Automatic undercut point design method and system by calculating graphical geometric relations

Abstract

The present application relates to a kind of automatic undercut design method and system by calculating graphic geometric relation, mainly is through the relationship between the regularized geometric position and form between various teeth and teeth, the cutting of geometric figure, parallel mapping, intersection subtraction etc. to locate the position of the specific control point of undercut, and through the iterative calculation of computer, such as distance calculation, nearest point calculation, the geometric information statistics of adjacent area to automatically correct the deviation of undercut point. The undercut point obtained by this method is relatively stable and close to the actual situation, and the curve composition of the undercut block is generated on the basis of the control unit by the computer, thereby generating a better quality grid. Production operators can save time and quickly design undercut, improving efficiency.

Description

Technical Field

[0001] This invention relates to the field of digital processing technology for oral images, and in particular to an automatic method and system for designing undercut points by calculating geometric relationships of graphics. Background Technology

[0002] Dentofacial deformity is an oral disease. Malformed teeth can affect the development of the dentofacial region, impacting oral health and function, and consequently affecting facial appearance.

[0003] Currently, in invisible orthodontic treatment, braces without undercuts can cause discomfort for patients. Appropriate undercuts make braces comfortable and prevent them from breaking. Most braces currently require artificial manipulation to create undercuts. Summary of the Invention

[0004] The technical problem to be solved by this invention is to design an automatic undercut design method and system that calculates geometric relationships of graphics. By using geometric methods, suitable undercuts can be generated quickly, reducing manual operation and solving existing technical problems.

[0005] To solve the above-mentioned technical problems, the automatic concave point design method of the present invention, which calculates the geometric relationship of a graphic, includes the following steps:

[0006] Step S1: Construct a local coordinate system based on the tooth segmentation coil, including the following steps:

[0007] Step S11: Take out two adjacent teeth and obtain the tooth segmentation coil of the crown edge after processing by the tooth segmentation software;

[0008] Step S12: The line connecting the center points of the cutting coils of the two teeth is taken as the x-axis. The Z-axis in the small coordinate axis of the teeth defined by the tooth separation software is taken as the Z-axis of the local coordinate system. The Y-axis of the two teeth is calculated by cross product, with the starting point being the midpoint of the line connecting the center points, which serves as the two determined local coordinate systems.

[0009] Step S2: Calculate the length of the adjacent surfaces of the left and right teeth, and write the height-to-width ratio offset coefficients for different tooth positions;

[0010] Step S3: Calculate the position of the undercut construction vertex on the projection plane of the tooth proximal surface;

[0011] Step S4: For points with severe vertex position offset, perform anomaly detection and automatically iterate and adjust to return to their original positions to determine the 8 vertices formed by the inverted concavity;

[0012] Step S5: Construct an inverted concave mesh based on the 8 vertices determined in step S4.

[0013] Furthermore, step S2 specifically includes the following steps:

[0014] Step S21: Obtain the projection distance of the line connecting each point of a set of tooth cutting lines to the origin along the y-axis direction at the origin of the local coordinate system.

[0015] Step S22: After obtaining a set of data as described above, calculate the difference between the maximum and minimum values ​​as the maximum length of the adjacent surface, which is defined as the maximum width of the tooth.

[0016] Step S23: Adjust the origin of the small coordinate system according to the morphological characteristics of the teeth to facilitate subsequent geometric cutting and projection calculations based on this; for example, the incisors and canines are generally inclined towards the labial side, so the origin of the coordinate system is moved towards the labial side by the corresponding distance.

[0017] Step S24: Based on the width and height ratio information table of each tooth position on its respective adjacent surface, compile the height-width ratio coefficient for different tooth positions to facilitate the adjustment of the undercut filling material that better matches the tooth positions.

[0018] Furthermore, in step S3, the undercut is an irregular cube, requiring four points to be marked on the sides of each adjacent tooth, two at the bottom and two at the top; connecting these four points of two teeth forms a cuboid structure, specifically including the following steps:

[0019] Step S31: Find the two bottom points of the undercut: Using the y-axis of the local coordinate system obtained in the above steps as the normal vector, construct a plane through the origin of the coordinate system. This plane can be regarded as the plane cutting the tooth. According to the scale information written in step S2, make the plane deflect to the left and right. Calculate the intersection of this plane with the cutting line of the tooth. The intersection point is taken as the two bottom points of the undercut.

[0020] Step S32: Calculate the height of the proximal surfaces of the teeth. By cutting the teeth into four quadrants, find the highest point of each tooth in each quadrant. Then, connect the highest point of each tooth to the bottom point found in step S31 and calculate the distance of the connecting line. Each tooth can obtain four heights and record them.

