CN115024839B - Orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio - Google Patents

Orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio Download PDF

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CN115024839B
CN115024839B CN202210402211.2A CN202210402211A CN115024839B CN 115024839 B CN115024839 B CN 115024839B CN 202210402211 A CN202210402211 A CN 202210402211A CN 115024839 B CN115024839 B CN 115024839B
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orthodontic archwire
curve
bending point
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CN115024839A (en
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姜金刚
谭棋匀
孙洋
张永德
王开瑞
吴殿昊
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Harbin University of Science and Technology
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A61C7/002—Orthodontic computer assisted systems
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A61C7/12—Brackets; Arch wires; Combinations thereof; Accessories therefor
    • A61C7/20—Arch wires
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A61C7/002—Orthodontic computer assisted systems
    • A61C2007/004—Automatic construction of a set of axes for a tooth or a plurality of teeth

Abstract

The invention discloses an orthodontic archwire error rate evaluation method based on a normalized bending point angular distance ratio, which relates to the field of orthodontic archwire bending evaluation. The invention takes the angle distance ratio of the curve bending points of the theoretical orthodontic archwire as the parameter for calculating the complexity of the curve bending points of the theoretical orthodontic archwire, omits the complicated step of determining the complexity calculation method of each curve bending point of the orthodontic archwire, improves the evaluation efficiency of the orthodontic archwire, and realizes the quantitative evaluation of the orthodontic archwire by calculating the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of the curve bending points of the actual orthodontic archwire.

Description

Orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio
Technical Field
The invention relates to an orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio, 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; although the processing method of the arch wire in the orthodontic appliance starts to transition from the traditional manual bending to the high-precision, automatic and digital direction along with the continuous innovation of the automatic and robot technology, the evaluation method of the orthodontic arch wire also needs to transition to the digital direction, but at the present stage, after the orthodontic arch wire is bent, a doctor still needs to evaluate the orthodontic arch wire according to experience to judge whether the use requirement is met, and the method depends on the clinical experience of the doctor seriously, and the doctor can only rely on the personal clinical experience to correct the bent orthodontic arch wire, so that the quantitative evaluation of the orthodontic arch wire is difficult to realize.
In addition, considering the individuation characteristics of the distribution information of the bending points on the orthodontic archwire curve, for example, the bending points on the patient individuation orthodontic archwire curve often have relatively smaller normalized bending point density, and the normalized bending point density of each bending point is smaller than a specified upper limit value, namely, the distribution of the bending points of the archwire has special attribute, when the orthodontic archwire is evaluated, no method can determine the error magnitude of the bending points of the orthodontic archwire through indexes at present, and the high-efficiency quantitative evaluation of the bending accuracy of the individuation orthodontic archwire is realized; the existing method for evaluating the orthodontic archwire according to experience cannot provide accurate and reliable guidance for correcting a shaping planning method for bending the archwire by adopting an orthodontic archwire bending robot, prolongs the correction period, seriously influences the clinical correction effect, simultaneously causes unnecessary consumption of manpower and material resources and prevents the orthodontic archwire bending robot from being applied to correction of wrong jaw deformity; in summary, a method capable of precisely quantitatively evaluating the bending accuracy of the orthodontic archwire 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 rate evaluation method based on a normalized bending point angular distance ratio, solves the problem that a class of quantitative evaluation methods for orthodontic archwires with smaller normalized bending point density is lacking in the current orthodontic archwire evaluation field, determines a complexity calculation method for the orthodontic archwires with smaller normalized bending point density in the orthodontic archwire evaluation process, and realizes the efficient quantitative evaluation of the orthodontic archwire bending accuracy by calculating the weighted error rate of the orthodontic archwire bending points.
An orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio 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 ) 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 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 Is positioned on the positive half axis of the y axis, and the theoretical orthodontic archwire curve has no intersection point with the positive half axis of the x axis, and thenRotating the theoretical orthodontic archwire curve clockwise along the positive direction of the y axis until the theoretical orthodontic archwire curve and the positive half axis of the x axis form an intersection point, 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, and 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 position information of the ith bending point of the theoretical orthodontic archwire curve in the final pose relative to the three-dimensional orthodontic archwire error calibration coordinate system w, 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 bending point information set by using an actual orthodontic archwire curve with n bending points manufactured according to a theoretical orthodontic archwire curve R P'＝{ R p′ 1 , R p' 2 , R p' 3 ,..., R p′ i ,..., R p' n }， R p′ i ＝( R α′ i , R β′ i , R γ′ i , R d′ i ) The ith bending point of the actual orthodontic archwire curve is relative to three dimensionsThe orthodontic archwire error marks the pose information of the coordinate system w, R α′ i An included angle formed by the connecting line between the ith bending point of the actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, R β′ i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, R γ′ i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, R d′ i calibrating the length of a connecting line between an ith bending point of an 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 actual orthodontic archwire curve is p' s The right end point of the actual orthodontic archwire curve is p' f ，p' s And p' f The midpoint of the connecting line between the two is R o', spatially transforming the actual orthodontic archwire curve: let the dot R o ' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point p ' of the actual archwire curve ' s The right end point p 'of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis' f The method comprises the steps that an actual orthodontic archwire curve is located on a y-axis positive half shaft, no intersection point exists between the actual orthodontic archwire curve and an x-axis positive half shaft, the actual orthodontic archwire curve is rotated clockwise along the y-axis positive direction until the intersection point occurs between the actual orthodontic archwire curve and the x-axis positive half shaft, the pose of the actual orthodontic archwire curve after spatial transformation is set as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, and an actual orthodontic archwire curve bending point information set under the final pose is calculated and input R P＝{ R p 1 , R p 2 , R p 3 ,..., R p i ,..., R p n }， R p i ＝( R α i , R β i , R γ i , R d i ) The pose information of the coordinate system w is marked for the ith bending point of the actual orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, R α i the ith bending point and three bending points of the actual orthodontic archwire curve in the final poseAn included angle formed by a connecting line between the origins o of the orthodontic archwire error calibration coordinate system w and the x axis, R β i 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, R γ i 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, R d i calibrating the length of 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;
step two, calculating and judging the actual orthodontic archwire curve end distance error:
the curve end distance error of the actual orthodontic archwire is defined and is represented by a symbol delta, and because the forming error of each bending point can be accumulated to the distance between two end points of the orthodontic archwire in the bending process of the orthodontic archwire, the end distance error delta needs to be calculated and judged, and delta= |is regulated T a- R a|， T a represents the left endpoint p of the theoretical orthodontic archwire curve s And theoretical orthodontic archwire curve right end point p f The straight-line distance between the two, R a represents the left endpoint p 'of the curve of the actual orthodontic archwire' s And the right end point p 'of the actual orthodontic archwire' f The distance between the two is defined as delta, and the upper limit value of the end distance error delta is defined as delta max Judging delta is less than or equal to delta max Whether it is true or not,
the method comprises the following steps:
if delta is less than or equal to delta max If the actual orthodontic archwire curve end distance error is within the allowable range, the step III is skipped;
if delta is less than or equal to delta max If the error is not satisfied, the actual orthodontic archwire curve end distance error exceeds the allowable range, and the actual orthodontic archwire curve end distance error is output to exceed the allowable range, and the orthodontic archwire evaluation is finished;
calculating complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending point of theoretical orthodontic archwire and using symbolsNumber C r Representation, C r Is the comprehensive quantitative description of the bending difficulty of the theoretical orthodontic archwire bending point, C of the theoretical orthodontic archwire curve bending point r The higher the value, i.e. the more difficult the bending point is in bending, the greater the impact of the magnitude of the error rate of the bending point on the evaluation of the actual orthodontic archwire, the complexity of the ith bending point of the theoretical orthodontic archwire curve is specified as Normalized bending point angular distance ratio representing ith bending point of theoretical orthodontic archwire curve, prescribing +.> T E i The angle-to-distance ratio of the bending points of the ith bending point of the theoretical orthodontic archwire curve is represented, and the angle-to-distance ratio of the bending points is a quantitative description of the bending complexity degree of a single bending point of the orthodontic archwire curve, prescribing +.> 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; />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 theoretical 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 +.>Representation theoryThe linear 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 for the maximum value of the curve bending point density of the theoretical orthodontic archwire, prescribe +.>The upper limit value of +.>A represents the number of parameters considered in calculating complexity;
