Three-dimensional orthodontic undercut model generation method based on control points

Abstract

A three-dimensional orthodontic undercut model generation method based on a control point gets rid of the dependence of the traditional technology on manual operation, and innovatively introduces an automatic identification and special processing mechanism for malocclusion teeth at the same time to ensure that a high automation level can be kept in a complex case. The method comprises the following steps of: (1) calculating a tooth occlusion area; (2) calculating adjacent areas and contact areas between teeth; (3) generating an initial control point; (4) adjusting and optimizing control points; (5) judging a triangular structure; (6) constructing a grid model through common undercut; and (7) constructing a grid model by a triangular undercut. According to the method, rapid and automatic generation of the tooth undercut digital model is realized, the working efficiency is remarkably improved, standardization of model construction is ensured, great convenience is provided for subsequent die pressing operation, and errors caused by human factors are effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the field of oral orthodontic technology, and specifically focuses on an innovative method for automatically generating an undercut model of an oral three-dimensional digital model, aiming to provide a more efficient and accurate undercut filling solution for the design process of oral medical products such as invisible braces. Background Art

[0002] In recent years, with the rapid development of orthodontic technology, a variety of dental correction devices have emerged on the market. Among them, invisible braces, as an innovative dental correction solution, significantly improve the comfort and efficiency of the correction process compared to traditional solid bracket correction technology by relying on digital design and manufacturing technology.

[0003] Invisible dental braces consist of a series of transparent shells that are manufactured using digital oral scanning technology and 3D printing technology. The internal cavity of each shell is precisely calculated to fit the patient's teeth tightly, and its shape is dynamically adjusted according to the target tooth state at each stage of the dental correction process, thereby continuously and gently applying force to the teeth, guiding the teeth to gradually move to the correct position and achieve neat tooth arrangement. In this process, due to the movement of teeth and the advancement of the correction stage, new braces need to be replaced regularly to ensure the maximum correction effect.

[0004] The existing invisible braces manufacturing process is relatively mature. First, the patient's mouth is scanned in detail with a high-precision oral scanner to obtain an accurate three-dimensional digital model of the patient's teeth. Then, a series of gradually corrected digital models of teeth are designed based on the patient's teeth and correction goals using CAD software, and the digital models are printed into physical models using 3D printing technology. Finally, the physical model is used as a positive mold to press out an invisible braces that highly matches the patient's tooth shape.

[0005] Given that there are undercut areas between adjacent teeth in the dental model, these undercut areas will not only lead to problems such as product demoulding or fold breakage during the production process, but may also cause difficulty in removing or wearing the appliance when the patient is treated. Therefore, it is necessary to fill the undercuts in the dental model.

[0006] In the traditional manual method, wax materials are often used to fill the undercut areas of tooth models during the physical model production stage. However, this method is not only inefficient and costly, but also difficult to ensure the consistency of quality of the filling effect, which seriously restricts the large-scale and standardized production of medical products. In order to overcome the above drawbacks, the industry has gradually turned to accurately filling the undercuts of the digital model of the teeth before the physical model is produced, in order to achieve a more efficient and reasonable production process.

[0007] Although digital technology is increasingly used in the field of dental medicine, promoting the birth of many semi-automatic and even fully automatic solutions for filling undercuts, in the process of digital generation of actual product models, how to accurately and efficiently determine the shape and position of undercuts, and how to flexibly respond to the changing tooth arrangement layout in real cases are still the technical difficulties currently faced.

[0008] In addition, how to find the best balance between medical precision and production efficiency is also a major challenge. Because the undercut area is crucial to ensure the close fit between the appliance and the teeth and to effectively apply the correction force, overfilling the undercut is convenient for production, but it may weaken the fit between the appliance and the tooth surface, resulting in insufficient structural strength, which in turn affects the treatment effect.

[0009] Existing digital generation technologies generally rely on users to manually adjust parameters many times, which is cumbersome and inefficient, and it is difficult to stably guarantee the accuracy and quality of the generated model. In view of this, the market urgently needs an innovative method that can automatically and accurately complete the task of filling the undercut area of ​​the tooth model, thereby significantly improving the efficiency and production quality of product design. It is in this context that the present invention came into being, aiming to make up for the shortcomings of the existing technology and provide a more efficient and accurate undercut filling solution for the design process of oral medical products such as invisible braces. Summary of the invention

[0010] The present invention aims to overcome the above-mentioned shortcomings of the existing undercut filling technology and proposes a method for generating a three-dimensional orthodontic undercut model based on control points.

[0011] The present invention relates to an automated tooth undercut model generation algorithm, which aims to get rid of the reliance of traditional technology on manual operation, and innovatively introduces automatic identification and special processing mechanisms for malocclusion teeth, ensuring a high level of automation even in complex cases, thereby generating an undercut model that meets both medical standards and production needs. In addition, in the preprocessing stage of tooth model data, the present invention also innovatively proposes a method for automatically calculating the tooth occlusal area, further improving processing efficiency. The present invention uses control points to control the undercut morphology, allowing users to easily refine and personalize the generated results, ultimately significantly improving the overall quality of the product and user experience.

[0012] The input of the present invention includes a tooth mesh model and the gum line on the surface of the model (i.e., the boundary line determined when the teeth and gums are segmented by the oral scan data). The system then performs a series of calculations on all undercut areas to determine the corresponding undercut control points. Finally, curves are generated using these control points, and an undercut mesh model is further constructed as output.

[0013] The tooth model input referred to in the present invention is a three-dimensional digital model obtained after scanning a patient's oral cavity with an oral scanning device and then through a series of processing steps, including but not limited to segmentation and numbering. In the present invention, teeth are classified into incisors, canines, premolars, molars, and wisdom teeth (third molars) according to their morphology and function in common medical classifications. Among them, wisdom teeth usually have less crown exposed outside the gum or are completely submerged under the gum, and their oral scanning results are significantly different from those of molars. Therefore, they are separately classified into a category. The tooth occlusion area defined in the present invention refers to the occlusal surface of posterior teeth (i.e., the occlusal surface) and the area near the incisal edge of anterior teeth.

