertex (105), bottom point (106), and second vertex (107) of the U-shaped path; S6. Construct a three-dimensional coordinate point set of the wire anchor point based on the lip contact point, the first wire feature anchor point (102), the second wire feature anchor point (103), and the U-shaped path.

2. The orthodontic retainer wire anchor point positioning method according to claim 1, characterized in that, S1 further includes the following steps: Read the tooth model data of adjacent tooth pairs, the tooth model data including the three-dimensional vertex coordinate data of the tooth model and the tooth identification file; The global center point of the tooth model is calculated, and the global reference features of adjacent tooth pairs are calculated based on a pre-defined directional bounding box algorithm.

3. The orthodontic retainer wire anchor point positioning method according to claim 2, characterized in that, The adjacent tooth pair consists of the anterior teeth and the first molars, and the anterior teeth consist of the central incisors, lateral incisors and canines; The global reference features include the center point of each tooth in an adjacent tooth pair and the tooth orientation bounding box.

4. The orthodontic retainer wire anchor point positioning method according to claim 3, characterized in that, S2 also includes the following steps: Based on global reference features, the individual teeth of adjacent tooth pairs are analyzed, and a direction vector is set. The direction vector starts from the overall center point of the tooth model and ends at the center point of the individual tooth to obtain the labial direction of the individual tooth. For each sampling point of a single tooth, the normal direction is calculated, and the labial surface point set of the single tooth is obtained by filtering. The labial surface point set of a single tooth is projected onto a preset two-dimensional plane, and the geometric center of the labial surface point set of a single tooth is calculated in the two-dimensional plane. The geometric center of the labial surface point set of a single tooth is reverse-mapped to the labial surface point set of a single tooth, and the labial contact point of a single tooth is calculated.

5. The orthodontic retainer wire anchor point positioning method according to claim 4, characterized in that, The set of labial surface points is the set of points where the angle between the normal direction of the center point of a single tooth and the labial direction of the single tooth is less than a first threshold; the two-dimensional plane takes the labial direction of the single tooth as its normal vector; the labial contact point is the point in the set of labial surface points of a single tooth that is closest to the center point of the labial side.

6. The orthodontic retainer wire anchor point positioning method according to claim 5, characterized in that, S3 also includes the following steps: The center points of the first and second teeth of adjacent tooth pairs are calculated based on global reference features, and the midpoint of the line connecting the center points of the first and second teeth is taken as the origin of the orthogonal coordinate system. The average direction of the labial direction vector of adjacent tooth pairs is calculated based on the labial direction of a single tooth, and the average direction is normalized and set as the Y-axis of an orthogonal coordinate system. Set the preset global vertical direction to the Z-axis of the orthogonal coordinate system; Calculate the cross product of the Y-axis and Z-axis to obtain the X-axis; fine-tune the Y-axis by calculating the cross product of the X-axis and Z-axis until the three coordinate axes are orthogonal to each other, thus completing the construction of the orthogonal coordinate system.

7. The orthodontic retainer wire anchor point positioning method according to claim 6, characterized in that, The orthogonal coordinate system describes the local spatial relationship of adjacent tooth pairs; the adjacent tooth pairs require the arrangement of complex wire structures; the Y-axis of the orthogonal coordinate system represents the labial-lingual direction; the Z-axis represents the gingival-maxillary direction; and the X-axis represents the mesiodistal direction.

8. The method for positioning the orthodontic retainer wire anchor point according to claim 7, characterized in that, S4 also includes the following steps: The saddle point (101) where the wire crosses the adjacent tooth pair is determined based on the orthogonal coordinate system. On the X-axis of the orthogonal coordinate system, thin slice data is selected; on the Y-axis of the orthogonal coordinate system, the thin slice data is discretized into a grid according to the preset sampling step size to obtain the discretized thin slice data. Traverse the discretized thin slice data, search for the maximum coordinate value of adjacent tooth pairs in the Z-axis direction, and construct the first height profile curve and the second height profile curve. The first height profile curve and the second height profile curve are compared point by point. At each Y-axis sampling point, the smaller value of the height values ​​of adjacent tooth pairs is taken, and a theoretical safe passage envelope is generated based on the smaller value. On the theoretically safe passage envelope, the optimal passing coordinates of the steel wire centerline are found according to the preset extreme value search algorithm; The safety gap offset is calculated based on the mesial and distal width data of adjacent tooth pairs. The optimal passing coordinate of the steel wire centerline is bidirectionally offset along the X-axis to generate the first steel wire feature anchor point (102) and the second steel wire feature anchor point (103). According to the preset inverse transformation matrix, the first steel wire feature anchor point (102) and the second steel wire feature anchor point (103) are transformed into global three-dimensional coordinate output.

9. The orthodontic retainer wire anchor point positioning method according to claim 8, characterized in that, The saddle point (101) where the wire passes through the adjacent tooth pair is the optimal spatial position when the wire passes through the contact area between the canine and the first premolar; the optimal passing coordinate is the global Z-axis maximum value point of the theoretical safe passage envelope.

10. The method for positioning the orthodontic retainer wire anchor point according to claim 9, characterized in that, S5 also includes the following steps: Set a cross-section point set, which includes all points in the canine model that have the same X-axis coordinate as the labial contact point (104) of the canine; set the point in the cross-section point set whose Y-axis coordinate is greater than 0 and whose Z-axis coordinate is the smallest as the first vertex (105) of the U-shaped path. The point whose Z-axis coordinate and Y-axis coordinate are the same as the first vertex (105) of the U-shaped path and whose X-axis coordinate is the same as the first steel wire feature anchor point (102) is set as the second vertex (107) of the U-shaped path. Set the line connecting the first vertex (105) and the second vertex (107) of the U-shaped path as the diameter of the semicircle and calculate its length L and radius R; Set the midpoint of the line connecting the first vertex (105) and the second vertex (107) of the U-shaped path as the center of the semicircular arc (201); Based on the coordinates of the center (201) of the semicircular arc and the radius R, the bottom point (106) of the U-shaped path is obtained by offsetting the center (201) of the semicircular arc (201) by the radius length R in the negative direction of the Z-axis. Fine-tune the first vertex (105), the bottom point (106), and the second vertex (107) of the U-shaped path along the average normal direction and set a safety distance to avoid mold penetration. Calculate the distances between the first vertex (105), the bottom point (106), and the second vertex (107) of the U-shaped path and the tooth model and compare them with the safety distance. If the distance is less than the safety distance, repeat the fine-tune operation. If the distance is greater than the safety distance, it means that there is no mold penetration and stop the fine-tune operation.

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