CN114943058B - Orthodontic archwire error fluctuation degree evaluation method based on position error judgment - Google Patents

Orthodontic archwire error fluctuation degree evaluation method based on position error judgment Download PDF

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CN114943058B
CN114943058B CN202210402504.0A CN202210402504A CN114943058B CN 114943058 B CN114943058 B CN 114943058B CN 202210402504 A CN202210402504 A CN 202210402504A CN 114943058 B CN114943058 B CN 114943058B
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姜金刚
谭棋匀
姚亮
张永德
孙海
孙健鹏
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Harbin University of Science and Technology
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Abstract

The invention discloses an orthodontic archwire error fluctuation degree evaluation method based on position error judgment, which relates to the field of orthodontic archwire bending evaluation. According to the invention, through the constraint of the pre-conditions, the complicated steps of calculating and classifying the complexity of each orthodontic arch wire curve bending point or the normalized bending point angular distance ratio are avoided, and the evaluation efficiency is improved. The quantitative evaluation of the bending stability of the orthodontic archwire with the characteristic is realized by calculating the line error fluctuation degree and the angle error fluctuation degree of the bending points of the m actual orthodontic archwire curves.

Description

Orthodontic archwire error fluctuation degree evaluation method based on position error judgment
Technical Field
The invention relates to an orthodontic archwire error fluctuation degree evaluation method based on position error judgment, and belongs to the technical field of orthodontic archwire bending evaluation.
Background
The misjaw deformity is the third largest oral disease endangering human health, and has higher morbidity, the fixed correction is a common and effective orthodontic treatment method in modern oral medicine, the bending of an orthodontic archwire is the key of the fixed correction technology, and in the traditional clinical application, the orthodontic archwire basically depends on manual bending of a professional doctor, so that the accuracy is difficult to ensure; in recent years, the traditional oral manufacturing and processing technology is revolutionarily changed and is also beneficial to the digital technology, and the processing of archwires in orthodontic appliances is proceeding to digital. However, after the orthodontic archwire is bent, a doctor still needs to evaluate the orthodontic archwire according to experience to judge whether the use requirement is met, the method is seriously dependent on clinical experience of the doctor, quantitative evaluation of the orthodontic archwire is difficult to realize, and only accurate evaluation of bending of a single orthodontic archwire curve can be realized, so that a method for quantitatively evaluating the bending stability of the orthodontic archwire by analyzing error rate data of a large number of actual orthodontic archwire curves bent according to the same theory is lacked.
In addition, considering the bending complexity of the bending points on the orthodontic archwire curve or the individuation characteristics of the angle pitch ratio of the normalized bending points on the orthodontic archwire curve, for example, the bending points on the patient individuation orthodontic archwire curve have smaller bending point complexity, the complexity of each bending point is not larger than a set demarcation value, the angle pitch ratio of the normalized bending points on the patient individuation orthodontic archwire curve is smaller, the angle pitch ratio of each normalized bending point of each bending point is not larger than a set demarcation value, namely, the complexity of the bending points of the orthodontic archwire curve and the shape of the orthodontic archwire curve have obvious characteristics, when the bending stability of the orthodontic archwire curve is evaluated, no method can determine the error fluctuation degree of the orthodontic archwire curve through indexes at present, and the high-efficiency quantitative evaluation of the bending stability of the orthodontic archwire curve is realized; the lack of the method causes that doctors and orthodontic archwire robots cannot obtain targeted guidance and improvement directions, prevents the improvement of bending technology of the doctors, seriously influences clinical correction effects, prevents the optimization of mechanical structures of the orthodontic archwire robots from limiting the iterative upgrade of orthodontic archwire bending algorithms and restricts the development of the orthodontic archwire bending robots; in summary, a method capable of precisely quantitatively evaluating the bending stability of the orthodontic archwire curve with special properties is needed in the technical field of the bending evaluation of the orthodontic archwire at present.
Disclosure of Invention
Aiming at the problems, the invention provides an orthodontic archwire error fluctuation degree evaluation method based on position error judgment, which solves the problem that the existing orthodontic archwire evaluation field lacks a quantitative evaluation method for the bending stability of an orthodontic archwire curve with smaller bending point complexity and smaller bending point angle distance normalization, and realizes the efficient quantitative evaluation for the bending stability of the orthodontic archwire curve by verifying the line error fluctuation degree and the angle error fluctuation degree in the orthodontic archwire evaluation process.
An orthodontic archwire error fluctuation degree evaluation method based on position error judgment comprises the following specific implementation processes:
step one, importing theoretical orthodontic archwire curve data and actual orthodontic archwire curve data:
an o-xyz three-dimensional orthodontic archwire error calibration coordinate system w is established according to a right-hand rule, a theoretical orthodontic archwire curve with n bending points designed by an orthodontist according to the dentition form of a patient is used for calculating and inputting a 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 α′ i , T β′ i , T γ′ i ,Td′ i ) The pose information of the ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w is obtained, the value range of i is more than or equal to 1 and less than or equal to n, T α′ i An included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, T β′ i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, T γ′ i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, T d′ i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the theoretical orthodontic archwire curve is p s The right end point of the theoretical orthodontic archwire curve is p f ，p s And p f The midpoint of the connecting line between the two is T o', spatially transforming the theoretical orthodontic archwire curve: let the dot T o' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the theoretical orthodontic archwireLeft end point p of silk curve s The right endpoint p of the theoretical orthodontic archwire curve is positioned on the negative half axis of the y axis f The method comprises the steps of locating at a y-axis positive half shaft, enabling a theoretical orthodontic archwire curve to have no intersection point with an x-axis positive half shaft, enabling the theoretical orthodontic archwire curve to rotate clockwise along the y-axis positive direction until the intersection point occurs between the theoretical orthodontic archwire curve and the x-axis positive half shaft, setting the pose of the theoretical orthodontic archwire curve after spatial transformation as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, calculating and inputting a theoretical orthodontic archwire curve bending point information set P under the final pose T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n }， T p i ＝( T α i , T β i , T γ i , T d i ) The pose information of the coordinate system w is marked for the ith bending point of the theoretical orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, T α i for the included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, T β i for the included angle formed by the connection line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the y axis, T γ i for the included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the z axis, T d i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w;
calculating and inputting an actual orthodontic archwire curve information set by using m actual orthodontic archwire curves with n bending points manufactured according to theoretical orthodontic archwire curvesThe j-th actual orthodontic archwire curve bending point information set is the value range of jIs 1.ltoreq.j.ltoreq.m->The pose information of a coordinate system w is marked for the ith bending point of the jth actual orthodontic archwire curve relative to the error of the three-dimensional orthodontic archwire,/for the jth actual orthodontic archwire curve >An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and an x axis is>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and a z axis is>Calibrating the length of a connecting line between an ith bending point of the jth actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the j-th actual orthodontic archwire curve is j p′ s The right end point of the j-th actual orthodontic archwire curve is j p′ f ， j p′ s And j p′ f the midpoint of the connecting line between them is +.>Spatially transforming the j-th actual orthodontic archwire curve: let point->Coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point of the j-th actual archwire curve j p′ s Is positioned at the right end point of the j-th actual orthodontic archwire curve on the negative half axis of the y axis j p′ f The method comprises the steps of locating at a y-axis positive half shaft, enabling a j-th actual orthodontic arch wire curve to have no intersection point with an x-axis positive half shaft, enabling the j-th actual orthodontic arch wire curve to rotate clockwise along the y-axis positive direction until the j-th actual orthodontic arch wire curve has an intersection point with the x-axis positive half shaft, setting the pose of the j-th actual orthodontic arch wire curve after space transformation as the final pose in a three-dimensional orthodontic arch wire error calibration coordinate system, calculating and inputting m actual orthodontic arch wire curve information sets under the final pose Bending point information set for j-th actual orthodontic archwire curve in final pose,/->Calibrating pose information of a coordinate system w for the ith bending point of the jth actual orthodontic archwire curve in the final pose relative to the three-dimensional orthodontic archwire error, and +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and an x-axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z axis is +.>Calibrating the length of a connecting line between an ith bending point of the actual orthodontic archwire curve in the final pose and an origin o of a coordinate system w for the error of the three-dimensional orthodontic archwire;