[0014] The undercut defined in the present invention generally refers to the interdental area between two adjacent teeth, that is, each undercut model corresponds to two adjacent teeth. However, in special cases, such as when maloccluded teeth and their surrounding adjacent teeth form a complex structure similar to a "pin" shape in natural arrangement, the present invention can automatically identify the "pin" shape structure formed by three misaligned teeth and regard this special area as a whole, and construct a special undercut model with a structure including three teeth as a group (in the following description, this special undercut is simply referred to as "pin undercut". Unless specifically specified as "pin undercut", the term "undercut" generally refers to the common undercut model formed based on two adjacent teeth).

[0015] The present invention first calculates and determines all control points in the undercut area, and then constructs the corresponding undercut grid model based on these control points. Specifically, for the common undercut area between two adjacent teeth, the present invention sets two groups of control points, which are located on the two adjacent teeth respectively. Each group of control points is further subdivided into lingual and labial parts, and each part contains 4 control points, so there are a total of 8 control points in a group. For the pin undercut area between three adjacent teeth, the present invention sets three groups of control points, which are located on the surfaces of the three teeth respectively. Each group contains 8 control points. Similar to the common undercut, each group can also be further divided into two equal parts according to the relationship with the other two teeth. Therefore, each common undercut area contains a total of 16 control points, and each pin undercut area contains 24 control points. These control points together determine the shape and position of the undercut as a whole.

[0016] To achieve the above object, the present invention designs a detailed technical solution, and the specific implementation process includes the following key steps: 1. Calculate the occlusal area of teeth; 2. Calculate the adjacent area and contact area between teeth; 3. Generate initial control points; 4. Adjust and optimize control points; 5. Determine the pin structure; 6. Construct a grid model for the common undercut; 7. Construct a grid model for the pin undercut. The following is a general description of the above steps:

[0017] Step 1: Calculate the occlusal area of ​​the teeth. The occlusal area of ​​the teeth in this step refers to the side of the posterior teeth that is opposite to the occlusal surface (i.e., the occlusal surface) and the area near the incisal edge of the anterior teeth. The core goal of this step is to obtain information about the occlusal area of ​​the teeth to assist in determining the height of the top control point in the subsequent steps, thereby achieving effective control of the height of the final undercut mesh model.

[0018] Step 2: Calculate the adjacent areas and contact areas between teeth. The definition of the adjacent areas in this step is crucial for setting the initial position of the control vertices of the undercuts in the future, and is intended to ensure that the direction of the final generated undercut mesh model can accurately meet the medical designer's requirements that the undercuts must cover the adjacent surfaces of the teeth while avoiding excessive intrusion into the remaining tooth surfaces. The identification of the tooth contact area is mainly used to evaluate the actual contact state between the teeth and whether the contact area can play the role of a bearing diaphragm, thereby guiding the fine adjustment of the height of the top control point of the undercut in the subsequent process.

[0019] Step 3: Generate initial control points. This step is closely dependent on the calculation results of the tooth adjacent area. The position of the control points is determined by using the boundary information of the adjacent area to ensure that the initial layout of the control points generally meets the relevant requirements of medical design and production.

[0020] Step 4: Adjust the optimized control points. Based on the results of step 3, this step combines the information of the tooth occlusal area and contact area to fine-tune the positions of the top and middle control points. This optimization process ensures that even when dealing with complex orthodontic cases with significant tooth height differences, the structural integrity of the invisible braces can be effectively maintained to prevent wrinkles and fractures during the production process. At the same time, it ensures that the height change of the undercut can be smoothly transitioned in the multi-step orthodontic design, avoiding unnecessary mutations, thereby improving design efficiency and treatment comfort.

[0021] Step 5: Determine the "pink" structure. In this step, the gum line is used as a reference to determine the "pink" structure. When three teeth are arranged in a "pink" shape to form an obvious triangle, it is defined as a "pink" structure, which provides guidance for subsequent processes and ensures that ordinary undercuts and "pink" undercuts can be accurately distinguished and treated separately.

[0022] Step 6: Constructing a mesh model for common undercuts: For common undercuts, the vertices required for the mesh model are calculated and the corresponding mesh model is constructed using the vertices.

[0023] Step 7: Constructing a mesh model for the inverted concave shape. For the inverted concave shape, calculate the vertices required for the mesh model and use the vertices to construct the corresponding mesh model.

[0024] The present invention aims to automatically generate an accurate undercut mesh model based on the specific morphology of teeth and their relative positional relationship. First, the occlusal area of ​​the teeth and the adjacent area and contact area information between the teeth are calculated respectively; then, the position of the initial control point is calculated through the adjacent area, and further, the position of the control point is optimized and adjusted according to the occlusal area and contact area information to ensure the accuracy of the model; finally, after determining the zigzag structure, for ordinary undercuts and zigzag undercuts, the undercut mesh model with a reasonable structure and fully adapted to the tooth morphology is constructed based on the control points.

[0025] The advantages of the present invention are as follows: the present invention calculates a personalized undercut model based on the specific shape of the teeth and their relative positional relationship, ensuring that the invisible braces fit the real shape of the teeth, greatly improving the wearing comfort and correction effect. In addition, the innovative method of the present invention realizes the rapid and automatic generation of digital models of tooth undercuts, which not only significantly improves work efficiency, but also ensures the standardization of model construction, provides great convenience for subsequent molding operations, and effectively reduces errors caused by human factors. In the design and implementation process, the present invention cleverly uses control points to control the shape of undercuts, allowing medical designers to intuitively and efficiently perform refined manual adjustments for a small number of special or complex situations through visual interaction, further enhancing the adaptability and accuracy of the undercut model. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic flow chart of the method for generating a three-dimensional undercut model of the present invention.

[0027] Figure 2 This is a flowchart of step 1 for calculating the occlusal area of ​​the teeth.

[0028] Figure 3 It is a schematic diagram of the local coordinate system of the tooth.

[0029] Fig. 4 is a schematic diagram of the occlusal area of ​​teeth, wherein Fig. 4(a) is a schematic diagram of the occlusal area of ​​incisors, Fig. 4(b) is a schematic diagram of the occlusal area of ​​canines, Fig. 4(c) is a schematic diagram of the occlusal area of ​​premolars, and Fig. 4(d) is a schematic diagram of the occlusal area of ​​molars or wisdom teeth.

