Orthodontic archwire evaluation method based on coplanar isogonal vectors

Abstract

The application discloses an orthodontic arch wire evaluation method based on coplanar isogonal vectors, and relates to the field of orthodontic arch wire bending evaluation. The application is based on a set of bending point information of a theoretical orthodontic arch wire curve after spatial transformation, a set of bending point information of an actual orthodontic arch wire curve after spatial transformation, judges the isogonal point distance of the orthodontic arch wire, then combines the judgment of the isogonal vector angle and the maximum included angle between the coplanar isogonal vector group of the orthodontic arch wire and a base vector, and establishes an orthodontic arch wire evaluation method based on coplanar isogonal vectors. The application effectively improves the efficiency of the parameterized evaluation of the orthodontic arch wire, realizes the quantitative evaluation of the orthodontic arch wire by calculating the isogonal point distance of the actual orthodontic arch wire curve, the isogonal vector angle and the maximum included angle between the coplanar isogonal vector group of the orthodontic arch wire and the base vector.

Description

Technical Field

[0001] This invention patent relates to an orthodontic archwire evaluation method based on coplanar equiangular vectors, belonging to the field of orthodontic archwire bending evaluation. Background Technology

[0002] Malocclusion is the third leading cause of oral health problems, with a high incidence rate. In modern dentistry, fixed orthodontic treatment is a common and effective method. The bending of orthodontic archwires is crucial to fixed orthodontic techniques. In recent years, influenced by digital manufacturing technology, traditional dental manufacturing processes are undergoing revolutionary changes. The field of orthodontics is also benefiting from digital technology, and the processing of archwires in orthodontic appliances is moving towards digitalization. Using orthodontic archwire bending robots to bend orthodontic archwires has become a new, fast, and effective method. However, evaluating the orthodontic archwires bent by the robot is a prerequisite for achieving digital processing, ensuring the effectiveness of robot bending, and guaranteeing bending accuracy. Currently, orthodontic archwire evaluation still largely relies on doctors' clinical experience to determine whether the archwires meet the requirements. This method not only heavily depends on doctors' experience but is also inefficient and lacks parameterized judgment criteria.

[0003] Furthermore, considering that the bending points on the orthodontic archwire curve are independent during bending, meaning that the bending of the current bending point is not affected by the bending effect of the previous bending point, but the bending effect of the orthodontic archwire between adjacent bending points is determined by these two bending points, the bending effect of the orthodontic archwire between adjacent points can be evaluated by the bending effect of adjacent points. However, current orthodontic archwire evaluation methods lack a method to evaluate orthodontic archwires by dividing and selecting a portion of orthodontic archwire points for judgment. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes an orthodontic archwire evaluation method based on coplanar equiangular vectors. This method solves the problem of the lack of a way to evaluate orthodontic archwires by dividing and selecting a portion of the archwire points. It achieves efficient, accurate, and rapid evaluation of orthodontic archwires, avoiding the need for extensive and complex calculations, and thus enabling efficient and accurate digital bending of orthodontic archwires.

[0005] An orthodontic archwire evaluation method based on coplanar isoangular vectors, characterized in that: the specific implementation process of the method is as follows:

[0006] Step 1: Import theoretical and actual orthodontic archwire curve data:

[0007] A three-dimensional orthodontic archwire error evaluation coordinate system w is established using the right-hand rule (o-xyz). A theoretical orthodontic archwire curve with n bending points, designed by the orthodontist based on the patient's dentition morphology, is calculated and input into the theoretical orthodontic archwire curve bending point information set P'. T ={ T p'1, T p'2, T p'3,..., T p' i ,..., T p' n}, T p' i =( T x' i , T y' i , T z' i (i) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where the value of i ranges from 1 to i to n. T x' i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T y' i Let be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T z' i Let p be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w; p is the left endpoint of the theoretical orthodontic archwire curve. s The theoretical right endpoint of the orthodontic archwire curve is p. f p s and p f The midpoint of the line connecting them is T o', spatial transformation of the theoretical orthodontic archwire curve: Let point T o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p of the theoretical orthodontic archwire curve s Located on the negative y-axis, the right endpoint p of the theoretical orthodontic archwire curve f Located on the positive y-axis, and with no intersection between the theoretical orthodontic archwire curve and the positive x-axis, the theoretical orthodontic archwire curve is rotated clockwise along the positive y-axis until it intersects with the positive x-axis. The pose of the theoretical orthodontic archwire curve after spatial transformation is set as its final pose in the three-dimensional orthodontic archwire error evaluation coordinate system w. The bending point information set P of the translated and rotated theoretical orthodontic archwire curve is calculated and input. T ={ T p1, T p2, T p3,...,T p i ,..., T p n}, T p i =( T x i , T y i , T z i ) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: T x i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T y i Let y be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T z i Let z be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation in the three-dimensional orthodontic archwire evaluation coordinate system w.