setting the curve position error of the actual orthodontic archwire:
defining the position error of an actual orthodontic archwire curve bending point, wherein the bending point position error is the quantitative description of the accuracy of the bending position of the orthodontic archwire curve bending point, and the evaluation of the actual orthodontic archwire curve bending point position error comprises two parts, namely the evaluation of the error rate of an actual orthodontic archwire curve bending point and the evaluation of the average offset error rate of the actual orthodontic archwire curve bending point; defining the line error rate of the actual orthodontic archwire curve point, symbolized by e d Representing a line error rate e d Is a quantitative description of the linear distance between a theoretical orthodontic archwire curve bending point and the origin o of a three-dimensional orthodontic archwire error calibration coordinate system and the error of the linear distance between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system, and the line error rate of the ith bending point of the actual orthodontic archwire curve in the final pose is expressed asDefining average bias error rate of actual orthodontic arch wire curve bending point by using symbol e a Indicating an average bias error rate e a The method is a quantitative description of the included angle between a theoretical orthodontic archwire curve bending point and each coordinate axis of a three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system, and the average offset error rate of the ith bending point of the actual orthodontic archwire curve in the final pose is expressed as follows>Wherein->Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve >Error rate between, stipulate->Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->
Step three, setting the complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending points of theoretical orthodontic archwire by using symbol C r Representation, C r Is the comprehensive quantitative description of the bending difficulty of the curve bending point of the theoretical orthodontic archwire, and C of the curve bending point of the theoretical orthodontic archwire r The higher the value, i.e., the more difficult the bending point is at the time of bending, the complexity of the ith bending point of the theoretical orthodontic archwire curve is specified asNormalized bending point angular distance ratio representing ith bending point of theoretical orthodontic archwire curve, gaugeFix-> T E i The angle-to-distance ratio of the bending point of the ith bending point of the theoretical orthodontic archwire curve is represented, and the angle-to-distance ratio of the bending point is a quantitative description of the bending complexity degree of a single bending point and prescribes +.> T θ i To act on curve bending point of orthodontic arch wire T p i Bending angle of the part->Representing the bending distance acting at the ith bending point of the theoretical orthodontic archwire curve, namely the theoretical orthodontic archwire curve bending point T p i-1 And (3) with T p i The length of the curve segment between the two is 1 st bending point of the theoretical orthodontic archwire curve T p 1 ，/>Representing bending points T p 1 To the left end point p of the theoretical orthodontic archwire curve s The length of the curve segment between the two, T E min is the minimum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire, T E max the maximum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire; provision of->The boundary value of (C) is% T E * ) b ；/>Normalized bending point density representing the ith bending point of a theoretical orthodontic archwire curve, prescribing +.> T ρ i Bending representing ith bending point of theoretical orthodontic archwire curveThe density of the bending points is the quantitative description of the tightness between a single bending point and adjacent bending points on the curve of the orthodontic archwire, and the definition of +.>The value 1 in the formula is expressed as 1 bending point, T l i represents the linear distance between the ith bending point of the theoretical orthodontic archwire curve and the nearest bending point, namely +.>Represents the distance between the ith-1 bending point of the theoretical orthodontic archwire curve and the ith bending point of the theoretical orthodontic archwire curve,/for the theoretical orthodontic archwire curve>Representing the distance between the i-th bending point of the theoretical orthodontic archwire curve and the i+1-th bending point of the theoretical orthodontic archwire curve, when i=1, prescribing +.>Represents the 1 st bending point of the theoretical orthodontic archwire curve and the left endpoint p of the theoretical orthodontic archwire curve s Straight line distance between>Representing the linear distance between the 1 st bending point of the theoretical orthodontic archwire curve and the 2 nd bending point of the theoretical orthodontic archwire curve, when i=n, prescribing +.> Represents the straight line distance between the n-1 th bending point of the theoretical orthodontic archwire curve and the n-th bending point of the theoretical orthodontic archwire curve, +.>Represents the nth bending point of the theoretical orthodontic archwire curveTheoretical orthodontic archwire curve right end point p f The straight-line distance between the two, T ρ min is the minimum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire, T ρ max the maximum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire; complexity formula->The numerical value 2 in (2) represents two parameters of the angle-to-distance ratio of the normalized bending point and the normalized bending single density are considered in calculating the complexity; complexity C of curve bending point of theoretical orthodontic archwire r Is C rb ；
Setting the error fluctuation degree and the angle error fluctuation degree of an actual orthodontic archwire curve line:
defining the line error fluctuation degree of the actual orthodontic archwire curve by the symbol sigma d Representation, sigma d Is the quantitative description of the bending distance stability of the actual orthodontic archwire curve, and the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curve is expressed as Line error rate representing the ith bending point of the jth actual orthodontic archwire curve, prescribingAverage value of line error rate of ith bending point of m actual orthodontic archwire curve is regulatedThe upper limit value of the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is (sigma d ) max The method comprises the steps of carrying out a first treatment on the surface of the Defining the angle error fluctuation degree of the actual orthodontic archwire curve by the symbol sigma a Representation, sigma a Is the quantitative description of the bending angle stability of the actual orthodontic archwire curve, and the angle error fluctuation degree of the ith bending point of the actual orthodontic archwire curve is expressed asThe angular error rate of the ith bending point of the jth actual orthodontic archwire curve is expressed and regulatedWherein->Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, prescribeAngle of ith bending point of theoretical orthodontic archwire curve T γ i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->Mean value of angle error rate of ith bending point of m actual orthodontic archwire curves, stipulated +. >The upper limit value of the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is (sigma a ) max ；
Fifthly, verifying the complexity and the normalized bending point angular distance ratio of the bending point of the theoretical orthodontic arch wire curve:
according to the formulaCalculating the complexity of the ith bending point on the theoretical orthodontic archwire curve, namely 1 C r Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 I is i=1, and is taken out by comparison i C r Maximum value of [ (] i C r ) max For conditions of% i C r ) max ≤C rb Verifying; according to the formula->Calculating the normalized bending point angular distance ratio of the ith bending point on the theoretical orthodontic archwire curve, namely +.>Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 Is obtained by comparing the normalized bending point angular distance ratio of +.>Maximum value of +.>For condition->The verification is carried out, specifically:
a) Verifying the complexity of a curve bending point of a theoretical orthodontic arch wire;