[0030] Figure 5 It is a flowchart of step 2 for calculating the adjacent area and contact area between teeth.

[0031] Figure 6 It is a schematic diagram of the adjacent areas and contact areas of teeth.

[0032] Figure 7 It is a flowchart of generating initial control points in step three.

[0033] Figure 8It is a flowchart of adjusting the optimization control points in step 4.

[0034] Fig. 9 This is a schematic diagram of the relevant variables for adjusting the optimization control points in step 4.

[0035] Figure 10 is a schematic diagram comparing the normal arrangement of teeth and the arrangement of teeth in a triangle, wherein Figure 10(a) is a schematic diagram of the normal arrangement of teeth, and Figure 10(b) is a schematic diagram of the arrangement of teeth in a triangle.

[0036] FIG11 is a schematic diagram of the arrangement and classification of the "pink" structure in step 5. FIG11(a) is a schematic diagram of the arrangement of teeth in a non-pink structure in "small-large-small", FIG11(b) is a schematic diagram of the arrangement of teeth in a non-pink structure in "large-small-large", FIG11(c) is a schematic diagram of the arrangement of teeth in a non-pink structure in a triangle, and FIG11(d) is a schematic diagram of the arrangement of teeth in a pink structure.

[0037] Figure 12 is a schematic diagram of the control point distribution of a common undercut and a zigzag undercut. Figure 12(a) is a schematic diagram of the control point distribution of a common undercut, and Figure 12(b) is a schematic diagram of the control point distribution of a zigzag undercut.

[0038] Fig. 13 is a schematic diagram of the division of the mesh model region of a common undercut and a zigzag undercut. Fig. 13(a) is a schematic diagram of the division of the mesh model region of a common undercut, and Fig. 13(b) is a schematic diagram of the division of the mesh model region of a zigzag undercut.

[0039] Figure 14 is a schematic diagram of the mesh model results of a common undercut and a zigzag undercut. Figure 14(a) is a schematic diagram of the mesh model results of a common undercut, and Figure 14(b) is a schematic diagram of the mesh model results of a zigzag undercut.

[0040] Fig.15 This is a physical picture of the mesh model result of a normal undercut.

[0041] Fig.16 This is the actual picture of the mesh model result of the inverted concave shape. DETAILED DESCRIPTION

[0042] The present invention will be further described in detail below with reference to the accompanying drawings.

[0043] See also Figure 1 The present invention includes steps one to seven, which are specifically described as follows:

[0044] Step 1: Calculate the occlusal area of ​​the teeth. The occlusal area of ​​the teeth in the present invention refers to the side of the posterior teeth that is opposite to the occlusal surface (i.e., the occlusal surface) and the area near the incisal edge of the anterior teeth. An example is shown in FIG4 . This step uses the tooth local coordinate system as the reference system. The tooth local coordinate system is shown in FIG4 . Figure 3, usually the X-axis is from the lingual side of the tooth to the labial side, the Y-axis is to the next tooth, and the Z-axis is from the root to the crown along the long axis of the tooth. The detailed operation process of this step is as follows Figure 2 As shown, it is divided into the following sub-steps:

[0045] 1.1 Preliminary screening of tooth facets that meet the rules based on normal vectors

[0046] First, the tooth face is preliminarily screened based on the normal vector of the face. Different screening rules are required because different tooth positions (incisors, canines, premolars, molars and wisdom teeth) have significant differences in morphology.

[0047] For incisors and canines, only the faces whose normal vectors have an angle with the positive direction of the Z axis within the set range are selected, specifically 45 degrees for incisors and 70 degrees for canines.

[0048] In addition to requiring that the normal vector of the mask be at an angle of 60 degrees to the positive direction of the Z axis, the screening of premolars also requires that the projection direction of its normal vector on the XY plane be at an angle of no more than 60 degrees to the direction of the mask's centroid pointing to the tooth center (Center), or at an angle of no more than 60 degrees to the direction of the mask's centroid pointing to the Y axis.

[0049] The screening of molars and wisdom teeth also requires that the angle between the normal vector of the patch and the positive direction of the Z axis is within 60 degrees, and that the projection direction of its normal vector on the XY plane is within 60 degrees from the direction in which the centroid of the patch points to the center of the tooth.

[0050] 1.2 Further screening based on the local coordinate system position of the tooth

[0051] A secondary screening was performed on the incisors and canines. The distance from the center of gravity of the patch to the YZ plane was calculated to evaluate the position of the patch in the local coordinate system of the tooth. The patches with a distance greater than 1 mm were judged as far away and excluded from the set.

[0052] 1.3 Further screening based on the Z-axis height of the tooth local coordinate system

[0053] Continue to filter the meshes based on their height on the Z axis. Remove the 5% of meshes with the lowest height in the set to reduce the influence of tooth attachments and ensure that the selected mesh set can more accurately reflect the occlusal area.

[0054] 1.4 Fitting the edge curve of the occlusal area

[0055] Finally, for the occlusal area patch set obtained through the above screening steps, the center of gravity is used as the center point, and the farthest point is sampled according to the angle. Subsequently, these farthest points are fitted into a smooth curve that can envelop most of the occlusal area patches in the order of angles using the NURBS curve fitting technology, which facilitates subsequent calculations. This step is intended to simplify the representation of the occlusal area and facilitate subsequent analysis and calculations.

[0056] Step 2: Calculate the adjacent area and contact area between teeth. The specific operation process of this step is as follows: Figure 5 It should be noted that each pair of adjacent teeth has two adjacent areas and two contact areas, located on the two teeth respectively, see Figure 6 .

[0057] 2.1 Vertex distance calculation and sorting

[0058] First, the mesh model vertices of the teeth on both sides are traversed respectively, and the minimum distance from each vertex to its adjacent tooth mesh model is calculated; then, all the calculated distances are sorted in ascending order.