[0008] Calculate and input the actual orthodontic archwire curve bending point information set P', which is the actual orthodontic archwire curve with n bending points, based on the theoretical orthodontic archwire curve. R ={ R p'1, R p'2, R p'3,… R p' i ,…, R p' n}, R p' i =( R x' i , R y' i , R z' i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x' i Let x be the x-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R y' i Let y be the y-coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z' i Let p' be the z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w; p' is the left endpoint of the actual orthodontic archwire curve. sThe actual right endpoint of the orthodontic archwire curve is p' f ,p' s and p' f The midpoint of the line connecting them is R o', perform a spatial transformation on the actual orthodontic archwire curve: Let point R o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p' of the actual orthodontic archwire curve s Located on the negative y-axis, the right endpoint p' of the actual orthodontic archwire curve f Located on the positive y-axis, and with no intersection between the actual orthodontic archwire curve and the x-axis; rotate the actual orthodontic archwire curve clockwise around the positive y-axis until it intersects the x-axis. Set the pose of the actual orthodontic archwire curve after spatial transformation to its pose in the three-dimensional orthodontic archwire evaluation coordinate system w. Calculate and input the set of bending point information P of the actual orthodontic archwire curve after setting. R ={ R p1, R p2, R p3,… R p i ,…, R p n}, R p i =( R x i , R y i , R z i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x i The x-coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the x-axis of the three-dimensional orthodontic archwire evaluation coordinate system w. R y i Let y be the y-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z i The z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w.

[0009] Step 2: Determining the distance between the isoangular points of the actual orthodontic archwire:

[0010] In the xoy plane, starting from the negative y-axis and ending at the positive y-axis, with the origin o as the endpoint, ... To bisect the angle equally, draw H·N+1 equal-angle rays h. mH·N+1 isoangular rays divide the upper half of the xoy plane, including the positive x-axis, into H·N equal parts. The isoangular rays h m With equal angle h m+1 The included angle between them is Divide the H·N equally divided angles into groups of H adjacent equally divided angles, resulting in N groups. The value of m ranges from m = 1, 2, 3, ..., H·N+1, where the isoangular ray h1 coincides with the negative y-axis. H·N+1 Let the ray h coincide with the positive y-axis. m In h m The ray h rotates about the origin o in the plane containing the z-axis. m Intersects the actual orthodontic archwire curve at point isoangular ray h m Intersects the theoretical orthodontic archwire curve at point Define an isoangular point, which represents the intersection of an isoangular ray and the orthodontic archwire curve; the isoangular point of the actual orthodontic archwire curve is defined as 'a'. m The isoangular point of the theoretical orthodontic archwire curve is defined as b. m Define an isoangular vector, using the symbol... An isoangular vector is defined as a vector whose starting point is the intersection of the same isoangular ray with the actual orthodontic archwire curve and its ending point is the intersection with the theoretical orthodontic archwire curve; the isoangular point 'a' of the actual orthodontic archwire curve is defined as... m An isoangular vector is represented as and The set of isoangular vectors of the isoangular points of the actual orthodontic archwire curve is calculated.

[0011] Define the isoangular point distance, denoted by the symbol L. The isoangular point distance represents the distance between the intersection of the same isoangular ray with the actual orthodontic archwire curve and with the theoretical orthodontic archwire curve. Define the isoangular point a of the actual orthodontic archwire curve. m Isometric point distance The set of isoangular point distances of the actual orthodontic archwire curve was calculated. The upper limit of the distance between the isoangular points of the actual orthodontic archwire curve is specified as L. max ;

[0012] judge Is it valid?

[0013] like If the condition is met, it means that the distance between all the isoangular points of the actual orthodontic archwire curve is within the specified range, then proceed to step three;

[0014] like If this condition is not met, it means that the distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range. Therefore, the output is: The distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range; Orthodontic archwire evaluation complete.

[0015] Step 3: Determining the angle of the isoangular vector of the actual orthodontic archwire curve:

[0016] Define an angle between an equal-angle vector and the z-axis, denoted by the symbol α. The direction vector of the z-axis is defined as... The isoangular vector of the actual orthodontic archwire curve is specified. equal-angle vectors The set of isoangular vector angles of the actual orthodontic archwire curve is calculated. The upper limit of the isoangular vector angle of the actual orthodontic archwire curve is specified as α. max ;

[0017] judge Is it valid?

[0018] like If the condition is met, it means that the angles of the isoangular vectors of the actual orthodontic archwire curve are all within the specified range, then proceed to step four;

[0019] like If this condition is not met, it means that the isoangular vector angle of the actual orthodontic archwire curve is not within the specified range; therefore, the output is: The isoangular vector angle of the actual orthodontic archwire curve is not within the specified range, and the orthodontic archwire evaluation is complete.

[0020] Step 4: Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve:

[0021] Define coplanar isoangular vectors, using the symbol The term "coplanar isoangular vector" means that setting the y-axis coordinate of the isoangular vector to 0 transforms the spatial vector into a planar vector on the same plane; the isoangular vector of the actual orthodontic archwire curve... y-axis coordinate The coplanar isoangular vectors in the xoz plane are represented as follows: The set of isoangular vectors of the theoretical orthodontic archwire curve is transformed into vectors in the xoz plane to obtain a set of coplanar isoangular vectors. Define a set of coplanar isoangular vectors, denoted by G. A set of coplanar isoangular vectors represents a vector group containing any coplanar isoangular vector and H consecutive coplanar vectors to its right. The coplanar isoangular vectors of actual orthodontic archwire curves are defined. Coplanar equal-angle vectors that are continuous with it on its right The coplanar isoangular vector group is represented by G. m ,and Define the coplanar angular vectors of the actual orthodontic archwire curves The angle between the z-axis and the z-axis is denoted as and Define the basis vectors of a coplanar set of equal-angle vectors, using the symbol... It is indicated that the basis vectors of a coplanar isoangular vector group are the coplanar isoangular vectors in the group that make the largest angle with the z-axis; the coplanar isoangular vector group G is defined as follows: m The basis vectors of the coplanar isoangular vector group are denoted as Define the angle between the vector and the basis vectors, using the symbol... The angle between the vector and the basis vectors represents the angle between a vector in a coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve is defined as the coplanar isoangular vector group G. m Coplanar isoangular vectors basis vectors of the coplanar isoangular vector group The included angle is denoted as and The range of values ​​for v is v = 1, 2, 3, ..., H; the maximum angle between a set of coplanar equal-angle vectors and a basis vector is defined by the symbol η. G The maximum angle between the coplanar isoangular vector group and the basis vectors represents the maximum angle between the coplanar isoangular vectors in the coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve coplanar isoangular vector group G is defined as... m The maximum angle between the coplanar isoangular vector group and the basis vectors The maximum angle between the actual orthodontic archwire coplanar equiangular vector set and the basis vectors is defined as η. max ;