if it is% i C r ) max ≤C rb Established, the theoretical orthodontic archwire curve bending point information set P in the final pose is described T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n The maximum bending point complexity in the cross-point model is not greater than the set complexity demarcation value C rb It can be seen that the complexity of each bending point on the obtained theoretical orthodontic archwire curve containing n bending points is not greater than the demarcation value C of the complexity of the bending point rb The complexity of the curve of the orthodontic archwire is smaller, but the situation that the normalized bending point angular distance of the bending point of the curve of the theoretical orthodontic archwire is smaller and the normalized bending point density is larger exists, and the normalized bending point angular distance ratio comprises the shape characteristics of the curve of the actual orthodontic archwire, so that the normalized bending point angular distance ratio of the curve of the theoretical orthodontic archwire is verified, and the step five b) is skipped;
if it is% i C r ) max ≤C rb If the curve is not true, the complexity of the curve bending point of the theoretical orthodontic archwire is not small, the evaluation method is not applicable to the curve of the orthodontic archwire, and the output of the evaluation method is not applicable to the curve of the orthodontic archwire, and the evaluation of the error fluctuation degree of the orthodontic archwire is finished;
b) Verifying the angle-to-distance ratio of a theoretical orthodontic archwire curve normalized bending point;
if it isEstablished, the theoretical orthodontic archwire curve bending point information set P in the final pose is described T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n The maximum normalized bending point angular distance ratio of the inner bending point is not larger than the preset normalized bending point demarcation value T E * ) b It can be known that the angle-to-distance ratio of the normalized bending point of each bending point on the obtained theoretical orthodontic archwire curve containing n bending points is not more than the upper limit value of the normalized bending point T E * ) max The shape of the orthodontic archwire curve is simple, and when evaluating the error fluctuation degree of the actual orthodontic archwire curve bent according to the theoretical orthodontic archwire curve with the characteristics, only the position error fluctuation degree of the bending point of the actual orthodontic archwire curve, namely the actual orthodontic archwire, needs to be evaluated Step six, jumping to the error fluctuation degree of the wire curve bending point line and the error fluctuation degree of the actual orthodontic arch wire curve bending point angle;
if it isIf the curve is not true, the complexity of the curve bending point of the theoretical orthodontic archwire or the angle-to-distance ratio of the normalized bending point is excessively large, the evaluation method is not applicable to the curve of the orthodontic archwire, and the output of the evaluation method is not applicable to the curve of the orthodontic archwire, and the evaluation of the error fluctuation degree of the orthodontic archwire is finished;
step six, evaluating the error fluctuation degree of the actual orthodontic archwire curve line and the error fluctuation degree of the actual orthodontic archwire curve angle:
according to i σ d And i σ a calculating the line error fluctuation degree and the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, wherein the initial value of i is i=1;
a) Actual orthodontic archwire curve line error fluctuation degree evaluation
According to the formulaCalculating the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ d ≤(σ d ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is within the allowable range, skipping to the step six b);
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range, outputting the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curves to exceed the allowable range, and ending the orthodontic archwire evaluation;
b) Evaluation of curve angle error fluctuation degree of actual orthodontic archwire
According to the formulaCalculating the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ a ≤(σ a ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ a ≤(σ a ) max The method includes the steps that (1) the angle error fluctuation degree of the ith bending point of m actual orthodontic archwire curves is in an allowable range, and the step (seven) is skipped;
if it is i σ a ≤(σ a ) max If not, the fact that the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range is indicated, and then the angle error fluctuation degree of the ith bending point of the output actual orthodontic archwire curves exceeds the allowable range, and the orthodontic archwire evaluation is finished;
step seven, judging whether the bending points of the m actual orthodontic archwire curves are evaluated completely or not:
judging whether the number n of i and the number n of the bending points of the actual orthodontic archwire curve are equal,
the method comprises the following steps:
if i=n is not satisfied, indicating that all bending points on the m actual orthodontic archwire curves are not evaluated, making i=i+1, namely, indicating that the next group of actual orthodontic archwire curve bending points are evaluated, and jumping to the step six);
if i=n is true, it is indicated that all the bending points on the m actual orthodontic archwire curves have been evaluated, and the line error fluctuation degree, the angle error fluctuation degree and the curvature error fluctuation degree of all the actual orthodontic archwire curve bending points are within the allowable range, and the orthodontic archwire evaluation is ended.
The beneficial effects of the invention are as follows:
1. the invention aims at an orthodontic archwire evaluation method, and provides a method for setting the demarcation value of the complexity of the bending point of an orthodontic archwire curve as C by taking the complexity of the bending point or the angle-to-distance ratio of the bending point as a pre-judging parameter of the curve evaluation of the orthodontic archwire rb The demarcation value of the angle-to-distance ratio of the normalized bending point of the curve bending point of the orthodontic archwire is% T E * ) b The maximum complexity of a bending point on an orthodontic archwire curve is not larger than the demarcation value C of the bending point complexity, which is verified in advance before the orthodontic archwire curve is evaluated rb And the maximum value of the angle-to-distance ratio of the normalized bending point of the bending point on the curve of the orthodontic archwire is not larger than the demarcation value of the angle-to-distance ratio of the normalized bending point T E * ) b The complexity iC of the bending point on the curve of the orthodontic arch wire can be obtained r Or normalized bending point angular distance ratio of orthodontic archwire curve bending point T E i The method meets the requirements, so that constraint of preconditions is provided for the method, the complexity of the bending points on the orthodontic archwire curve or the angular distance ratio characteristic of the normalized bending points are determined, complicated steps of calculating and classifying the complex or normalized bending points of each orthodontic archwire curve before evaluating the orthodontic archwire curve and applying different evaluation schemes are avoided, and the evaluation efficiency is improved.
2. Aiming at an orthodontic archwire curve with the special attribute of smaller complexity of bending points and smaller angle distance of normalized bending points, the invention provides a concept of position error of the bending points of the orthodontic archwire curve; considering that the shape of an orthodontic archwire curve with smaller complexity of the bending point and smaller angle-to-distance ratio of the normalized bending point is simpler, errors are not easy to generate in the process of bending the shape of the orthodontic archwire curve, the invention does not need to evaluate the stability of the shape bending of the actual orthodontic archwire curve, only evaluates the line error fluctuation degree and the angle error fluctuation degree of the orthodontic archwire curve, and finishes the quantitative evaluation of the bending stability of the bending point of the orthodontic archwire curve, and simplifies the evaluation process on the premise of meeting the rating requirement;
4. compared with an orthodontic wire error fluctuation degree evaluation method based on curvature error pre-judgment in the same day of the patent of the invention, although both methods are suitable for a personalized actual orthodontic wire curve with special properties, the method mentioned in the orthodontic wire error fluctuation degree evaluation method based on curvature error pre-judgment is focused on the premise that the complexity of each actual orthodontic wire curve bending point is larger than the curve point complexity demarcation value or the angle distance ratio of the normalized curve point is larger than the angle distance ratio demarcation value of the normalized curve point, so that the curvature error fluctuation degree of the actual orthodontic wire curve bending point is pre-judged, the on-going evaluation is calibrated through the evaluation calibration value, and after the curvature error fluctuation degree of all the curve points of the actual orthodontic wire curve meets the requirement, the line error fluctuation degree and the angle error fluctuation degree of the actual orthodontic wire curve bending point are evaluated; the precondition of the method is that the complexity of each actual orthodontic arch wire curve bending point and the angle-to-distance ratio of the normalized bending point are smaller than the corresponding set demarcation value, so that only the line error fluctuation degree and the angle error fluctuation degree of the actual orthodontic arch wire curve bending point are verified, and calibration is not required by the calibration value; the two methods are different in application conditions when the actual orthodontic archwire curve evaluation is carried out, so that the proposal of the method and the other method compensate each other, and further the series of methods for the actual orthodontic archwire curve evaluation are perfected.