[0059] 2.2 Calculate adjacent areas

[0060] Among the sorted distances, the minimum value is selected and a fixed increment of 0.8 mm based on experience is added. The corresponding tooth surface vertices within this range are regarded as vertices of the adjacent region. Then, the patches directly connected to these vertices are regarded as patches of the adjacent region. In particular, when dealing with the situation between incisors and incisors or incisors and canines, it is necessary to appropriately increase the distance range for adjacent region screening according to the torsion angle (in a pair of adjacent tooth relationships, the torsion angle of a tooth is defined as the angle between the average normal vector of the adjacent region patch of the tooth and the Y axis of its local coordinate system). Based on these adjacent region patches, the key variables used in subsequent steps are defined. First, the center of gravity (adjRegionCenter) and the average normal vector (adjRegionNormal) are calculated, and then the adjacent region plane is defined using the two. Subsequently, the direction of the adjacent region toward the labial side (directionFront) is obtained by cross-producting adjRegionNormal with the initial upward direction (directionUp, i.e., the average value of the Z axis direction of the local coordinate systems of the two adjacent teeth). Furthermore, the cross product of adjRegionNormal and directionFront is used to eliminate the component of directionUp in the adjRegionNormal direction.

[0061] 2.3 Extraction and optimization of adjacent region boundaries

[0062] The boundaries of the adjacent regions are extracted from the results of step 2.2. To deal with the possible disconnected regions, the boundaries with the maximum continuous length are selected, and the NURBS curve fitting technique is used to fit the curve and resample to optimize the representation of the boundaries of the adjacent regions between teeth.

[0063] 2.4 Calculation of contact area

[0064] In the distance sorting results of step 2.1, vertices within a fixed value of 0.15 mm based on experience are further screened out, and these vertices are identified as the contact area vertices of the teeth. It should be noted that due to the large gaps between teeth, the contact area may be empty, that is, there is no area close enough to be approximated as contact. For this special case, there is a special treatment in the subsequent step 4.

[0065] Step 3: Generate initial control points. The specific operation process of this step is as follows: Figure 7 As shown, the calculation is completed side by side for the two adjacent teeth with undercuts, and a total of 2 calculation processes covering the top, middle, gingival and bottom control points are performed in sequence.

[0066] 3.1 Calculate the top control point

[0067] Since the tooth shape has a great influence on the shape of the adjacent area of ​​the teeth (the adjacent area between the front teeth is generally cone-shaped, and the adjacent area between the back teeth is generally heart-shaped), different calculation methods are used for the top control points of the undercuts between teeth in different tooth positions.

[0068] For the concave area between incisors or between incisors and canines, traverse the boundary points of the adjacent area of ​​the teeth, calculate the projection of the vector from the center of gravity of the area to the boundary point (hereinafter referred to as "boundary point vector") on the plane of the adjacent area (defined in step 2), and calculate the cosine value of these projections and the upward direction (directionUp). Select the first 10% boundary points with the largest cosine value (i.e. the smallest angle), calculate the mean of these points, and use them as the mean point of the top control points on both sides of the lips and tongue.

[0069] For other concave areas, the projection length of each boundary point vector in the upward direction (directionUp) is calculated instead. The first 10% boundary points with the longest projection length are selected, and their average is calculated as the average point of the top control points on both sides of the lip and tongue.

[0070] After calculating the mean point of the top control points on both sides of the lips and tongue, move the mean point in the positive and negative directions of the labial direction (directionFront) by an empirical distance (0.3mm for the undercut between the front teeth, 0.8mm for the undercut between the back teeth, and 0.75mm for the undercut between the front teeth and the back teeth), and find the nearest point on the surface of the tooth mesh model again as the top control point of the labial and lingual sides.

[0071] 3.2 Calculate the central control point

[0072] Traverse the boundary points of the tooth adjacent area and calculate the projection of each boundary point vector on the adjacent area plane. Calculate the cosine value of these projections and the labial direction (directionFront), and select the first 10% boundary points with the largest cosine value (smallest angle) and the smallest cosine value (largest angle).

[0073] The means of the two groups of points were calculated, and the nearest points of the respective means were found on the surface of the tooth mesh model, which were used as the middle control points of the labial and lingual sides, respectively.

[0074] 3.3 Calculation of gingival control points

[0075] Project the middle control points on both sides of the lips and tongue and the gum line along the upward direction (directionUp) to the same plane with the upward direction (directionUp) as the normal vector. Take the center of gravity of the projected gum line as the origin, and the angle between the two middle control points and the origin as the initial search angle. Based on experience, appropriately expand the search angle range by 15 degrees on both sides.

[0076] Search for points on the gum line within this range, and select a point as the gum control point so that its projection relative to the projection of the middle control point is closest to the preset target distance of 1mm (based on experience). Since this point is taken from the gum line on the surface of the tooth mesh model, it will also be located on the surface of the tooth mesh model.

[0077] 3.4 Calculate the bottom control point

[0078] Move the gum control point in the opposite direction of the upward direction (directionUp) (i.e. downward) by 5 mm (based on experience). Find the nearest point of the new position on the tooth mesh model surface as the bottom control point to ensure that the bottom of the final generated undercut mesh model can be properly embedded in the gums.

[0079] Step 4: Adjust and optimize control points. This step aims to fine-tune the position and relative distribution of control points to optimize the final effect. Figure 8As shown in the figure, the height difference between the incisal points of the two adjacent teeth is used to calculate the upper limit of the distance that the material is allowed to extend from the incisal edge of the tooth to the tooth gap during pressing, and the actual distance that the material extends from the incisal edge of the tooth to the tooth gap when the undercut is not filled is obtained by combining the contact area information. The extension distance limit and the actual extension distance are compared to determine the appropriate control point adjustment strategy in different situations. For related variables in the subsequent description of this step, see Fig. 9 .

[0080] 4.1 Determine the cutting edge

[0081] For the two adjacent teeth with undercuts, calculate side by side, project the edge curve of the occlusal area of ​​the tooth and the mean of the top control points on the same side along the upward direction (directionUp) onto the same plane with the upward direction (directionUp) as the normal vector, and then find the edge point of the projected occlusal area that is closest to the projection point of the mean of the top control points, and the corresponding original edge point of the occlusal area is used as the incisal edge point.

[0082] 4.2 Calculation of extension distance limit

[0083] Calculate the height difference between the incisal points of two adjacent teeth, and map the height difference to the maximum distance (materialExtendLimit) that the membrane material (the material used when pressing the invisible braces on the physical model) is allowed to extend downward from the incisal edge of the teeth according to the set negative correlation function, so that the greater the height difference, the smaller the extension distance limit (materialExtendLimit) value. In the present invention, trigonometric functions are used to represent the mapping relationship. When the height difference is 0, the maximum extension distance limit (materialExtendLimit) is 1.2mm, and when the height difference is greater than or equal to 1.5mm, the minimum extension distance limit (materialExtendLimit) is 0.8mm.