[0021] Step S33: Using the height distance obtained in step S32, perform proportional movement by multiplying the height on the small coordinate axis by the height coefficient to obtain the two top points;

[0022] Step S34: Using the two top points obtained in step S33 and the offset coefficient obtained in step S2, the top points are offset, and then the top points are mapped onto the tooth interproximal mesh by finding the nearest point. This gives the initial generation of the undercut points between two adjacent teeth.

[0023] Furthermore, step S4 specifically includes the following steps:

[0024] Step S41: Detect cases where the length difference between the base points generated between two adjacent teeth is large and asymmetrical;

[0025] Step S42: After detecting the situation in step S41, calculate the distance between the two bottom points on both sides. Taking the side with the shorter distance as the standard, find the nearest point on the tooth surface grid of the other tooth with the bottom and top points of the standard side. Replace the bottom point on the other side with the nearest point found.

[0026] Step S43: Iterate again to check the distance difference after step S42. If it is still too small, automatically expand the bottom point. That is, offset the position of the base point according to the Y-axis direction of the small coordinate, and then find the nearest point and update it.

[0027] Step S44: Since there are significant changes in the shape and position of teeth 5 and 6, we check for abnormalities here and expand the mesh for cases where the distance between the bottom point and the top point is not appropriate. We then find the actual vertex of the adjacent mesh using the nearest point method.

[0028] Step S45: If the detection point is too low, the point is appropriately raised by moving it a certain distance along the z-axis, and the positions of the points relative to each other are updated accordingly;

[0029] Step S46: Check the height of the two points at the top. If one point is too low and the other point is too high, fit the position of the lower point to the position of the higher point to achieve a unified and coordinated relationship.

[0030] Step S47: If one of the bottom points is severely deviated, perform a retraction and repositioning process on that point, and finally map it onto the mesh tooth surface;

[0031] Step S48: For the situation between the posterior molars, in order to avoid the point from shifting to the top area of ​​the crown, the nearest point is found between them to achieve a point symmetry, uniformity and compactness of the adjacent surfaces;

[0032] Step S49: After a series of iterative adjustments through steps S41 to S48, in order to avoid the occurrence of deviation points, a final repositioning check is performed on the top and bottom points according to the specific tooth position characteristics to minimize the deviation of the undercut point.

[0033] Step S410: Avoid the top points from coinciding into a single point to prevent the points from being unable to be separated during the step-by-step process;

[0034] The eight vertices formed by the inverted concave shape were finally determined.

[0035] Furthermore, in step S410, if points are found to overlap, the IDs of other points on the same surface are calculated, and this ID is used to replace another point to form the positions of the two points, thus avoiding overlapping points and the problem of significant changes after points diverge.

[0036] Furthermore, step S5 includes the following steps:

[0037] Step S51: Add the 4 points on each side to the 6 points on one side of the structure that continues to extend downwards from the bottom;

[0038] Step S52: Connect the 6 points on the left and the 6 points on the right in sequence, and take points in segments to use as sample points for constructing a closed fitted b-spline curve.

[0039] Step S53: Select points on the curve sequentially at intervals to form the edge points of the constructed mesh;

[0040] Step S54: Based on the edge line points, construct a grid by connecting the bottom and side points to form an inverted concave square grid.

[0041] Furthermore, the expression for the b-spline curve in step S52 is: Where u is a vector of a point; N i p (u) Let represent the i-th p-th (p+1-th) b-spline basis function.

[0042] This invention also provides an automatic concave point design system that calculates geometric relationships in graphics, comprising:

[0043] One or more processors; and

[0044] One or more memories storing a computer-executable program, wherein the aforementioned method is performed when the processor executes the computer-executable program.

[0045] The beneficial effects of this invention are as follows: The automatic undercut point design method and system of this invention, which calculates geometric relationships, mainly locates the specific control points of the undercut by dividing the geometric figures into sections, parallel mappings, and intersection subtractions based on the regular geometric positions and shapes between various teeth. Then, through computer-aided calculations, such as distance calculation, nearest point calculation, and statistical analysis of geometric information from neighboring regions, it automatically corrects any misaligned undercut points. The undercut points obtained by this method are relatively stable and closely resemble actual conditions. Furthermore, the computer generates the curve composition of the undercut blocks based on the control sheet, thus generating a high-quality mesh. Production operators can save time and quickly design undercuts, improving efficiency. Attached Figure Description

[0046] The specific embodiments of the present invention will be further explained below with reference to the accompanying drawings.