[0022] Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve;

[0023] Initialize m = 1;

[0024] The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The set of angles between the common plane's equal-angle vectors and the z-axis Actual orthodontic archwire curves coplanar equiangular vector set G m The coplanar isoplanar vector corresponding to the maximum angle between the coplanar isoplanar vector and the z-axis is the actual orthodontic archwire curve coplanar isoplanar vector set G. m coplanar isoangular vector group basis vectors The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The coplanar angular vectors of the common plane and the actual orthodontic archwire curve are coplanar angular vector groups G m coplanar isoangular vector group basis vectors The set of angles between the vectors and the basis vectors The calculated set of coplanar equiangular vectors G of the actual orthodontic archwire curves m The maximum angle between the coplanar isoangular vector group and the basis vectors

[0025] judge Is it valid?

[0026] like The validity of this statement indicates that the actual orthodontic archwire curves are coplanar, equiangular vector groups G. m If the maximum angle between the coplanar equal-angle vector group and the basis vectors is within the specified range, then proceed to step five;

[0027] like This is incorrect, indicating that the actual orthodontic archwire curves are coplanar, equiangular vector sets G. m If the maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, then the output is: the actual orthodontic archwire curve coplanar isoangular vector group G. m The maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, and the orthodontic archwire evaluation is complete;

[0028] Step 5: Determine whether all coplanar isoangular vector groups of the actual orthodontic archwire curve have been evaluated:

[0029] Determine whether m + H = H·N + 1 is true;

[0030] If m+H=H·N+1 does not hold, it means that the coplanar equiangular vector group of the actual orthodontic archwire curve has not been fully evaluated. Let m=m+H and then jump to step four.

[0031] If m+H=H·N+1 holds true, it means that the coplanar isoangular vector groups of the actual orthodontic archwire curve have all been evaluated, and the maximum angle between the coplanar isoangular vector groups of the actual orthodontic archwire curve and the basis vectors is within the specified range. Output: The distance between isoangular points, the isoangular vector angle, and the maximum angle between the coplanar isoangular vector groups and the basis vectors of the actual orthodontic archwire curve are all within the specified range, and the orthodontic archwire evaluation is complete.

[0032] The beneficial effects of this invention are as follows:

[0033] 1. In the process of evaluating orthodontic archwires, this invention proposes the concept of isoangular point distance. The difference between the bending effect of the actual orthodontic archwire and the theoretical orthodontic archwire is parametrically described by the distance between the intersection point of the same ray with the actual orthodontic archwire curve and the intersection point with the theoretical orthodontic archwire curve. This facilitates the next step of evaluating orthodontic archwires based on isoangular vectors.

[0034] 2. In the process of evaluating orthodontic archwires, this invention proposes the concept of the maximum angle between a set of coplanar isoangular vectors and the basis vectors. The maximum angle between the coplanar isoangular vectors in the set of coplanar isoangular vectors and the basis vectors of the set of coplanar isoangular vectors is used to quantitatively describe the pose changes of the actual orthodontic archwires within a certain range. By combining the maximum angle between the set of coplanar isoangular vectors and the basis vectors with the distance between isoangular points and the angle of the isoangular vectors, the bending effect of the orthodontic archwires can be evaluated efficiently and parametrically.

[0035] 3. Compared to "An Orthodontic Archwire Evaluation Method Based on Bending Point Value," although both methods are applicable to a class of personalized orthodontic archwire curves with special attributes, the method mentioned in "An Orthodontic Archwire Evaluation Method Based on Bending Point Value" focuses on evaluating the archwire based on the different bending effects required at the bending points, using the bending point value as a parameter to determine the radius of the archwire envelope, thus providing a direct evaluation. This method, however, focuses on evaluating the archwire under the same bending effect requirements at all points, using the point distance L of equiangular points, the angle α of equiangular vectors, and the maximum angle between the coplanar equiangular vector group and the basis vectors. As an evaluation parameter for orthodontic archwires, the bending effect of a point can be used to describe the bending effect of the orthodontic archwire segment, which reduces the workload while ensuring evaluation accuracy. The two methods are applied differently in actual orthodontic archwire evaluation. Therefore, the proposed method compensates for the other method, thereby improving the series of methods for actual orthodontic archwire evaluation.