[0084] 4.3 Evaluating the actual extension distance

[0085] Calculate the actual extension distance of the material from the incisal edge of the tooth downward without filling the undercut, that is, the absolute value of the distance from the lower incisal point to the highest point of the tooth contact area along the upward direction (directionUp). If there is no contact area between the teeth, the actual extension distance is considered to be infinite.

[0086] 4.4 Control point adjustment

[0087] If the actual extension distance is less than the extension distance limit (materialExtendLimit), it means that the contact area is sufficient to support the diaphragm. At this time, the highest point of the contact area is directly used as the mean point of the new top control point to update the top control point. For the contact area of ​​premolars, molars and wisdom teeth, considering their special shapes, the original top control point is raised to the same height as the highest point of the contact area.

[0088] If the actual extension distance is greater than the extension distance limit (materialExtendLimit), it means that the contact area does not exist or is insufficient to support the membrane. At this time, the height of the top control point on the side of the higher cutting edge point is adjusted to the height of the cutting edge point on that side minus the extension distance limit (materialExtendLimit); and for the top control point on the side of the lower cutting edge point, the lower one of the top control point on the opposite side and the cutting edge point on this side is taken, and the top control point on this side is adjusted to the same height as the lower one.

[0089] Step 5, determine the T-structure. This step uses the gum line as a reference to determine the T-structure. The difference between the normal arrangement of teeth and the T-arrangement is shown in Figure 10. When three teeth are arranged in a T-arrangement to form an obvious triangle, it is defined as a T-structure. For ease of explanation, assume that there are three teeth arranged in the order of A, B, and C, with B in the middle. First, project the gum line in the direction of the mean of the Z-axis of the local coordinate system of each of the three teeth onto the same plane with this direction as the normal vector, and then use the Andrew algorithm to calculate the ordered convex hull boundary of the projection result. Subsequently, search for a class of line segments on the boundary of the convex hull, requiring that its two end points come from the gum line projections of A and C respectively. According to the geometric characteristics, the existence of such line segments can be summarized into three types:

[0090] If there is no line segment that meets the conditions, it means that the middle tooth B touches the convex hull boundary on both the lingual and labial sides, and is therefore larger than the teeth on both sides, forming a "small-large-small" arrangement pattern, as shown in Figure 11(a). In this case, it does not form a herringbone structure, and proceed to step six.

[0091] If there are two such line segments, it means that the middle tooth B does not touch the convex hull boundary on the lingual and labial sides, and is therefore smaller than the teeth on both sides, forming a "big-small-big" arrangement pattern, as shown in Figure 11(b). It does not form a herringbone structure, and proceeds to step six.

[0092] If and only if there is such a line segment, it means that the middle tooth B only touches the convex hull boundary on one side of the lingual side or the labial side, and the three teeth are arranged in a triangular manner. At this time, further calculate the minimum distance from the projection of the gum line of tooth B to the line segment, calculate the ratio of the minimum distance to the length of the line segment, and compare it with the preset empirical threshold (0.25 in the present invention) to determine whether a T-shaped structure is formed. If the ratio is greater than the threshold condition, it is confirmed that the three teeth form a T-shaped structure, as shown in Figure 11 (d), and proceed to step seven; otherwise, the T-shaped structure condition is not met, as shown in Figure 11 (c), and proceed to step six.

[0093] Step 6: Constructing a mesh model for common undercuts. In this step, the vertices required for the mesh model are calculated for common undercuts and the corresponding mesh model is constructed using the vertices. The results are shown in Figures 14(a) and Fig.15 .

[0094] 6.1 Calculating mesh model vertices

[0095] Arrange each series of control points on the surfaces of two adjacent teeth in the order of labial bottom control point, labial gingival control point, labial middle control point, labial top control point, lingual top control point, lingual middle control point, lingual gingival control point, and lingual bottom control point to construct two control point sequences, as shown in Figure 12 (a), and perform Catmull-Rom spline interpolation on each control point sequence to generate a smooth control curve. Subsequently, according to a predetermined target grid density (the density is determined according to actual production requirements), sampling is performed on each control curve to extract curve points. In the present invention, sampling is performed on the control curve at an average geodesic distance of 0.6 mm, and the number of curve points obtained on the two control curves is controlled to be equal. Finally, the nearest points of these curve points on the corresponding tooth surface are determined, and these nearest points constitute the vertices of the concave grid model.

[0096] 6.2 Using vertices to build a mesh model

[0097] This step constructs a fine grid structure through orderly arranged vertex data, and specifically subdivides the undercut model into three main parts: the outer surface, the inner side, and the bottom, see Figure 13 (a). The outer surface is a continuous area from the lingual side through the occlusal side to the labial side, and is seamlessly sutured by means of a ruled surface (a special type of surface, the main characteristic of which is that each point on the surface has at least one straight line passing through it, that is, it can be formed by a straight line through continuous motion) to ensure the smoothness and continuity of the outer surface. The specific operation is to first obtain two groups of undercut grid model vertices located on two adjacent teeth, the number of vertices in these two groups of models is equal and one-to-one corresponding, and first connect them in pairs; then insert more groups of vertices on these lines according to the maximum vertex spacing and the set grid density (in the present invention, it is guaranteed that the vertices are inserted at a distance of about 0.6mm at the maximum spacing), and the inserted vertices are also guaranteed to be consistent in number and can correspond, and then they are connected one by one in a Z shape to complete the suture. The inner side is the part of the undercut that is adjacent to the adjacent teeth on both sides, which is completely blocked by the adjacent teeth. A three-dimensional mesh hole filling algorithm (the method used in the present invention, the three-dimensional mesh hole filling algorithm, comes from the literature: Liepa P. Filling holes in meshes [C], Proceedings of the 2003 Eurographics / ACM Siggraph Symposium on Geometry Processing. 2003: 200-205) is used to achieve defect-free suture. The bottom is a quadrilateral area that is completely covered by the gums. The three-dimensional mesh hole filling algorithm is also used to suture to ensure that the entire mesh model is closed and the mesh density is consistent.