5. Compared with the invention patent 'an orthodontic archwire error fluctuation degree evaluation method based on bending point complexity judgment' declared by the inventor on the same day, the method takes the special attribute that the bending points on the personalized orthodontic archwire curve have smaller complexity and normalized bending point angular distance ratio as the premise, does not judge the complexity and normalized bending point angular distance ratio of each bending point on the orthodontic archwire curve, further determines whether to evaluate the weighted curvature error rate of the bending points, not only satisfies the error fluctuation degree evaluation of the actual orthodontic archwire curve, but also reduces the complexity of an orthodontic archwire evaluation algorithm and improves the evaluation efficiency.
Drawings
For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
FIG. 1 is a flow chart of a method for evaluating the error fluctuation degree of an orthodontic archwire based on position error judgment;
FIG. 2 is a schematic illustration of the position of a theoretical orthodontic archwire curve prior to spatial transformation;
FIG. 3 is a schematic illustration of the position of m actual orthodontic archwire curves prior to spatial transformation;
FIG. 4 is a schematic illustration of the actual orthodontic archwire curve in the final pose for the 7 th actual orthodontic archwire curve with a point angle error fluctuation greater than the upper limit;
FIG. 5 is a schematic diagram of an actual orthodontic archwire curve with m bending point error fluctuations in the final pose all within the allowable range;
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention patent, the present invention patent is described below by way of specific embodiments shown in the drawings, but it should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention patent, and furthermore, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the concepts of the present invention patent.
Implementation example 1: as shown in fig. 1, 2, 3, 4 and 5, the present embodiment adopts the following technical solutions: an orthodontic archwire error fluctuation degree evaluation method based on position error judgment comprises the following specific implementation processes:
step one, importing theoretical orthodontic archwire curve data and actual orthodontic archwire curve data:
an o-xyz three-dimensional orthodontic archwire error calibration coordinate system w is established according to a right-hand rule, a theoretical orthodontic archwire curve with n bending points designed by an orthodontist according to the dentition form of a patient is used for calculating and inputting a 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 α′ i , T β′ i , T γ′ i , T d′ i ) For the pose information of the ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, the value range of i is more than or equal to 1 and less than or equal to in， T α′ i An included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, T β′ i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, T γ′ i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, T d′ i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the theoretical orthodontic archwire curve is p s The right end point of the theoretical orthodontic archwire curve is p f ，p s And p f The midpoint of the connecting line between the two is T o', spatially transforming the theoretical orthodontic archwire curve: let the dot T o' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left endpoint p of the theoretical orthodontic archwire curve s The right endpoint p of the theoretical orthodontic archwire curve is positioned on the negative half axis of the y axis f The method comprises the steps of locating at a y-axis positive half shaft, enabling a theoretical orthodontic archwire curve to have no intersection point with an x-axis positive half shaft, enabling the theoretical orthodontic archwire curve to rotate clockwise along the y-axis positive direction until the intersection point occurs between the theoretical orthodontic archwire curve and the x-axis positive half shaft, setting the pose of the theoretical orthodontic archwire curve after spatial transformation as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, calculating and inputting a theoretical orthodontic archwire curve bending point information set P under the final pose T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n }， T p i ＝( T α i , T β i , T γ i , T d i ) The pose information of the coordinate system w is marked for the ith bending point of the theoretical orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, T α i calibrating the origin of a coordinate system w for the ith bending point of a theoretical orthodontic archwire curve and the error of a three-dimensional orthodontic archwire in the final poseThe angle formed by the connecting line between o and the x axis, T β i for the included angle formed by the connection line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the y axis, T γ i for the included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the z axis, T d i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w;
calculating and inputting an actual orthodontic archwire curve information set by using m actual orthodontic archwire curves with n bending points manufactured according to theoretical orthodontic archwire curvesThe value range of j is more than or equal to 1 and less than or equal to m for the j-th actual orthodontic arch wire curve bending point information set>The pose information of a coordinate system w is marked for the ith bending point of the jth actual orthodontic archwire curve relative to the error of the three-dimensional orthodontic archwire,/for the jth actual orthodontic archwire curve >An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and an x axis is>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is>Connecting line between ith bending point of jth actual orthodontic archwire curve and origin o of three-dimensional orthodontic archwire error calibration coordinate system wIncluded angle with z-axis, +.>Calibrating the length of a connecting line between an ith bending point of the jth actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the j-th actual orthodontic archwire curve is j p' s The right end point of the j-th actual orthodontic archwire curve is j p' f ， j p' s And j p' f the midpoint of the connecting line between them is +.>Spatially transforming the j-th actual orthodontic archwire curve: let point->Coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point of the j-th actual archwire curve j p' s Is positioned at the right end point of the j-th actual orthodontic archwire curve on the negative half axis of the y axis j p' f The method comprises the steps of locating at a y-axis positive half shaft, enabling a j-th actual orthodontic arch wire curve to have no intersection point with an x-axis positive half shaft, enabling the j-th actual orthodontic arch wire curve to rotate clockwise along the y-axis positive direction until the j-th actual orthodontic arch wire curve has an intersection point with the x-axis positive half shaft, setting the pose of the j-th actual orthodontic arch wire curve after space transformation as the final pose in a three-dimensional orthodontic arch wire error calibration coordinate system, calculating and inputting m actual orthodontic arch wire curve information sets under the final pose Bending point information set for j-th actual orthodontic archwire curve in final pose,/->Calibrating pose information of a coordinate system w for the ith bending point of the jth actual orthodontic archwire curve in the final pose relative to the three-dimensional orthodontic archwire error, and +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and an x-axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z axis is +.>Calibrating the length of a connecting line between an ith bending point of the actual orthodontic archwire curve in the final pose and an origin o of a coordinate system w for the error of the three-dimensional orthodontic archwire;
setting errors of actual orthodontic archwire curve bending point positions:
defining the position error of an actual orthodontic archwire curve bending point, wherein the bending point position error is the quantitative description of the accuracy of the bending position of the orthodontic archwire curve bending point, and the evaluation of the actual orthodontic archwire curve bending point position error comprises two parts, namely the evaluation of the error rate of an actual orthodontic archwire curve bending point and the evaluation of the average offset error rate of the actual orthodontic archwire curve bending point; defining the line error rate of the actual orthodontic archwire curve point, symbolized by e d Representing a line error rate e d Is the quantitative description of the linear distance between a theoretical orthodontic archwire curve bending point and the origin o of a three-dimensional orthodontic archwire error calibration coordinate system and the error of the linear distance between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system, and prescribes the actual j-th bar in the final poseThe line error rate of the ith bending point of the orthodontic archwire curve is expressed asDefining average bias error rate of actual orthodontic arch wire curve bending point by using symbol e a Indicating an average bias error rate e a The method is a quantitative description of the included angle between a theoretical orthodontic archwire curve bending point and each coordinate axis of a three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system, and the average offset error rate of the ith bending point of the actual orthodontic archwire curve in the final pose is expressed as follows>Wherein->Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve >Error rate between, stipulate->Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->