[0036] 4. Compared with "A Point-to-Interval Orthodontic Archwire Evaluation Method", this patent first judges the distance between the isoangular points of the orthodontic archwire. When the requirements are met, it further evaluates the archwire using the isoangular vector angle and the maximum angle between the coplanar isoangular vector group and the basis vector as parameters. This can reduce the workload and effectively improve the efficiency of orthodontic archwire evaluation while ensuring the accuracy of the evaluation. Attached Figure Description

[0037] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0038] Figure 1 This is a flowchart of an orthodontic archwire evaluation method based on coplanar isoangular vectors;

[0039] Figure 2 This is a pose diagram of the orthodontic archwire in the three-dimensional orthodontic archwire evaluation coordinate system.

[0040] Figure 3 This is a schematic diagram of the rotation of an isoangular ray;

[0041] Figure 4 A schematic diagram of an isoangular vector;

[0042] Figure 5 A schematic diagram of the rotation of isoangular rays and isoangular vectors in the three-dimensional orthodontic archwire evaluation coordinate system with 19 bending points; Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention patent clearer, the invention patent is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of this invention patent. Furthermore, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of this invention patent.

[0044] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, this specific embodiment adopts the following technical solution: an orthodontic archwire evaluation method based on coplanar isoangular vectors, the specific implementation process of which is as follows:

[0045] Step 1: Import theoretical and actual orthodontic archwire curve data:

[0046] A three-dimensional orthodontic archwire error evaluation coordinate system w is established using the right-hand rule (o-xyz). A theoretical orthodontic archwire curve with n bending points, designed by the orthodontist based on the patient's dentition morphology, is calculated and input into the theoretical orthodontic archwire curve bending point information set P'. T ={ T p'1, T p'2, T p'3,..., T p' i ,..., T p' n}, T p' i =( T x' i , T y' i , T z' i (i) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where the value of i ranges from 1 to i to n. T x' i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T y' i Let be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T z' iLet p be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w; p is the left endpoint of the theoretical orthodontic archwire curve. s The theoretical right endpoint of the orthodontic archwire curve is p. f p s and p f The midpoint of the line connecting them is T o', spatial transformation of the theoretical orthodontic archwire curve: Let point T o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p of the theoretical orthodontic archwire curve s Located on the negative y-axis, the right endpoint p of the theoretical orthodontic archwire curve f Located on the positive y-axis, and with no intersection between the theoretical orthodontic archwire curve and the positive x-axis, the theoretical orthodontic archwire curve is rotated clockwise along the positive y-axis until it intersects with the positive x-axis. The pose of the theoretical orthodontic archwire curve after spatial transformation is set as its final pose in the three-dimensional orthodontic archwire error evaluation coordinate system w. The bending point information set P of the translated and rotated theoretical orthodontic archwire curve is calculated and input. T ={ T p1, T p2, T p3,..., T p i ,..., T p n}, T p i =( T x i , T y i , T z i ) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: T x i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T y i Let y be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T z i Let z be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation in the three-dimensional orthodontic archwire evaluation coordinate system w.

[0047] Calculate and input the actual orthodontic archwire curve bending point information set P', which is the actual orthodontic archwire curve with n bending points, based on the theoretical orthodontic archwire curve. R ={ R p'1,R p'2, R p'3,… R p' i ,…, R p' n}, R p' i =( R x' i , R y' i , R z' i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x' i Let x be the x-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R y' i Let y be the y-coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z' i Let p' be the z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w; p' is the left endpoint of the actual orthodontic archwire curve. s The actual right endpoint of the orthodontic archwire curve is p' f ,p' s and p' f The midpoint of the line connecting them is R o', perform a spatial transformation on the actual orthodontic archwire curve: Let point R o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p' of the actual orthodontic archwire curve s Located on the negative y-axis, the right endpoint p' of the actual orthodontic archwire curve f Located on the positive y-axis, the actual orthodontic archwire curve has no intersection with the x-axis. Rotate the actual orthodontic archwire curve clockwise around the y-axis until it intersects with the x-axis. Set the pose of the actual orthodontic archwire curve after spatial transformation to its pose in the three-dimensional orthodontic archwire evaluation coordinate system w. Calculate and input the set of bending point information P of the actual orthodontic archwire curve after setting. R ={ R p1, R p2, R p3,… R p i ,…, R p n}, R p i =( R x i , R y i ,R z i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x i The x-coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the x-axis of the three-dimensional orthodontic archwire evaluation coordinate system w. R y i Let y be the y-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z i The z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w.

[0048] Step 2: Determining the distance between the isoangular points of the actual orthodontic archwire:

[0049] In the xoy plane, starting from the negative y-axis and ending at the positive y-axis, with the origin o as the endpoint, ... To bisect the angle equally, draw H·N+1 equal-angle rays h. m H·N+1 isoangular rays divide the upper half of the xoy plane, including the positive x-axis, into H·N equal parts. The isoangular rays h m With equal angle h m+1 The included angle between them is Divide the H·N equally divided angles into groups of H adjacent equally divided angles, resulting in N groups. The value of m ranges from m = 1, 2, 3, ..., H·N+1, where the isoangular ray h1 coincides with the negative y-axis. H·N+1 Let the ray h coincide with the positive y-axis. m In h m The ray h rotates about the origin o in the plane containing the z-axis. m Intersects the actual orthodontic archwire curve at point isoangular ray h m Intersects the theoretical orthodontic archwire curve at point Define an isoangular point, which represents the intersection of an isoangular ray and the orthodontic archwire curve; the isoangular point of the actual orthodontic archwire curve is defined as 'a'. m The isoangular point of the theoretical orthodontic archwire curve is defined as b. m Define an isoangular vector, using the symbol... An isoangular vector is defined as a vector whose starting point is the intersection of the same isoangular ray with the actual orthodontic archwire curve and its ending point is the intersection with the theoretical orthodontic archwire curve; the isoangular point 'a' of the actual orthodontic archwire curve is defined as... m An isoangular vector is represented as and The set of isoangular vectors of the isoangular points of the actual orthodontic archwire curve is calculated.