[0098] Step 7: Constructing a mesh model for the inverted concave. In this step, the vertices required for the mesh model are calculated for the inverted concave and the corresponding mesh model is constructed using the vertices. The results are shown in Figures 14(b) and Fig.16 For the convenience of subsequent explanation, it is assumed that there is a shaped like a pinyin structure, which contains three teeth A, B, and C.

[0099] 7.1 Calculating Mesh Model Vertices

[0100] The internal structure of the "pin" indentation corresponding to the "pin" structure contains three teeth arranged in a triangular layout, denoted as teeth A, B, and C. A total of three independent tooth pairs are formed between the teeth, denoted as pair AB, pair BC, and pair CA. Each tooth pair independently performs steps three and four to generate the corresponding control point set. Each control point set contains 16 control points, divided into two groups on the surfaces of the two teeth, each containing 8 control points. Each group is further divided into two parts, the lingual side and the labial side, each containing 4 control points. For tooth A, from the control point sets of the two tooth pairs pair AB and pair CA related to this tooth, respectively select one group of 8 control points belonging to the surface of A; and further determine whether the part belonging to the outside of the triangle of the "pin" structure in the two groups is the lingual side or the labial side, and obtain the part belonging to the outside of the triangle of the "pin" structure, and each group gets 4 control points; for these control points, sort them in the order of the bottom control point, gingival control point, middle control point, top control point in pair CA, and the bottom control point, gingival control point, middle control point, top control point in pair AB, to construct a complete and ordered sequence of 8 control points, and use the Catmull-Rom spline interpolation method on the control point sequence to generate a smooth control curve. Teeth B and C use the same steps, and a total of three control curves are obtained, as shown in Figure 12(b). Subsequently, according to the predetermined target grid density (this density is determined according to actual production requirements), sample on each control curve and extract the curve points. In the present invention, sampling is performed on the control curve at an average geodesic distance of 0.6 mm, and the number of curve points obtained on the three control curves is controlled to be equal. Finally, determine the nearest points of these curve points on the corresponding tooth surfaces, and these nearest points form the vertices of the indentation grid model.

[0101] 7.2 Using vertices to construct a grid model

[0102] This step constructs a fine mesh structure through orderly arranged vertex data, and specifically subdivides the concave model into four main parts: the top surface, the outer side surface, the inner side surface and the bottom, see Figure 13 (b). The outer side surface and the top surface together form a continuous outer surface of the inverted concave facing the outside of the teeth and gums (i.e., the outer surface portion corresponding to the ordinary concave model). The top surface is the central triangular area at the top of the outer surface, which is stitched using a three-dimensional mesh hole filling algorithm. The outer side surface is the remaining part of the outer surface other than the top surface, which is seamlessly stitched in the form of a ruled surface to ensure smoothness and continuity. The specific operation is to first obtain three groups of concave mesh model vertices located on three teeth, respectively. The number of vertices in these three groups of models is equal and can be equally divided into two halves. Each half can correspond to one-to-one with the other half of the vertices on the adjacent side, and they are first connected in pairs; then, according to the maximum vertex spacing and the set grid density, more half groups of vertices are inserted on these lines (in the present invention, it is guaranteed that the vertices are inserted at a distance of about 0.6 mm at the maximum spacing), and the inserted vertices also have a corresponding relationship, and then they are connected one by one in a Z shape to complete the stitching. The inner side is the part of the indentation next to the three teeth, which is completely blocked by the teeth and is stitched using a 3D mesh hole filling algorithm. The bottom is a hexagonal area, which is completely covered by the gums and is also stitched using a 3D mesh hole filling algorithm to ensure the closure of the entire mesh model and the uniformity of the mesh density.

[0103] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for generating a three-dimensional orthodontic undercut model based on control points, characterized in that: The input is the tooth mesh model and the gum line on the surface of the model, that is, the boundary line determined when the teeth and gums are segmented in the oral scan data. The final output is the undercut mesh model. The processing process includes the following steps: 1) Calculate the occlusal area of ​​the teeth; for each type of tooth, select the facets belonging to the occlusal area according to different set rules, and fit the edge curve of the occlusal area; 2) Calculate the adjacent areas and contact areas between teeth; first calculate the vertex distances between teeth and sort them, then filter out adjacent area patches according to the set rules, extract and optimize the boundaries of the adjacent areas, and filter out the vertices of the contact areas; 3) Generate initial control points; calculate the top control point, middle control point, gum control point, and bottom control point in sequence based on the adjacent area information; 4) Adjust and optimize the control points; first determine the incisal point based on the occlusal area information and calculate the extension distance limit, then evaluate the actual extension distance based on the contact area information, and finally adjust the control points according to the set rules for different situations; 5) Determine the T-shaped structure; calculate the convex hull of the gingival line projection, and determine whether there is a T-shaped structure based on the result; 6) constructing a mesh model of the common undercut; calculating the vertices of the mesh model of the common undercut according to the control points, and using the vertices to construct the mesh model of the common undercut; 7) Constructing a mesh model of the inverted concave shape; calculating the vertices of the inverted concave shape mesh model according to the control points, and using the vertices to construct the mesh model of the inverted concave shape.

2. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: The tooth occlusal area described in step (1) refers to the side of the posterior teeth that is opposite to the occlusal area, and the area near the incisal edge of the anterior teeth; in step (1), the tooth local coordinate system is used as the reference system, and usually the X-axis is from the lingual side of the tooth to the labial side, the Y-axis is pointing to the side of the next tooth, and the Z-axis is along the long axis of the tooth from the root to the crown; step (1) is specifically divided into the following sub-steps: 11) Preliminary screening of tooth facets that meet the rules based on normal vectors; for incisors and canines, select faces whose normal vectors have an angle with the positive direction of the Z axis within a set range; for premolars, in addition to requiring that the angle between the normal vector of the facet and the positive direction of the Z axis is within a set range, it is also required that the angle between the projection direction of the normal vector on the XY plane and the direction from the center of gravity of the facet to the center of the tooth does not exceed a set threshold, or the angle between the projection direction of the normal vector on the XY plane and the direction from the center of gravity of the facet to the center of the tooth does not exceed a set threshold; for molars and wisdom teeth, it is also required that the angle between the normal vector of the facet and the positive direction of the Z axis is within a set range, and that the projection direction of the normal vector on the XY plane and the direction from the center of gravity of the facet to the center of the tooth does not exceed a set threshold; 12) Further screening based on the position of the local coordinate system of the teeth; performing secondary screening on the incisors and canines, calculating the distance from the center of gravity of the face patch to the YZ plane, and thus judging the face patches with a distance greater than the set threshold as being far away and excluding them from the set; 13) Further screening based on the Z-axis height of the tooth local coordinate system; continue screening based on the height of the facets on the Z-axis; remove a predetermined percentage of the facets with the lowest height in the set to reduce the influence of the tooth attachments; 14) Fitting the edge curve of the occlusal area; for the occlusal area patch set obtained through the above screening step, the center of gravity is taken as the center point, and the farthest point is sampled according to the angle; then, these farthest points are fitted into a smooth curve in angular order using curve fitting technology.

3. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: The adjacent area and contact area between the teeth in step (2) are calculated by the following sub-steps: 21) Vertex distance calculation and sorting: First, traverse the mesh model vertices of the teeth on both sides respectively, and calculate the minimum distance from each vertex to its adjacent tooth mesh model; then, sort all the calculated distances in ascending order; 22) Calculate adjacent areas; Among the sorted distances, the minimum value is selected and a set fixed increment is added, and the corresponding tooth surface vertices within this range are defined as vertices of the adjacent area; further, the patches directly connected to these vertices are defined as patches of the adjacent area; Based on these adjacent region patches, define the key variables used in the subsequent steps; first calculate their center of gravity adjRegionCenter and average normal vector adjRegionNormal, and then use the two to define the adjacent region plane; then, by cross-producting adjRegionNormal with the initial upward direction directionUp, obtain the direction directionFront of the adjacent region toward the lip side; Furthermore, the cross product of adjRegionNormal and directionFront is used to eliminate the component of directionUp in the adjRegionNormal direction; 23) Extraction and optimization of adjacent region boundaries; selecting the boundary with the maximum continuous length from the results of sub-step (22), and fitting the curve using curve fitting technology and resampling to optimize the representation of the adjacent region boundaries between teeth; 24) Calculate the contact area; In the distance sorting result of sub-step (21), all vertices within a set smaller fixed value range are further screened out, and these vertices are defined as the contact area vertices of the teeth.

4. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: The top control point, middle control point, gum control point, and bottom control point of each pair of teeth in step (3) are calculated in sequence through the following sub-steps: 31) Calculate the top control point; for the concave area between incisors or between incisors and canines, traverse the boundary points of the adjacent areas of the teeth, calculate the projection of the vector of the center of gravity of the area pointing to the boundary point, that is, the boundary point vector, on the plane of the adjacent area, and calculate the cosine value of these projections and the upward direction directionUp; select a predetermined percentage of boundary points with the largest cosine value, calculate the mean of these points, and use it as the mean point of the top control points on both sides of the lips and tongue; for the concave area in other cases, calculate the projection length of each boundary point vector in the upward direction directionUp instead; select a predetermined percentage of boundary points with the longest projection length, calculate their mean, and use it as the mean point of the top control points on both sides of the lips and tongue; After calculating the mean point of the top control points on both sides of the lip and tongue, move the mean point in the positive and negative directions of the lip direction directionFront by the set distance respectively, and find the nearest point on the surface of the tooth mesh model again as the top control point of the lip and tongue sides; 32) Calculate the middle control point; traverse the boundary points of the tooth adjacent area, calculate the projection of each boundary point vector on the adjacent area plane; calculate the cosine value of these projections and directionFront in the labial direction, and select the first predetermined percentage boundary points with the largest and smallest cosine values ​​respectively; finally calculate the mean of these two groups of points, and find the nearest point of each mean on the surface of the tooth mesh model, which are used as the middle control points of the labial side and the lingual side respectively; 33) Calculate the gingival control point; project the middle control points on both sides of the lips and tongue and the gingival line along the upward direction directionUp to the same plane with the upward direction directionUp as the normal vector; take the center of gravity of the gingival line after projection as the origin, take the angle between the line connecting the two middle control points after projection and the origin as the initial search angle, and expand the search angle range according to the set value; search for points on the gingival line within this range, and select a point as the gingival control point, so that the outward displacement distance of its projection relative to the projection of the middle control point is closest to the preset target distance; 34) Calculate the bottom control point; move the gum control point in the opposite direction of the upward direction directionUp by a set distance; find the nearest point of the new position on the surface of the tooth mesh model as the bottom control point.

5. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1 and claim 4, characterized in that: Step (4) specifically includes the following sub-steps for adjusting the control points of each pair of teeth: 41) Determine the incisal edge point; for the two adjacent teeth with undercuts, calculate side by side, project the edge curve of the occlusal area of ​​the tooth and the mean of the top control point on the same side along the upward direction directionUp onto the same plane with the upward direction directionUp as the normal vector, and then find the projected occlusal area edge point that is closest to the projection point of the mean of the top control point, and the corresponding original occlusal area edge point is used as the incisal edge point; 42) Calculate the extension distance limit; calculate the height difference between the incisal edge points of two adjacent teeth, and map the height difference to the maximum distance materialExtendLimit that the membrane material is allowed to extend downward from the incisal edge of the tooth according to the set negative correlation function, so that the greater the height difference, the smaller the extension distance limit materialExtendLimit value; 43) Evaluate the actual extension distance; calculate the actual extension distance of the material from the incisal edge of the tooth downward without filling the undercut, that is, the absolute value of the distance from the lower incisal edge point to the highest point of the tooth contact area in the upward direction; if there is no contact area between the teeth, the actual extension distance is considered to be infinite; 44) Control point adjustment; adjust the position of the control point based on the result of comparing the actual extension distance with the extension distance limit; if the actual extension distance is less than the extension distance limit materialExtendLimit, it indicates that the contact area is sufficient to support the diaphragm. At this time, the highest point of the contact area is directly used as the mean point of the new top control point to update the top control point; for the contact areas of premolars, molars and wisdom teeth, considering their special shapes, the original top control point is raised to the same height as the highest point of the contact area; if the actual extension distance is greater than the extension distance limit materialExtendLimit, it indicates that the contact area does not exist or is insufficient to support the diaphragm; at this time, the height of the top control point on the side of the higher incisal point is adjusted to the height of the incisal point on that side minus the extension distance limit materialExtendLimit; and for the top control point on the side of the lower incisal point, take the lower one of the top control point on the opposite side and the incisal point on this side, and adjust the top control point on this side to the same height.

6. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: Step (5) uses the gum line as a reference to determine the T-shaped structure. When three teeth are arranged in a T-shaped pattern to form an obvious triangle, it is defined as a T-shaped structure. First, the gum line is projected onto the same plane with the mean direction of the Z axis of the local coordinate system of each of the three teeth as the normal vector, and then the ordered convex hull boundary of the projection result is calculated. Subsequently, a type of line segment is searched on the boundary of the convex hull, and its two end points are required to come from the gum line projection of the teeth on both sides. According to the geometric characteristics, the existence of such line segments can be summarized into three types: 51) If there is no line segment that meets the conditions, it means that the middle tooth touches the convex hull boundary on both the lingual and labial sides, and the middle tooth is larger than the teeth on both sides. This situation does not constitute a t-shaped structure, and then proceed to step (6); 52) If there are two such line segments, it means that the middle tooth does not touch the convex hull boundary on the lingual and labial sides. The middle tooth is smaller than the teeth on both sides and does not form a chevron structure. Then proceed to step (6). 53) When and only when there is such a line segment, the middle tooth touches the convex hull boundary only on one side of the lingual side or the labial side, and the three teeth are arranged in a triangular manner; at this time, further calculate the minimum distance from the projection of the gum line of the middle tooth to the line segment, calculate the ratio of the minimum distance to the length of the line segment, and compare it with the set threshold to determine whether a T-shaped structure is formed; if the ratio is greater than the threshold condition, it is confirmed that the three teeth form a T-shaped structure, and then proceed to step (7); otherwise, the T-shaped structure condition is not met, and then proceed to step (6).

7. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: Step (6) calculates the vertices required for the mesh model for the case of common undercuts and uses the vertices to construct the corresponding mesh model, specifically including the following sub-steps: 61) Calculate the vertices of the mesh model; arrange each series of control points on the surfaces of two adjacent teeth in the order of labial bottom control point, labial gingival control point, labial middle control point, labial top control point, lingual top control point, lingual middle control point, lingual gingival control point, and lingual bottom control point to construct two control point sequences, and perform spline interpolation on each control point sequence to generate a smooth control curve; then, sample each control curve according to a predetermined target mesh density to extract curve points; finally, determine the nearest points of these curve points on the corresponding tooth surface, and these nearest points constitute the vertices of the undercut mesh model; 62) Use vertices to build a mesh model; subdivide the undercut model into three main parts: the outer surface, the inner side, and the bottom; The outer surface is a continuous area from the lingual side through the occlusal side to the labial side, which is seamlessly sutured using a ruled curved surface method; the inner surface is the part of the undercut adjacent to the adjacent teeth on both sides, which is completely blocked by the adjacent teeth and is sutured using a three-dimensional mesh hole-filling algorithm; the bottom is a quadrilateral area that is completely covered by the gums and is also sutured using a three-dimensional mesh hole-filling algorithm.

8. The method for generating a three-dimensional orthodontic undercut model based on control points according to claim 1, characterized in that: Step (7) calculates the vertices required for the mesh model for the case of the inverted concave shape and uses the vertices to construct the corresponding mesh model, specifically including the following sub-steps: 71) Calculate the vertices of the mesh model; the inner part of the "" structure corresponding to the "" undercut" contains three teeth arranged in a triangular layout, denoted as teeth A, B, and C, and three independent tooth pairs are formed between the two teeth, denoted as pairAB, pairBC, and pairCA. Each tooth pair independently executes steps (3) and (4) to generate a corresponding set of control points, wherein each control point set contains a total of 16 control points, which are divided into two groups on the surfaces of the two teeth, each containing 8 control points, and each group is further divided into two parts, the lingual side and the labial side, each containing 4 control points; for tooth A, from the control point sets of the two tooth pairs pairAB and pairCA related to the tooth, select a group of 8 control points belonging to the surface of A respectively; and further determine whether the part belonging to the outside of the "" triangle of the two groups is the lingual side part or the labial side part, and obtain the part belonging to the outside of the "" triangle of the "" structure, and obtain 4 control points in each group; For these control points, the order of bottom control point, gum control point, middle control point, top control point in pair CA and bottom control point, gum control point, middle control point, top control point in pair AB is arranged to construct a complete and orderly sequence of 8 control points, and a smooth control curve is generated for the control point sequence using the spline interpolation method; the same steps are used for teeth B and C to obtain a total of three control curves; then, according to the predetermined target mesh density, sampling is performed on each control curve to extract the curve points; finally, the nearest points of these curve points on the corresponding tooth surface are determined, and these nearest points constitute the vertices of the undercut mesh model; 72) Use vertices to construct a mesh model; subdivide the undercut model into four main parts: a top surface, an outer side surface, an inner side surface, and a bottom surface; the outer side surface and the top surface together constitute a continuous outer surface of the undercut facing the outside of the teeth and gums; The top surface is the central triangular area at the top of the outer surface, which is stitched using a three-dimensional mesh hole-filling algorithm; the outer side surface is the remaining part of the outer surface other than the top surface, which is seamlessly stitched using a ruled surface method; the inner side surface is the part of the inverted concave adjacent to the three teeth of the inverted structure, which is completely blocked by the teeth and is stitched using a three-dimensional mesh hole-filling algorithm; The bottom is a hexagonal area that is completely covered by the gums and is also sutured using a 3D mesh hole-filling algorithm.

9. A control point-based three-dimensional orthodontic undercut model generation device, characterized in that: It comprises a memory and one or more processors, wherein the memory stores executable codes, and when the one or more processors execute the executable codes, they are used to implement a control point-based three-dimensional oral orthodontic undercut model generation method according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, a control point-based three-dimensional oral orthodontic undercut model generation method according to any one of claims 1 to 8 is implemented.

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