Step three, setting the complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending points of theoretical orthodontic archwire by using symbol C r Representation, C r Is the comprehensive quantitative description of the bending difficulty of the bending point of the theoretical orthodontic archwire curve, and the complexity of the ith bending point of the theoretical orthodontic archwire curve is expressed asNormalized bending point angular distance ratio representing ith bending point of theoretical orthodontic archwire curve, stipulation T E i The angle-to-distance ratio of the bending point representing the ith bending point of the theoretical orthodontic archwire curve is a quantitative description of the bending complexity of a single bending point on the orthodontic archwire curve, provision ∈> T θ i To act on curve bending point of orthodontic arch wire T p i Bending angle of the part->Representing the bending distance acting at the ith bending point of the theoretical orthodontic archwire curve, namely the theoretical orthodontic archwire curve bending point T p i-1 And (3) with T p i The length of the curve segment between the two is 1 st bending point of the theoretical orthodontic archwire curve T p 1 ，/>Representing bending points T p 1 To the theoretical orthodontic bowLeft end point p of silk curve s The length of the curve segment between the two, T E min is the minimum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire, T E max the maximum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire; provision of->The boundary value of (C) is% T E * ) b ；/>Normalized bending point density representing the ith bending point of a theoretical orthodontic archwire curve, prescribing +.> T ρ i The bending point density of the ith bending point of the theoretical orthodontic archwire curve is represented, and the bending point density is the quantitative description of the tightness degree between a single bending point and adjacent bending points on the orthodontic archwire curve, and is stipulated->The value 1 in the formula is expressed as 1 bending point, T l i represents the linear distance between the ith bending point of the theoretical orthodontic archwire curve and the nearest bending point, namely +.>Represents the straight line distance between the ith-1 bending point of the theoretical orthodontic archwire curve and the ith bending point of the theoretical orthodontic archwire curve, +.>Represents the straight line distance between the ith bending point of the theoretical orthodontic archwire curve and the (i+1) th bending point of the theoretical orthodontic archwire curve, and when i=1, the rule is +.>Represents the 1 st bending point of the theoretical orthodontic archwire curve and the left end point of the theoretical orthodontic archwire curve p s Straight line distance between>Represents the straight line distance between the 1 st bending point of the theoretical orthodontic archwire curve and the 2 nd bending point of the theoretical orthodontic archwire curve, and when i=n, the straight line distance is regulatedRepresents the straight line distance between the n-1 th bending point of the theoretical orthodontic archwire curve and the n-th bending point of the theoretical orthodontic archwire curve, +.>Represents the nth bending point of the theoretical orthodontic archwire curve and the right endpoint p of the theoretical orthodontic archwire curve f The straight-line distance between the two, T ρ min is the minimum value of the curve bending point density of the theoretical orthodontic archwire, T ρ max the maximum value of the curve bending point density of the theoretical orthodontic archwire; complexity formula->The numerical value 2 in (1) represents two parameters of the angle-to-distance ratio of a normalized bending point and the single density of the normalized bending point are considered when calculating the complexity of the bending point of the theoretical orthodontic arch wire; complexity C of curve bending point of theoretical orthodontic archwire r Is C rb ；
Setting the error fluctuation degree of the curve bending point line and the angle error fluctuation degree of the actual orthodontic archwire:
defining the line error fluctuation degree of the curve bending point of the actual orthodontic arch wire by using the symbol sigma d Representation, sigma d Is the quantitative description of the bending distance stability of the bending point of the actual orthodontic archwire curve, and the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curve is expressed as Representing the line error rate of the ith bending point of the jth actual orthodontic archwire curve,/>Average value of line error rate of ith bending point of m actual orthodontic archwire curve is regulatedThe upper limit value of the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is (sigma d ) max The method comprises the steps of carrying out a first treatment on the surface of the Defining the angle error fluctuation degree of the bending point of the actual orthodontic arch wire curve by using the symbol sigma a Representation, sigma a Is the quantitative description of the bending angle stability of the bending point of the actual orthodontic archwire curve, and the fluctuation degree of the angle error of the ith bending point of the actual orthodontic archwire curve is expressed asWherein->Mean value of angle error rate of ith bending point of m actual orthodontic archwire curves, stipulated +.>The upper limit value of the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is (sigma a ) max ；
Fifthly, verifying the complexity and the normalized bending point angular distance ratio of the bending point of the theoretical orthodontic arch wire curve:
according to the formulaCalculating the complexity of the ith bending point on the theoretical orthodontic archwire curve, namely 1 C r Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 I is i=1, and is taken out by comparison i C r Maximum value of [ (] i C r ) max For conditions of% i C r ) max ≤C rb Verifying; according to the formula->Calculating the normalized bending point angular distance ratio of the ith bending point on the theoretical orthodontic archwire curve, namely +. >Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 Is obtained by comparing the normalized bending point angular distance ratio of +.>Maximum value of +.>For condition->The verification is carried out, specifically:
a) Verifying the complexity of a curve bending point of a theoretical orthodontic arch wire;
if it is% i C r ) max ≤C rb Established, the theoretical orthodontic archwire curve bending point information set P in the final pose is described T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n The maximum bending point complexity in the cross-point model is not greater than the set complexity demarcation value C rb It can be seen that the complexity of each bending point on the obtained theoretical orthodontic archwire curve containing n bending points is not greater than the demarcation value C of the complexity of the bending point rb The situation that the normalized bending point angular distance of the theoretical orthodontic archwire curve bending point is smaller and the normalized bending point density is larger still exists, so that the theoretical orthodontic archwire curve normalized bending point angular distance ratio is verified, and the step five b) is skipped;
if it is% i C r ) max ≤C rb Failure, indicating that the complexity of the point of bending of the theoretical orthodontic archwire curve is large, the evaluation method is not applicable to the orthodontic archwire curveOutputting that the evaluation method is not applicable to the orthodontic archwire curve, and ending the orthodontic archwire error fluctuation degree evaluation;
b) Verifying the angle-to-distance ratio of a theoretical orthodontic archwire curve normalized bending point;
If it isEstablished, the theoretical orthodontic archwire curve bending point information set P in the final pose is described T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n The maximum normalized bending point angular distance ratio of the inner bending point is not larger than the preset normalized bending point demarcation value T E * ) b It can be known that the angle-to-distance ratio of the normalized bending point of each bending point on the obtained theoretical orthodontic archwire curve containing n bending points is not more than the upper limit value of the normalized bending point T E * ) max Step six, jumping to the step six;