[0050] Define the isoangular point distance, denoted by the symbol L. The isoangular point distance represents the distance between the intersection of the same isoangular ray with the actual orthodontic archwire curve and with the theoretical orthodontic archwire curve. Define the isoangular point a of the actual orthodontic archwire curve. m Isometric point distance The set of isoangular point distances of the actual orthodontic archwire curve was calculated. The upper limit of the distance between the isoangular points of the actual orthodontic archwire curve is specified as L. max ;

[0051] judge Is it valid?

[0052] like If the condition is met, it means that the distance between all the isoangular points of the actual orthodontic archwire curve is within the specified range, then proceed to step three;

[0053] like If this condition is not met, it means that the distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range. Therefore, the output is: The distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range; Orthodontic archwire evaluation complete.

[0054] Step 3: Determining the angle of the isoangular vector of the actual orthodontic archwire curve:

[0055] Define an angle between an equal-angle vector and the z-axis, denoted by the symbol α. The direction vector of the z-axis is defined as... The isoangular vector of the actual orthodontic archwire curve is specified. equal-angle vectors The set of isoangular vector angles of the actual orthodontic archwire curve is calculated. The upper limit of the isoangular vector angle of the actual orthodontic archwire curve is specified as α. max ;

[0056] judge Is it valid?

[0057] like If the condition is met, it means that the angles of the isoangular vectors of the actual orthodontic archwire curve are all within the specified range, then proceed to step four;

[0058] like If this condition is not met, it means that the isoangular vector angle of the actual orthodontic archwire curve is not within the specified range; therefore, the output is: The isoangular vector angle of the actual orthodontic archwire curve is not within the specified range, and the orthodontic archwire evaluation is complete.

[0059] Step 4: Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve:

[0060] Define coplanar isoangular vectors, using the symbol The term "coplanar isoangular vector" means that setting the y-axis coordinate of the isoangular vector to 0 transforms the spatial vector into a planar vector on the same plane; the isoangular vector of the actual orthodontic archwire curve... y-axis coordinate The coplanar isoangular vectors in the xoz plane are represented as follows: The set of isoangular vectors of the theoretical orthodontic archwire curve is transformed into vectors in the xoz plane to obtain a set of coplanar isoangular vectors. Define a set of coplanar isoangular vectors, denoted by G. A set of coplanar isoangular vectors represents a vector group containing any coplanar isoangular vector and H consecutive coplanar vectors to its right. The coplanar isoangular vectors of actual orthodontic archwire curves are defined. Coplanar equal-angle vectors that are continuous with it on its right The coplanar isoangular vector group is represented by G. m ,and Define the coplanar angular vectors of the actual orthodontic archwire curves The angle between the z-axis and the z-axis is denoted as and Define the basis vectors of a coplanar set of equal-angle vectors, using the symbol... It is indicated that the basis vectors of a coplanar isoangular vector group are the coplanar isoangular vectors in the group that make the largest angle with the z-axis; the coplanar isoangular vector group G is defined as follows: m The basis vectors of the coplanar isoangular vector group are denoted as Define the angle between the vector and the basis vectors, using the symbol... The angle between the vector and the basis vectors represents the angle between a vector in a coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve is defined as the coplanar isoangular vector group G. m Coplanar isoangular vectors basis vectors of the coplanar isoangular vector group The included angle is denoted as and The range of values ​​for v is v = 1, 2, 3, ..., H; the maximum angle between a set of coplanar equal-angle vectors and a basis vector is defined by the symbol η. G The maximum angle between the coplanar isoangular vector group and the basis vectors represents the maximum angle between the coplanar isoangular vectors in the coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve coplanar isoangular vector group G is defined as... m The maximum angle between the coplanar isoangular vector group and the basis vectors The maximum angle between the actual orthodontic archwire coplanar equiangular vector set and the basis vectors is defined as η. max ;

[0061] Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve;

[0062] Initialize m = 1;

[0063] The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The set of angles between the common plane's equal-angle vectors and the z-axis Actual orthodontic archwire curves coplanar equiangular vector set G m The coplanar isoplanar vector corresponding to the maximum angle between the coplanar isoplanar vector and the z-axis is the actual orthodontic archwire curve coplanar isoplanar vector set G. m coplanar isoangular vector group basis vectors The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The coplanar angular vectors of the common plane and the actual orthodontic archwire curve are coplanar angular vector groups G m coplanar isoangular vector group basis vectors The set of angles between the vectors and the basis vectors The calculated set of coplanar equiangular vectors G of the actual orthodontic archwire curves m The maximum angle between the coplanar isoangular vector group and the basis vectors

[0064] judge Is it valid?