step four, verifying the normalized bending point density of the theoretical orthodontic archwire curve:
According to the formulaCalculating normalized bending point density of ith bending point on theoretical orthodontic archwire curve, namely +.>Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 Is taken out by comparisonMaximum value of +.>For condition->The verification is performed such that,
the method comprises the following steps:
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 n The maximum normalized bending point density within the predetermined value is not more than the set normalized bending point density upper limit value +.>The normalized bending point density of each bending point on the theoretical orthodontic archwire curve is less than or equal to the upper limit value +.>It can be known that on the obtained actual orthodontic archwire curve comprising n bending points, all the bending points can meet the requirement of an evaluation system on the normalized bending point density of the actual orthodontic archwire curve, namely the bending difficulty caused by the normalized bending point density of the theoretical orthodontic archwire curve is smaller, so that when the complexity calculation is carried out on the bending points of the actual orthodontic archwire curve bent by the theoretical orthodontic archwire curve with the special normalized bending point angle-to-distance ratio, the influence of the normalized bending point density of the theoretical orthodontic archwire curve is not required to be considered, and the method only calculates the complexity of the bending points of the theoretical orthodontic archwire curve by taking the normalized bending point angle-to-distance ratio of the theoretical orthodontic archwire curve as a parameter, wherein at the moment, A=1, " >Jumping to a fifth step;
if it isIf the evaluation method is not applicable to the orthodontic archwire curve, outputting the orthodontic archwire error rate evaluation ending;
setting an actual orthodontic archwire curve bending point weighted curvature error rate, an actual orthodontic archwire curve bending point weighted line error rate and an actual orthodontic archwire curve bending point average offset error rate:
defining weighted curvature error rate of actual orthodontic archwire curve bending point by using symbolsIndicating a weighted curvature error rate +.>For the quantitative description of the error between the curvature of a theoretical orthodontic arch wire curve bending point and the curvature of an actual orthodontic arch wire curve bending point corresponding to the theoretical orthodontic arch wire curve bending point, the weighted curvature error of the ith bending point of the actual orthodontic arch wire curve is specified as +> i e c The curvature error rate of the ith bending point of the actual orthodontic archwire curve is expressed, stipulated +.> T K i Representing the curvature of the ith bending point of the theoretical orthodontic archwire curve, R K i representing the curvature of the ith bending point of the actual orthodontic archwire curve, and prescribing the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve>The upper limit value of +.>Defining the weighted line error rate of the curve bending point of the actual orthodontic archwire, and using the symbol +. >Indicating a weighted line error rate +.>Is the theoretical orthodonticQuantitative description of errors of linear distance between arch wire curve bending point and three-dimensional orthodontic arch wire error calibration coordinate system origin o and linear distance between actual orthodontic arch wire curve bending point corresponding to theoretical orthodontic arch wire curve bending point and three-dimensional orthodontic arch wire error calibration coordinate system origin o, and weight line error rate of ith bending point of the actual orthodontic arch wire curve is expressed as +.> i e d Line error rate representing the ith bending point of the actual orthodontic archwire curve, prescribing +.>Specifying the actual orthodontic archwire curve bending point weighted line error rate +.>The upper limit of +.>Defining weighted average bias error rate of actual orthodontic archwire curve bending point by using symbol +.>Indicating a weighted average bias error rate +.>For the quantitative description of the included angle between the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between the 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, the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve is specified to be expressed as > i e a Mean offset error representing the ith bending point of an actual orthodontic archwire curveDifferential rate, stipulate->Wherein the method comprises the steps of i e α Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle with the ith bending point of the actual orthodontic archwire curve R α i Error rate between, stipulate-> i e β Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle with the ith bending point of the actual orthodontic archwire curve R β i Error rate between, stipulate-> i e γ Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle with the ith bending point of the actual orthodontic archwire curve R γ i Error rate between, stipulate->Defining weighted average bias error rate of actual orthodontic archwire curve bending point>The upper limit of +.>
Step six, evaluating the error rate of the actual orthodontic archwire curve:
according to the formulaCalculating the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve according to the formula +.>Calculating actual orthodontic archwireWeighted line error rate of the ith curve point according to the formulaCalculating a weighted average bias error rate of an ith bending point of an actual orthodontic archwire curve, wherein the initial value of i is i=1;
a) Evaluation of weighted curvature error rate of actual orthodontic archwire curve bending point
According to the formulaThe calculated weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve is judged +. >Whether it is true or not,
the method comprises the following steps:
if it isIf the error rate of the weighted curvature of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six b);
if it isIf the error rate exceeds the allowable range, outputting that the error rate exceeds the allowable range, and ending the orthodontic archwire evaluation;
b) Evaluation of error rate of actual orthodontic archwire curve bending point weighted line