[0047] Figure 1 This is a flowchart of the steps of the present invention;

[0048] Figure 2(a) is a schematic diagram of the automatic concave effect optimization (I);

[0049] Figure 2(b) is a schematic diagram of the automatic concave effect optimization (II);

[0050] Figure 3 A schematic diagram of the dividing coils between adjacent teeth;

[0051] Figure 4 A schematic diagram showing the establishment of the x-axis by taking the midpoint of the dividing coil of adjacent teeth. Detailed Implementation

[0052] Combination Figure 1 Figure 2(a), Figure 2(b) Figure 3 and Figure 4 The automatic concave point design method based on calculating geometric relationships in this embodiment includes the following steps:

[0053] Step S1: Construct a local coordinate system based on the tooth segmentation coil, including the following steps:

[0054] Step S11: Remove two adjacent teeth to obtain the tooth segmentation coils at the crown edge after processing by the tooth segmentation software, such as... Figure 3 As shown;

[0055] Step S12: The line connecting the center points of the cutting coils of each of the two teeth is taken as the x-axis. The Z-axis of the small coordinate axis of the teeth defined by the tooth segmentation software is taken as the Z-axis of this local coordinate system. The Y-axis of each of the two teeth is calculated using a cross product, with the starting point being the midpoint of the line connecting the center points. These serve as the two determined local coordinate systems. Figure 4 As shown;

[0056] Step S2: Calculate the proximal surface length of each of the left and right teeth, and formulate the height-to-width ratio offset coefficients for different tooth positions; specifically, this includes the following steps:

[0057] Step S21: Obtain the projection distance of the line connecting each point of a set of tooth cutting lines to the origin along the y-axis direction at the origin of the local coordinate system.

[0058] Step S22: After obtaining a set of data as described above, calculate the difference between the maximum and minimum values ​​as the maximum length of the adjacent surface, which is defined as the maximum width of the tooth.

[0059] Step S23: Adjust the origin of the small coordinate system according to the morphological characteristics of the teeth to facilitate subsequent geometric cutting and projection calculations based on this; for example, the incisors and canines are generally inclined towards the labial side, so the origin of the coordinate system is moved towards the labial side by the corresponding distance.

[0060] Step S24: Based on the width and height ratio information table of the adjacent surfaces of different tooth positions, compile the height-width ratio coefficients for different tooth positions to facilitate the adjustment of the undercut filling material that better fits the tooth positions;

[0061] Step S3: Calculate the position of the undercut construction vertex on the projection plane of the adjacent tooth surface; the undercut is an irregular cube, requiring 4 points to be determined on each side of the adjacent teeth, including 2 points at the bottom and 2 points at the top; connecting the 4 points of two teeth can form a cuboid structure, specifically including the following steps:

[0062] Step S31: Find the two bottom points of the undercut: Using the y-axis of the local coordinate system obtained in the above steps as the normal vector, construct a plane through the origin of the coordinate system. This plane can be regarded as the plane cutting the tooth. According to the scale information written in step S2, make the plane deflect to the left and right. Calculate the intersection of this plane with the cutting line of the tooth. The intersection point is taken as the two bottom points of the undercut.

[0063] Step S32: Calculate the height of the proximal surfaces of the teeth. By cutting the teeth into four quadrants, find the highest point of each tooth in each quadrant. Then, connect the highest point of each tooth to the bottom point found in step S31 and calculate the distance of the connecting line. Each tooth can obtain four heights and record them.

[0064] Step S33: Using the height distance obtained in step S32, perform proportional movement by multiplying the height on the small coordinate axis by the height coefficient to obtain the two top points;

[0065] Step S34: Using the two top points obtained in step S33 and the offset coefficient obtained in step S2, the top points are offset, and then the top points are mapped onto the tooth interproximal mesh by finding the nearest point. This gives the initial generation of the undercut point between two adjacent teeth.

[0066] Step S4: Perform anomaly detection and automatic iterative adjustment for points with severe vertex position offsets to determine the 8 vertices formed by the inverted concavity; specifically including the following steps:

[0067] Step S41: Detect cases where the length difference between the base points generated between two adjacent teeth is large and asymmetrical;

[0068] Step S42: After detecting the situation in step S41, calculate the distance between the two bottom points on both sides. Taking the side with the shorter distance as the standard, find the nearest point on the tooth surface grid of the other tooth with the bottom and top points of the standard side. Replace the bottom point on the other side with the nearest point found.

[0069] Step S43: Iterate again to check the distance difference after step S42. If it is still too small, automatically expand the bottom point. That is, offset the position of the base point according to the Y-axis direction of the small coordinate, and then find the nearest point and update it.

[0070] Step S44: Since there are significant changes in the shape and position of teeth 5 and 6, we check for abnormalities here and expand the mesh for cases where the distance between the bottom point and the top point is not appropriate. We then find the actual vertex of the adjacent mesh using the nearest point method.

[0071] Step S45: If the detection point is too low, the point is appropriately raised by moving it a certain distance along the z-axis, and the positions of the points relative to each other are updated accordingly;

[0072] Step S46: Check the height of the two points at the top. If one point is too low and the other point is too high, fit the position of the lower point to the position of the higher point to achieve a unified and coordinated relationship.