[0065] like The validity of this statement indicates that the actual orthodontic archwire curves are coplanar, equiangular vector groups G. m If the maximum angle between the coplanar equal-angle vector group and the basis vectors is within the specified range, then proceed to step five;

[0066] like This is incorrect, indicating that the actual orthodontic archwire curves are coplanar, equiangular vector sets G. m If the maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, then the output is: the actual orthodontic archwire curve coplanar isoangular vector group G. m The maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, and the orthodontic archwire evaluation is complete;

[0067] Step 5: Determine whether all coplanar isoangular vector groups of the actual orthodontic archwire curve have been evaluated:

[0068] Determine whether m + H = H·N + 1 is true;

[0069] If m+H=H·N+1 does not hold, it means that the coplanar equiangular vector group of the actual orthodontic archwire curve has not been fully evaluated. Let m=m+H and then jump to step four.

[0070] If m+H=H·N+1 holds true, it means that the coplanar isoangular vector groups of the actual orthodontic archwire curve have all been evaluated, and the maximum angle between the coplanar isoangular vector groups of the actual orthodontic archwire curve and the basis vectors is within the specified range. Output: The distance between isoangular points, the isoangular vector angle, and the maximum angle between the coplanar isoangular vector groups and the basis vectors of the actual orthodontic archwire curve are all within the specified range, and the orthodontic archwire evaluation is complete.

[0071] Example 2: As Figure 2 , Figure 3 , Figure 4 , Figure 5 As shown, taking an orthodontic archwire with 19 bending points as an example, the theoretical orthodontic archwire curve bending point information set P' is input. T ={ T P'1, T P'2, T P'3, ..., T P' 21}, Input the theoretical orthodontic archwire space curve bending point information set P after translation and rotation. T ={ T P1, T P2, T P3, ..., T P 21}, Input the actual orthodontic archwire space curve bending point information set P' R ={ R P'1, R P'2, R P'3, ..., R P' 21}, Input the actual orthodontic archwire space curve bending point information set P after setting. R ={ R P1, R P2, R P3, ..., R P 21 In the xoy plane, starting from the negative y-axis and ending at the positive y-axis, with the origin o as the endpoint, draw 19 equal-angled rays h, each bisected by 10°. m Nineteen isoangular rays divide the upper half of the xoy plane, which includes the positive x-axis, into 18 equal parts. The isoangular ray h... m With equal angle h m+1 The included angle between them is 10°. Divide the 18 equally spaced angles into groups of 6 adjacent equally spaced angles, resulting in 3 groups. The value of m ranges from m = 1, 2, 3, ..., 19. Among them, the isoangular ray h1 coincides with the negative half-axis of the y-axis, and the isoangular ray h... 19 Let the ray h coincide with the positive y-axis. m In h mThe ray h rotates about the origin o in the plane containing the z-axis. m Intersects the actual orthodontic archwire curve at point isoangular ray h m Intersects the theoretical orthodontic archwire curve at point The set of isoangular vectors of the isoangular points of the actual orthodontic archwire curve is calculated. The set of isoangular point distances of the actual orthodontic archwire curve was calculated. The upper limit of the distance between the isoangular points of the actual orthodontic archwire curve is specified as L. max ; Assumption If the condition is met, proceed to step three to calculate the set of isoangular vector angles at isoangular points of the actual orthodontic archwire curve. The upper limit of the angle of the isoangular vector of the actual orthodontic archwire curve is defined as α. max Assuming If the above steps are established, proceed to step four and set the isoangular vector of the actual orthodontic archwire curve. y-axis coordinate The coplanar isoangular vectors in the xoz plane are represented as follows: The set of isoangular vectors of the theoretical orthodontic archwire is transformed into coplanar vectors in the xoz plane to obtain the set of coplanar isoangular vectors. The maximum angle between the actual orthodontic archwire coplanar equiangular vector set and the basis vectors is defined as η. max The maximum angle between the coplanar isoangular vector set of the actual orthodontic archwire curve and the basis vectors is determined. m is initialized to 1, and the coplanar isoangular vector set of the actual orthodontic archwire curve is calculated. The set of angles between the common plane's equal-angle vectors and the z-axis The coplanar isoplanar vector corresponding to the maximum angle between the coplanar isoplanar vectors in the actual orthodontic archwire curve coplanar isoplanar vector group G1 is the basis vector of the actual orthodontic archwire curve coplanar isoplanar vector group G1. The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The basis vectors of the coplanar isoplanar vector group G1, which is coplanar with the actual orthodontic archwire curve. The set of angles between the vectors and the basis vectors The maximum angle between the coplanar isoplanar vector group G1 of the actual orthodontic archwire curve and the basis vectors was calculated. Assumption If this condition is not met, it means that the maximum angle between the coplanar isoangular vector group G1 of the actual orthodontic archwire curve and the basis vector is not within the specified range. Output: The maximum angle between the coplanar isoangular vector group G1 of the actual orthodontic archwire curve and the basis vector is not within the specified range. Orthodontic archwire evaluation is complete.