According to the formulaThe calculated line error rate of the ith bending point of the actual orthodontic archwire curve is judgedWhether or not to useIt is true that the method is that,
the method comprises the following steps:
if it isIf the weighted line error rate of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six) is carried out;
if it isIf the error rate of the weighted line of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, outputting that the error rate of the weighted line of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, and ending the orthodontic archwire evaluation;
c) Evaluation of weighted average bias error rate of actual orthodontic archwire bending point
According to the formulaThe average bias error rate of the ith bending point of the calculated actual orthodontic archwire curve is judged +. >Whether it is true or not,
the method comprises the following steps:
if it isThe method includes the steps that (1) the weighted average bias error rate of the ith bending point of an actual orthodontic archwire curve is in an allowable range, and the step (seven) is skipped;
if it isIf the error rate exceeds the allowable range, outputting that the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, and ending the orthodontic archwire evaluation;
step seven, judging whether the actual orthodontic archwire curve bending point is 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 actual orthodontic archwire curve bending points are not evaluated, making i=i+1, namely, indicating that the next actual orthodontic archwire curve bending point is evaluated, and jumping to the step six a);
if i=n is true, it is indicated that all actual orthodontic archwire curve bending points have been evaluated, and the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are within the allowable range, then the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are output to be 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, provides a pre-judging parameter for evaluating an orthodontic archwire by taking the normalized bending point density as an orthodontic archwire, and sets the upper limit value of the normalized bending point density of an orthodontic archwire curve asThe maximum normalized bending point density of bending points on an orthodontic archwire curve is verified to be not more than the upper limit value of the normalized bending point density in advance before the orthodontic archwire is evaluated>The normalized bending point density of each bending point on the orthodontic archwire curve can be obtained>Meets the requirements, thereby providing precondition constraint for the method, determining the complexity calculation method of the bending points of the orthodontic archwire curve, avoiding the need of judging the bending points of each orthodontic archwire curve before evaluating the orthodontic archwire curveThereby determining complicated steps of the complexity calculation method of the bending point of the orthodontic archwire and improving the evaluation efficiency.
2. The invention provides a weighted curvature error rate of bending points of an orthodontic archwire curve aiming at the orthodontic archwire curve with the special attribute of smaller normalized bending point densityConcept of (2) and set->The upper limit value of +.>Considering that the normalized bending point density can only reflect the characteristic among the bending points of the orthodontic archwire curve, the normalized bending point density of the orthodontic archwire curve is smaller, which indicates that the distance among the bending points of the orthodontic archwire is larger, and the shape characteristic of the curve section of the orthodontic archwire among the bending points of the orthodontic archwire curve can not be reflected by the normalized bending points; the deviation of the position of the actual orthodontic archwire curve bending point in the three-dimensional orthodontic archwire error calibration coordinate system w and the position of the theoretical orthodontic archwire curve bending point in the three-dimensional orthodontic archwire error calibration coordinate system w is calculated, and the quantitative evaluation of the accuracy of the actual orthodontic archwire bending point bending position can only be completed by combining the complexity of the actual orthodontic archwire curve bending point determined by the actual orthodontic archwire curve with the special bending point density; thus, the method proposes to use the weighted curvature error rate +. >And as supplementary judgment, the complexity of the bending points of the orthodontic archwire curve is combined, the weighted curvature error rate of the bending points of the orthodontic archwire curve is calculated, and the quantitative evaluation of the accuracy of the bending shape of the orthodontic archwire curve is realized.
3. Compared with the invention patent 'an orthodontic archwire error rate evaluation method based on normalized bending point density' filed by the inventor on the same day, although both methods are applicable to the method withThe personalized orthodontic archwire curve with special attribute is characterized in that the premise of the method mentioned in the method for evaluating the error rate of the orthodontic archwire based on the normalized bending point density is that the normalized bending point angular distance ratio of each theoretical orthodontic archwire curve bending point meets the set requirement, and the normalized bending point density of the theoretical orthodontic archwire curve bending point is used onlyAs the parameter considered when calculating the complexity of the curve bending point of the theoretical orthodontic archwire, the method focuses on the premise that the normalized bending point density of each curve bending point of the theoretical orthodontic archwire meets the set requirement, and further, the angle distance of the normalized bending point of the curve bending point of the theoretical orthodontic archwire is only +.>Compared with the parameters considered when the complexity of the curve bending point of the orthodontic archwire is calculated and the method provides the weighted curvature error rate of the curve bending point of the orthodontic archwire >Evaluating the accuracy of the curve bending shape of the orthodontic archwire; the two methods are different in application conditions when the actual orthodontic archwire is evaluated, so that the proposal of the method and the other method compensate each other, and further the series of methods for evaluating the actual orthodontic archwire are perfected.