if it isIf the curve is not true, the complexity of the curve bending point of the theoretical orthodontic archwire or the angle distance of the normalized bending point is larger, the evaluation method is not applicable to the curve of the orthodontic archwire, and the output of the evaluation method is not applicable to the curve of the orthodontic archwire, and the evaluation of the error fluctuation degree of the orthodontic archwire is finished;
step six, evaluating the error fluctuation degree of the curve bending point line of the actual orthodontic archwire and the error fluctuation degree of the curve angle of the actual orthodontic archwire:
according to i σ d And i σ a calculating the line error fluctuation degree and the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, wherein the initial value of i is i=1;
a) Evaluation of error fluctuation degree of curve bending point line of actual orthodontic archwire
According to the formulaCalculating the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ d ≤(σ d ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is within the allowable range, skipping to the step six b);
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range, outputting the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curves to exceed the allowable range, and ending the orthodontic archwire evaluation;
b) Evaluation of error fluctuation degree of curve bending point angle of actual orthodontic archwire
According to the formulaCalculating the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ a ≤(σ a ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ a ≤(σ a ) max The method includes the steps that (1) the angle error fluctuation degree of the ith bending point of m actual orthodontic archwire curves is in an allowable range, and the step (seven) is skipped;
if it is i σ a ≤(σ a ) max If not, the fact that the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range is indicated, and then the angle error fluctuation degree of the ith bending point of the output actual orthodontic archwire curves exceeds the allowable range, and the orthodontic archwire evaluation is finished;
step seven, judging whether the bending points of the m actual orthodontic archwire curves are evaluated completely or not:
judging whether the number n of i and the number n of the bending points of the actual orthodontic archwire curve are equal,
The method comprises the following steps:
if i=n is not satisfied, indicating that all bending points on the m actual orthodontic archwire curves are not evaluated, making i=i+1, namely, indicating that the next group of actual orthodontic archwire curve bending points are evaluated, and jumping to the step six);
if i=n is true, it is indicated that all the bending points on the m actual orthodontic archwire curves have been evaluated, and the line error fluctuation degree and the angle error fluctuation degree of all the actual orthodontic archwire curve bending points are within the allowable range, and the orthodontic archwire evaluation is finished.
Implementation example 2: as shown in fig. 4, in the process of evaluating the error fluctuation degree of the orthodontic archwire based on the position error judgment on m=20 actual orthodontic archwire curves including n=16 bending points, the initial value of i is i=1, and the demarcation value of the complexity of the bending points is set as C rb Normalized bending point angular distance ratio demarcation value =0.5 T E * ) b =0.4, calculating the complexity of 16 theoretical orthodontic archwire curve bending points according to the formula for calculating the complexity of theoretical orthodontic archwire bending points in the third step, and taking out the maximum value from the complexity of 16 theoretical orthodontic archwire curve bending points as the maximum value 9 C r ) max ＝ 9 C r =0.46, by comparison 9 C r ) max ＜C rb Calculating the normalized bending point angular distance ratio of 16 theoretical orthodontic archwire curve bending points according to a formula for calculating the complexity of the theoretical orthodontic archwire bending points, and taking out the maximum value as the maximum value By comparison, get +.>Setting an upper limit value (sigma) of the bending point line error fluctuation degree d ) max =0.06, the upper limit value (σ) of the bending point angle error fluctuation degree a ) max Jumping to step six to evaluate the actual orthodontic archwire curve bending point line error fluctuation degree and the angle error fluctuation degree, wherein the initial value of i is i=1, and in step six a), the method comprises the following steps of i σ d Is derived from the calculation formula of (2) 1 σ d ＝0.03＜(σ d ) max Jump to step six b) according to i σ a Is derived from the calculation formula of (2) 1 σ a ＝0.04＜(σ a ) max Jumping to a step seven, according to the judgment that 1=16 is not established at this time, i=i+1 is caused to jump to six a) to evaluate the line error fluctuation degree and the angle error fluctuation degree of the subsequent bending points, according to the step, calculating that the line error fluctuation degree and the angle error fluctuation degree of the 2 nd, 3 rd, 4 th, 5 th and 6 th bending points of 20 actual orthodontic archwire curves are smaller than the corresponding upper limit values, and when the 7 th bending point line error fluctuation degree of the 20 actual orthodontic archwire curves is calculated, obtaining 7 σ d ＝0.1＞(σ d ) max And outputting that the line error fluctuation degree of the 7 th bending point of the actual orthodontic archwire curve exceeds the allowable range, and evaluating the subsequent actual orthodontic archwire curve bending point is not performed any more, and the orthodontic archwire evaluation is finished.
Implementation example 3: as shown in fig. 5, in the process of evaluating the error fluctuation degree of the orthodontic archwire based on the position error judgment on m=20 actual orthodontic archwire curves including n=16 bending points, the initial value of i is i=1, and the demarcation value of the complexity of the bending points is set as C rb Normalized bending point angular distance ratio demarcation value =0.5 T E * ) b =0.4, calculating the complexity of 16 theoretical orthodontic archwire curve bending points according to the formula for calculating the complexity of theoretical orthodontic archwire bending points in the third step, and taking out the maximum value from the complexity of 16 theoretical orthodontic archwire curve bending points as the maximum value 8 C r ) max ＝ 8 C r =0.39, by comparison 8 C r ) max ＜C rb Calculating the normalized bending point angular distance ratio of 16 theoretical orthodontic archwire curve bending points, and taking out the maximum value from the normalized bending point angular distance ratioBy comparison to obtainSetting an upper limit value (sigma) of the bending point line error fluctuation degree d ) max =0.06, curved point angle error waveUpper limit value (sigma) of mobility a ) max Jumping to step six to evaluate the actual orthodontic archwire curve bending point line error fluctuation degree and the angle error fluctuation degree, wherein the initial value of i is i=1, and in step six a), the method comprises the following steps of i σ d Is derived from the calculation formula of (2) 1 σ d ＝0.05＜(σ d ) max Jump to step six b) according to i σ a Is derived from the calculation formula of (2) 1 σ a ＝0.06＜(σ a ) max Jumping to a step seven, and according to the judgment that 1=16 is not established at this time, i=i+1 and jumping to six a) to evaluate the line error fluctuation degree and the angle error fluctuation degree of the subsequent bending points, according to the step, calculating the 2 nd, 3 rd, 4 th, 5 th, 6 th, 7 th, 8 th, 9 th, 10 th, 11 th, 12 th, 13 th, 14 th, 15 th and 16 th bending points of 20 actual orthodontic archwire curves, wherein the line error fluctuation degree and the angle error fluctuation degree of all the actual orthodontic wire curves are smaller than the corresponding upper limit values, and outputting that the line error fluctuation degree and the angle error fluctuation degree of all the actual orthodontic wire curves are within the allowable range, and ending the orthodontic archwire evaluation. / >

Claims (1)

1. An orthodontic archwire error fluctuation degree evaluation method based on position error judgment is characterized by comprising the following steps of: the method comprises the following specific implementation processes:
step one, importing theoretical orthodontic archwire curve data and actual orthodontic archwire curve data:
an o-xyz three-dimensional orthodontic archwire error calibration coordinate system w is established according to a right-hand rule, a theoretical orthodontic archwire curve with n bending points designed by an orthodontist according to the dentition form of a patient is used for calculating and inputting a 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 α' i , T β' i , T γ' i , T d' i ) Pose information of coordinate system w is marked for ith bending point of theoretical orthodontic archwire curve relative to three-dimensional orthodontic archwire errorThe value range of i is 1-n, T α' i an included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, T β' i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, T γ' i an included angle formed by a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, T d' i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the theoretical orthodontic archwire curve is p s The right end point of the theoretical orthodontic archwire curve is p f ，p s And p f The midpoint of the connecting line between the two is T o', spatially transforming the theoretical orthodontic archwire curve: let the dot T o' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left endpoint p of the theoretical orthodontic archwire curve s The right endpoint p of the theoretical orthodontic archwire curve is positioned on the negative half axis of the y axis f The method comprises the steps of locating at a y-axis positive half shaft, enabling a theoretical orthodontic archwire curve to have no intersection point with an x-axis positive half shaft, enabling the theoretical orthodontic archwire curve to rotate clockwise along the y-axis positive direction until the intersection point occurs between the theoretical orthodontic archwire curve and the x-axis positive half shaft, setting the pose of the theoretical orthodontic archwire curve after spatial transformation as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, calculating and inputting a theoretical orthodontic archwire curve bending point information set P under the final pose T ＝{ T p 1 , T p 2 , T p 3 ,..., T p i ,..., T p n }， T p i ＝( T α i , T β i , T γ i , T d i ) The pose information of the coordinate system w is marked for the ith bending point of the theoretical orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, T α i ith bending point of theoretical orthodontic archwire curve in final pose and three-dimensional orthodontic archwire errorCalibrating an included angle formed by a connecting line between origins o of the coordinate system w and an x axis, T β i for the included angle formed by the connection line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the y axis, T γ i For the included angle formed by the connecting line between the ith bending point of the theoretical orthodontic archwire curve in the final pose and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the z axis, T d i calibrating the length of a connecting line between an ith bending point of a theoretical orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w;
calculating and inputting an actual orthodontic archwire curve information set by using m actual orthodontic archwire curves with n bending points manufactured according to theoretical orthodontic archwire curves The value range of j is more than or equal to 1 and less than or equal to m for the j-th actual orthodontic arch wire curve bending point information set>The pose information of a coordinate system w is marked for the ith bending point of the jth actual orthodontic archwire curve relative to the error of the three-dimensional orthodontic archwire,/for the jth actual orthodontic archwire curve>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and an x axis is>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is>An included angle formed by a connecting line between the ith bending point of the jth actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and a z axis is >Calibrating the length of a connecting line between an ith bending point of the jth actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; the left end point of the j-th actual orthodontic archwire curve is j p' s The right end point of the j-th actual orthodontic archwire curve is j p' f ， j p' s And j p' f the midpoint of the connecting line between them is +.>Spatially transforming the j-th actual orthodontic archwire curve: let point->Coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point of the j-th actual archwire curve j p' s Is positioned at the right end point of the j-th actual orthodontic archwire curve on the negative half axis of the y axis j p' f The method comprises the steps of locating at a y-axis positive half shaft, enabling a j-th actual orthodontic arch wire curve to have no intersection point with an x-axis positive half shaft, enabling the j-th actual orthodontic arch wire curve to rotate clockwise along the y-axis positive direction until the j-th actual orthodontic arch wire curve has an intersection point with the x-axis positive half shaft, setting the pose of the j-th actual orthodontic arch wire curve after space transformation as the final pose in a three-dimensional orthodontic arch wire error calibration coordinate system, calculating and inputting m actual orthodontic arch wire curve information sets under the final pose Bending point information set for j-th actual orthodontic archwire curve in final pose,/->Calibrating pose information of a coordinate system w for the ith bending point of the jth actual orthodontic archwire curve in the final pose relative to the three-dimensional orthodontic archwire error, and +. >An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and an x-axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis is +.>An included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve in the final pose and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z axis is +.>Calibrating the length of a connecting line between an ith bending point of the actual orthodontic archwire curve in the final pose and an origin o of a coordinate system w for the error of the three-dimensional orthodontic archwire;
setting errors of actual orthodontic archwire curve bending point positions:
defining the position error of an actual orthodontic archwire curve bending point, wherein the bending point position error is the quantitative description of the accuracy of the bending position of the orthodontic archwire curve bending point, and the evaluation of the actual orthodontic archwire curve bending point position error comprises two parts, namely the error rate evaluation of an actual orthodontic archwire curve bending point and the actual error rate evaluation of an actual orthodontic archwire curve bending point, respectivelyEvaluating the average offset error rate of the curve bending points of the orthodontic archwire; defining the line error rate of the actual orthodontic archwire curve point, symbolized by e d Representing a line error rate e d Is a quantitative description of the linear distance between a theoretical orthodontic archwire curve bending point and the origin o of a three-dimensional orthodontic archwire error calibration coordinate system and the error of the linear distance between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system, and the line error rate of the ith bending point of the actual orthodontic archwire curve in the final pose is expressed asDefining average bias error rate of actual orthodontic arch wire curve bending point by using symbol e a Indicating an average bias error rate e a The method is a quantitative description of the included angle between a theoretical orthodontic archwire curve bending point and each coordinate axis of a three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between an actual orthodontic archwire curve bending point corresponding to the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system, and the average offset error rate of the ith bending point of the actual orthodontic archwire curve in the final pose is expressed as follows>Wherein the method comprises the steps ofAngle of ith bending point of theoretical orthodontic archwire curve T α i Angle with the ith bending point of the jth actual orthodontic archwire curve Error rate between, stipulate-> Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate-> Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle +.f. to the ith point of curvature of the jth actual orthodontic archwire curve>Error rate between, stipulate->
Step three, setting the complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending points of theoretical orthodontic archwire by using symbol C r Representation, C r Is the comprehensive quantitative description of the bending difficulty of the bending point of the theoretical orthodontic archwire curve, and the complexity of the ith bending point of the theoretical orthodontic archwire curve is expressed as Normalized bending point angular distance ratio representing ith bending point of theoretical orthodontic archwire curve, stipulation T E i The angle-to-distance ratio of the bending point representing the ith bending point of the theoretical orthodontic archwire curve is a quantitative description of the bending complexity of a single bending point on the orthodontic archwire curve, provision ∈> T θ i To act on curve bending point of orthodontic arch wire T p i The bending angle of the position is equal to the bending angle, T p i-1 T p i representing the bending distance acting at the ith bending point of the theoretical orthodontic archwire curve, namely the theoretical orthodontic archwire curve bending point T p i-1 And (3) with T p i The length of the curve segment between the two is 1 st bending point of the theoretical orthodontic archwire curve T p 1 ， T p 0 T p 1 Representing bending points T p 1 To the left end point p of the theoretical orthodontic archwire curve s The length of the curve segment between the two, T E min is the minimum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire, T E max the maximum value of the curve bending point angular distance ratio of the theoretical orthodontic archwire; provision of->The boundary value of (C) is% T E * ) b ；/>Normalized bending point density representing the ith bending point of a theoretical orthodontic archwire curve, prescribing +.