Claims

1. A method for evaluating orthodontic archwires based on coplanar isoangular vectors, characterized in that: The specific implementation process of the method is as follows: Step 1: Import theoretical and actual orthodontic archwire curve data: A three-dimensional orthodontic archwire error evaluation coordinate system w is established using the right-hand rule (o-xyz). A theoretical orthodontic archwire curve with n bending points, designed by the orthodontist based on the patient's dentition morphology, is calculated and input into the theoretical orthodontic archwire curve bending point information set P'. T ={ T p'1, T p'2, T p'3,..., T p' i ,..., T p' n }, T p' i =( T x' i , T y' i , T z' i (i) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where the value of i ranges from 1 to i to n. T x' i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T y' i Let be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w. T z' i Let p be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire evaluation coordinate system w; p is the left endpoint of the theoretical orthodontic archwire curve. s The theoretical right endpoint of the orthodontic archwire curve is p. f p s and p f The midpoint of the line connecting them is T o', spatial transformation of the theoretical orthodontic archwire curve: Let point T o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p of the theoretical orthodontic archwire curve s Located on the negative y-axis, the right endpoint p of the theoretical orthodontic archwire curve f Located on the positive y-axis, and with no intersection between the theoretical orthodontic archwire curve and the positive x-axis, the theoretical orthodontic archwire curve is rotated clockwise along the positive y-axis until it intersects with the positive x-axis. The pose of the theoretical orthodontic archwire curve after spatial transformation is set as its final pose in the three-dimensional orthodontic archwire error evaluation coordinate system w. The bending point information set P of the translated and rotated theoretical orthodontic archwire curve is calculated and input. T ={ T p1, T p2, T p3,..., T p i ,..., T p n }, T p i =( T x i , T y i , T z i ) represents the pose information of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: T x i Let x be the x-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T y i Let y be the y-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation, in the three-dimensional orthodontic archwire evaluation coordinate system w. T z i Let z be the z-axis coordinate of the i-th bending point of the theoretical orthodontic archwire curve after translation and rotation in the three-dimensional orthodontic archwire evaluation coordinate system w. Calculate and input the actual orthodontic archwire curve bending point information set P', which is the actual orthodontic archwire curve with n bending points, based on the theoretical orthodontic archwire curve. R ={ R p'1, R p'2, R p'3,… R p' i ,…, R p' n }, R p' i =( R x' i , R y' i , R z' i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x' i Let x be the x-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R y' i Let y be the y-coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z' i Let p' be the z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire evaluation coordinate system w; p' is the left endpoint of the actual orthodontic archwire curve. s The actual right endpoint of the orthodontic archwire curve is p' f ,p' s and p' f The midpoint of the line connecting them is R o', perform a spatial transformation on the actual orthodontic archwire curve: Let point R o' coincides with the origin o of the three-dimensional orthodontic archwire evaluation coordinate system w, and the left endpoint p' of the actual orthodontic archwire curve s Located on the negative y-axis, the right endpoint p' of the actual orthodontic archwire curve f Located on the positive y-axis, and with no intersection between the actual orthodontic archwire curve and the positive x-axis; rotate the actual orthodontic archwire curve clockwise around the positive y-axis until it intersects the x-axis. Set the pose of the actual orthodontic archwire curve after spatial transformation to its pose in the three-dimensional orthodontic archwire evaluation coordinate system w. Calculate and input the set of bending point information P of the actual orthodontic archwire curve after setting. R ={ R p1, R p2, R p3,… R p i ,…, R p n }, R p i =( R x i , R y i , R z i ) represents the pose information of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w, where: R x i The x-coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the x-axis of the three-dimensional orthodontic archwire evaluation coordinate system w. R y i Let y be the y-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w. R z i The z-axis coordinate of the i-th bending point of the actual orthodontic archwire curve after translation and rotation, relative to the three-dimensional orthodontic archwire evaluation coordinate system w. Step 2: Determining the distance between the isoangular points of the actual orthodontic archwire: In the xoy plane, starting from the negative y-axis and ending at the positive y-axis, with the origin o as the endpoint, ... To bisect the angle equally, draw H·N+1 equal-angle rays h. m H·N+1 isoangular rays divide the upper half of the xoy plane, including the positive x-axis, into H·N equal parts. The isoangular rays h m With equal angle h m+1 The included angle between them is Divide the H·N equally divided angles into groups of H adjacent equally divided angles, resulting in N groups. The value of m ranges from m = 1, 2, 3, ..., H·N+1, where the isoangular ray h1 coincides with the negative y-axis. H·N+1 Let the ray h coincide with the positive y-axis. m In h m The ray h rotates about the origin o in the plane containing the z-axis. m Intersects the actual orthodontic archwire curve at point isoangular ray h m Intersects the theoretical orthodontic archwire curve at point Define an isoangular point, which represents the intersection of an isoangular ray and the orthodontic archwire curve; the isoangular point of the actual orthodontic archwire curve is defined as 'a'. m The isoangular point of the theoretical orthodontic archwire curve is defined as b. m Define an isoangular vector, using the symbol... An isoangular vector is defined as a vector whose starting point is the intersection of the same isoangular ray with the actual orthodontic archwire curve and its ending point is the intersection with the theoretical orthodontic archwire curve; the isoangular point 'a' of the actual orthodontic archwire curve is defined as... m An isoangular vector is represented as and The set of isoangular vectors of the isoangular points of the actual orthodontic archwire curve is calculated. Define the isoangular point distance, denoted by the symbol L. The isoangular point distance represents the distance between the intersection of the same isoangular ray with the actual orthodontic archwire curve and with the theoretical orthodontic archwire curve. Define the isoangular point a of the actual orthodontic archwire curve. m Isometric point distance The set of isoangular point distances of the actual orthodontic archwire curve was