[0073] Step S47: If one of the bottom points is severely deviated, perform a retraction and repositioning process on that point, and finally map it onto the mesh tooth surface;

[0074] Step S48: For the situation between the posterior molars, in order to avoid the point from shifting to the top area of ​​the crown, the nearest point is found between them to achieve a point symmetry, uniformity and compactness of the adjacent surfaces;

[0075] Step S49: After a series of iterative adjustments through steps S41 to S48, in order to avoid the occurrence of deviation points, a final repositioning check is performed on the top and bottom points according to the specific tooth position characteristics to minimize the deviation of the undercut point.

[0076] Step S410: Avoid the top points from coinciding with a single point to prevent the points from not being separated during the step-by-step process; if points are found to coincide, calculate the IDs of other points on the same face and use this ID to replace another point to form the positions of the two points, thus avoiding the problem of overlapping points and significant changes after the points are separated.

[0077] The eight vertices formed by the inverted concave shape were finally determined;

[0078] Step S5: Construct a concave mesh based on the 8 vertices determined in Step S4; specifically, this includes the following steps:

[0079] Step S51: Add the 4 points on each side to the 6 points on one side of the structure that continues to extend downwards from the bottom;

[0080] Step S52: Connect the 6 points on the left and the 6 points on the right in sequence, and take points in segments to use as sample points for constructing a closed fitted b-spline curve.

[0081] The expression for a b-spline curve is: Where u is a vector of a point; N i p (u) Denotes the i-th p-th (p+1-th) b-spline basis function;

[0082] Step S53: Select points on the curve sequentially at intervals to form the edge points of the constructed mesh;

[0083] Step S54: Based on the edge line points, construct a grid by connecting the bottom and side points to form an inverted concave square grid.

[0084] This embodiment also provides an automatic concave point design system that calculates geometric relationships in graphics, including:

[0085] One or more processors; and

[0086] One or more memories storing a computer-executable program, wherein the aforementioned method is performed when the processor executes the computer-executable program.

[0087] This embodiment of the automatic undercut point design method and system, which calculates geometric relationships, primarily uses the relationships between the regular geometric positions and shapes of various teeth to locate the specific control points of the undercut through geometric cutting, parallel mapping, intersection subtraction, and other methods. It then uses computer-aided calculations, such as distance calculation, nearest point calculation, and statistical analysis of geometric information from neighboring regions, to automatically correct any misaligned undercut points. The undercut points obtained through this method are relatively stable and closely resemble actual conditions. Furthermore, the computer generates the curve composition of the undercut blocks based on the control sheet, resulting in a high-quality mesh. Production operators can save time and quickly design undercuts, improving efficiency.

[0088] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. An automatic concave point design method based on calculating geometric relationships of graphics, characterized in that: Includes the following steps: Step S1: Construct a local coordinate system based on the tooth segmentation coil, including the following steps: Step S11: Take out two adjacent teeth and obtain the tooth segmentation coil of the crown edge after processing by the tooth segmentation software; Step S12: The line connecting the center points of the dividing coils of the two teeth is taken as the X-axis. The Z-axis in the small coordinate system of the teeth defined by the tooth dividing software is taken as the Z-axis of the local coordinate system. The Y-axis of the two teeth is calculated by cross product, with the starting point being the midpoint of the line connecting the center points, which serves as the two determined local coordinate systems. Step S2: Calculate the proximal surface length of each of the left and right teeth, and formulate the height-to-width ratio offset coefficients for different tooth positions, including the following steps: Step S21: Obtain the projection distance of the line connecting each point of a set of tooth cutting lines to the origin in the Y-axis direction of the local coordinate system. Step S22: After obtaining a set of projection distance data, calculate the difference between the maximum and minimum values ​​as the maximum length of the adjacent surface, which is defined as the maximum width of the tooth. Step S23: Adjust the origin of the small coordinate system according to the morphological characteristics of the teeth to facilitate subsequent geometric cutting and projection calculations based on this. Step S24: Based on the width and height ratio information table of the adjacent surfaces of different tooth positions, compile the height-width ratio coefficients for different tooth positions to facilitate the adjustment of undercut filling materials that better fit the tooth positions; Step S3: Calculate the position of the undercut construction vertex on the projection plane of the tooth proximal surface; Step S4: For points with severe vertex position offset, perform anomaly detection and automatically iterate and adjust to return to their original positions to determine the 8 vertices formed by the inverted concavity; Step S5: Construct an inverted concave mesh based on the 8 vertices determined in step S4.

2. An automatic concave point design system based on calculating geometric relationships in graphics, characterized in that: include: One or more processors; as well as One or more memories storing a computer-executable program that, when executed by the processor, performs the method of claim 1.

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