> T ρ i The bending point density of the ith bending point of the theoretical orthodontic archwire curve is represented, and the bending point density is the quantitative description of the tightness degree between a single bending point and adjacent bending points on the orthodontic archwire curve, and is stipulated->The value 1 in the formula is expressed as 1 bending point, T l i represents the linear distance between the ith bending point of the theoretical orthodontic archwire curve and the nearest bending point, namely +.> Represents the straight line distance between the ith-1 bending point of the theoretical orthodontic archwire curve and the ith bending point of the theoretical orthodontic archwire curve, +.>Represents the straight line distance between the ith bending point of the theoretical orthodontic archwire curve and the (i+1) th bending point of the theoretical orthodontic archwire curve, and when i=1, the rule is +.> Represents the 1 st bending point of the theoretical orthodontic archwire curve and the left endpoint p of the theoretical orthodontic archwire curve s Straight line distance between>Representing the linear distance between the 1 st bending point of the theoretical orthodontic archwire curve and the 2 nd bending point of the theoretical orthodontic archwire curve, when i=n, prescribing +.> Represents the straight line distance between the n-1 th bending point of the theoretical orthodontic archwire curve and the n-th bending point of the theoretical orthodontic archwire curve,represents the nth bending point of the theoretical orthodontic archwire curve and the right endpoint p of the theoretical orthodontic archwire curve f The straight-line distance between the two, T ρ min is the minimum value of the curve bending point density of the theoretical orthodontic archwire, T ρ max the maximum value of the curve bending point density of the theoretical orthodontic archwire; complexity formula->The numerical value 2 in (1) represents two parameters of the angle-to-distance ratio of a normalized bending point and the single density of the normalized bending point are considered when calculating the complexity of the bending point of the theoretical orthodontic arch wire; complexity C of curve bending point of theoretical orthodontic archwire r Is C rb ；
Setting the error fluctuation degree of the curve bending point line and the angle error fluctuation degree of the actual orthodontic archwire:
defining the line error fluctuation degree of the curve bending point of the actual orthodontic arch wire by using the symbol sigma d Representation, sigma d Is the quantitative description of the bending distance stability of the bending point of the actual orthodontic archwire curve, and the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curve is expressed as Representing the line error rate of the ith bending point of the jth actual orthodontic archwire curve,/>Mean value of line error rate representing the ith bending point of m actual orthodontic archwire curves, prescribing +.>Line error wave of ith bending point of m actual orthodontic archwire curvesThe upper limit of the mobility is (sigma d ) max The method comprises the steps of carrying out a first treatment on the surface of the Defining the angle error fluctuation degree of the bending point of the actual orthodontic arch wire curve by using the symbol sigma a Representation, sigma a Is the quantitative description of the bending angle stability of the bending point of the actual orthodontic archwire curve, and the fluctuation degree of the angle error of the ith bending point of the actual orthodontic archwire curve is expressed asWherein->Mean value of angle error rate of ith bending point of m actual orthodontic archwire curves, stipulated +.>The upper limit value of the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is (sigma a ) max ；
Fifthly, verifying the complexity and the normalized bending point angular distance ratio of the bending point of the theoretical orthodontic arch wire curve:
according to the formulaCalculating the complexity of the ith bending point on the theoretical orthodontic archwire curve, namely 1 C r Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 I is i=1, and is taken out by comparison i C r Maximum value of [ (] i C r ) max For conditions of% i C r ) max ≤C rb Verifying; according to the formula->Calculating the normalized bending point angular distance ratio of the ith bending point on the theoretical orthodontic archwire curve, namely +. >Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 Is obtained by comparing the normalized bending point angular distance ratio of +.>Maximum value of +.>For condition->The verification is carried out, specifically:
a) Verifying the complexity of a curve bending point of a theoretical orthodontic arch wire;
if it is% i C r ) max ≤C rb If so, verifying the normalized bending point angular distance ratio of the theoretical orthodontic archwire curve, and jumping to the step five);
if it is% i C r ) max ≤C rb If the curve is not true, the complexity of the curve bending point of the theoretical orthodontic archwire is larger, the evaluation method is not applicable to the curve of the orthodontic archwire, and the output of the evaluation method is not applicable to the curve of the orthodontic archwire, and the evaluation of the error fluctuation degree of the orthodontic archwire is finished;
b) Verifying the angle-to-distance ratio of a theoretical orthodontic archwire curve normalized bending point;
if it isIf yes, jumping to the step six;
if it isIf the curve is not true, the complexity of the curve bending point of the theoretical orthodontic archwire or the angle distance of the normalized bending point is larger, the evaluation method is not applicable to the curve of the orthodontic archwire, and the output of the evaluation method is not applicable to the curve of the orthodontic archwire, and the evaluation of the error fluctuation degree of the orthodontic archwire is finished;
step six, evaluating the error fluctuation degree of the curve bending point line of the actual orthodontic archwire and the error fluctuation degree of the curve angle of the actual orthodontic archwire:
According to i σ d And i σ a calculating the line error fluctuation degree and the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, wherein the initial value of i is i=1;
a) Evaluation of error fluctuation degree of curve bending point line of actual orthodontic archwire
According to the formulaCalculating the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ d ≤(σ d ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves is within the allowable range, skipping to the step six b);
if it is i σ d ≤(σ d ) max If the line error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range, outputting the line error fluctuation degree of the ith bending point of the actual orthodontic archwire curves to exceed the allowable range, and ending the orthodontic archwire evaluation;
b) Evaluation of error fluctuation degree of curve bending point angle of actual orthodontic archwire
According to the formulaCalculating the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves, and judging i σ a ≤(σ a ) max Whether it is true or not,
the method comprises the following steps:
if it is i σ a ≤(σ a ) max The establishment of the angle error wave of the ith bending point of the m actual orthodontic archwire curves is illustratedIf the degree of motion is within the allowable range, jumping to the step seven;
if it is i σ a ≤(σ a ) max If not, the fact that the angle error fluctuation degree of the ith bending point of the m actual orthodontic archwire curves exceeds the allowable range is indicated, and then the angle error fluctuation degree of the ith bending point of the output actual orthodontic archwire curves exceeds the allowable range, and the orthodontic archwire evaluation is finished;
Step seven, judging whether the bending points of the m actual orthodontic archwire curves are evaluated completely or not:
judging whether the number n of i and the number n of the bending points of the actual orthodontic archwire curve are equal,
the method comprises the following steps:
if i=n is not satisfied, indicating that all bending points on the m actual orthodontic archwire curves are not evaluated, making i=i+1, namely, indicating that the next group of actual orthodontic archwire curve bending points are evaluated, and jumping to the step six);
if i=n is true, it is indicated that all the bending points on the m actual orthodontic archwire curves have been evaluated, and the line error fluctuation degree and the angle error fluctuation degree of all the actual orthodontic archwire curve bending points are within the allowable range, then the line error fluctuation degree and the angle error fluctuation degree of all the actual orthodontic archwire curve bending points are output to be within the allowable range, and the orthodontic archwire evaluation is finished.
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