calculated. The upper limit of the distance between the isoangular points of the actual orthodontic archwire curve is specified as L. max ; judge Is it valid? like If the condition is met, it means that the distance between all the isoangular points of the actual orthodontic archwire curve is within the specified range, then proceed to step three; like If this condition is not met, it means that the distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range. Therefore, the output is: The distance between the isoangular points of the actual orthodontic archwire curve is outside the specified range; Orthodontic archwire evaluation complete. Step 3: Determining the angle of the isoangular vector of the actual orthodontic archwire curve: Define an angle between an equal-angle vector and the z-axis, denoted by the symbol α. The direction vector of the z-axis is defined as... The isoangular vector of the actual orthodontic archwire curve is specified. equal-angle vectors The set of isoangular vector angles of the actual orthodontic archwire curve is calculated. The upper limit of the isoangular vector angle of the actual orthodontic archwire curve is specified as α. max ; judge Is it valid? like If the condition is met, it means that the angles of the isoangular vectors of the actual orthodontic archwire curve are all within the specified range, then proceed to step four; like If this condition is not met, it means that the isoangular vector angle of the actual orthodontic archwire curve is not within the specified range; therefore, the output is: The isoangular vector angle of the actual orthodontic archwire curve is not within the specified range, and the orthodontic archwire evaluation is complete. Step 4: Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve: Define coplanar isoangular vectors, using the symbol The term "coplanar isoangular vector" means that setting the y-axis coordinate of the isoangular vector to 0 transforms the spatial vector into a planar vector on the same plane; the isoangular vector of the actual orthodontic archwire curve... y-axis coordinate The coplanar isoangular vectors in the xoz plane are represented as follows: The set of isoangular vectors of the theoretical orthodontic archwire curve is transformed into vectors in the xoz plane to obtain a set of coplanar isoangular vectors. Define a set of coplanar isoangular vectors, denoted by G. A set of coplanar isoangular vectors represents a vector group containing any coplanar isoangular vector and H consecutive coplanar vectors to its right. The coplanar isoangular vectors of actual orthodontic archwire curves are defined. Coplanar equal-angle vectors that are continuous with it on its right The coplanar isoangular vector group is represented by G. m ,and Define the coplanar angular vectors of the actual orthodontic archwire curves The angle between the z-axis and the z-axis is denoted as and Define the basis vectors of a coplanar set of equal-angle vectors, using the symbol... It is indicated that the basis vectors of a coplanar isoangular vector group are the coplanar isoangular vectors in the group that make the largest angle with the z-axis; the coplanar isoangular vector group G is defined as follows: m The basis vectors of the coplanar isoangular vector group are denoted as Define the angle between the vector and the basis vectors, using the symbol... The angle between the vector and the basis vectors represents the angle between a vector in a coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve is defined as the coplanar isoangular vector group G. m Coplanar isoangular vectors basis vectors of the coplanar isoangular vector group The included angle is denoted as and The range of values ​​for v is v = 1, 2, 3, ..., H; the maximum angle between a set of coplanar equal-angle vectors and a basis vector is defined by the symbol η. G The maximum angle between the coplanar isoangular vector group and the basis vectors represents the maximum angle between the coplanar isoangular vectors in the coplanar isoangular vector group and the basis vectors of the coplanar isoangular vector group; the actual orthodontic archwire curve coplanar isoangular vector group G is defined as... m The maximum angle between the coplanar isoangular vector group and the basis vectors The maximum angle between the actual orthodontic archwire coplanar equiangular vector set and the basis vectors is defined as η. max ; Determine the maximum angle between the coplanar equiangular vector group and the basis vectors of the actual orthodontic archwire curve; Initialize m = 1; The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The set of angles between the common plane's equal-angle vectors and the z-axis Actual orthodontic archwire curves coplanar equiangular vector set G m The coplanar isoplanar vector corresponding to the maximum angle between the coplanar isoplanar vector and the z-axis is the actual orthodontic archwire curve coplanar isoplanar vector set G. m coplanar isoangular vector group basis vectors The actual orthodontic archwire curve coplanar equiangular vector set was calculated. The coplanar angular vectors of the common plane and the actual orthodontic archwire curve are coplanar angular vector groups G m coplanar isoangular vector group basis vectors The set of angles between the vectors and the basis vectors The calculated set of coplanar equiangular vectors G of the actual orthodontic archwire curves m The maximum angle between the coplanar isoangular vector group and the basis vectors judge Is it valid? like The validity of this statement indicates that the actual orthodontic archwire curves are coplanar, equiangular vector groups G. m If the maximum angle between the coplanar equal-angle vector group and the basis vectors is within the specified range, then proceed to step five; like This is incorrect, indicating that the actual orthodontic archwire curves are coplanar, equiangular vector sets G. m If the maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, then the output is: the actual orthodontic archwire curve coplanar isoangular vector group G. m The maximum angle between the coplanar isoangular vector group and the basis vectors is not within the specified range, and the orthodontic archwire evaluation is complete; Step 5: Determine whether all coplanar isoangular vector groups of the actual orthodontic archwire curve have been evaluated: Determine whether m + H = H·N + 1 is true; If m+H=H·N+1 does not hold, it means that the coplanar equiangular vector group of the actual orthodontic archwire curve has not been fully evaluated. Let m=m+H and then jump to step four. If m+H=H·N+1 holds true, it means that the coplanar isoangular vector groups of the actual orthodontic archwire curve have all been evaluated, and the maximum angle between the coplanar isoangular vector groups of the actual orthodontic archwire curve and the basis vectors is within the specified range. Output: The distance between isoangular points, the isoangular vector angle, and the maximum angle between the coplanar isoangular vector groups and the basis vectors of the actual orthodontic archwire curve are all within the specified range, and the orthodontic archwire evaluation is complete.

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