4. Compared with the invention patent 'an orthodontic archwire error rate evaluation method based on bending point complexity judgment' declared by the inventor on the same day,the method is based on the premise that the bending points on the personalized orthodontic archwire curve have special attribute with smaller normalized bending point density, does not judge the complexity of each bending point on the theoretical orthodontic archwire curve and does not need to evaluate the weighted curvature error rate of the bending pointsIs judged by (1); normalized Density of the bending points before evaluation of orthodontic archwires>The judgment is carried out, so that the normalized density of the bending points of the theoretical orthodontic archwire curve is not considered in the process of calculating the complexity of the bending points of the theoretical orthodontic archwire curve, and only the normalized angular distance ratio of the bending points is considered in the process of calculating the complexity of the bending points of the theoretical orthodontic archwire curve, thereby not only meeting the error evaluation of the actual orthodontic archwire curve, but also reducing the complexity of an orthodontic archwire evaluation algorithm and improving 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 an orthodontic archwire error rate evaluation method based on normalized bending point-to-angular distance ratio;
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 an actual orthodontic archwire curve prior to spatial transformation;
FIG. 4 is a schematic illustration of a theoretical orthodontic archwire curve in a final pose and an actual orthodontic archwire curve with a bending point error exceeding an upper limit;
FIG. 5 is a schematic illustration of a theoretical orthodontic archwire curve in a final pose and an actual orthodontic archwire curve with errors 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 rate evaluation method based on normalized bending point angular distance ratio 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 ) 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 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 Located on the y-axisThe theoretical orthodontic archwire curve and the x-axis orthodontic half shaft have no intersection point, the theoretical orthodontic archwire curve is rotated clockwise along the y-axis orthodontic direction until the intersection point appears between the theoretical orthodontic archwire curve and the x-axis orthodontic half shaft, the pose of the theoretical orthodontic archwire curve after spatial transformation is set as the final pose in the three-dimensional orthodontic archwire error calibration coordinate system w, and the theoretical orthodontic archwire curve bending point information set P under the final pose is calculated and input 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 position information of the ith bending point of the theoretical orthodontic archwire curve in the final pose relative to the three-dimensional orthodontic archwire error calibration coordinate system w, 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 bending point information set by using an actual orthodontic archwire curve with n bending points manufactured according to a theoretical orthodontic archwire curve R P'＝{ R p′ 1 , R p' 2 , R p' 3 ,..., R p′ i ,..., R p' n }， R p′ i ＝( R α′ i , R β′ i , R γ′ i , R d′ i ) The pose information of the coordinate system w is marked for the ith bending point of the actual orthodontic archwire curve relative to the error of the three-dimensional orthodontic archwire, R α i ' is the included angle formed by the x axis and the connecting line between the ith bending point of the actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, R β′ i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, R γ′ i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, R d′ i calibrating the length of a connecting line between an ith bending point of an 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 actual orthodontic archwire curve is p' s The right end point of the actual orthodontic archwire curve is p' f ，p' s And p' f The midpoint of the connecting line between the two is R o', spatially transforming the actual orthodontic archwire curve: let the dot R o ' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point p ' of the actual archwire curve ' s The right end point p 'of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis' f The method comprises the steps that an actual orthodontic archwire curve is located on a y-axis positive half shaft, no intersection point exists between the actual orthodontic archwire curve and an x-axis positive half shaft, the actual orthodontic archwire curve is rotated clockwise along the y-axis positive direction until the intersection point occurs between the actual orthodontic archwire curve and the x-axis positive half shaft, the pose of the actual orthodontic archwire curve after spatial transformation is set as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, and an actual orthodontic archwire curve bending point information set under the final pose is calculated and input R P＝{ R p 1 , R p 2 , R p 3 ,..., R p i ,..., R p n }， R p i ＝( R α i , R β i , R γ i , R d i ) The pose information of the coordinate system w is marked for the ith bending point of the actual orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, R α i 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, R β i 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, R γ i 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, R d i calibrating the length of 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;
step two, calculating and judging the actual orthodontic archwire curve end distance error:
the curve end distance error of the actual orthodontic archwire is defined, and is represented by a symbol delta, and delta= |is regulated T a- R a|， T a represents the left endpoint p of the theoretical orthodontic archwire curve s And theoretical orthodontic archwire curve right end point p f The straight-line distance between the two, R a represents the left endpoint p 'of the curve of the actual orthodontic archwire' s And the right end point p 'of the actual orthodontic archwire' f The distance between the two is defined as delta, and the upper limit value of the end distance error delta is defined as delta max Judging delta is less than or equal to delta max Whether it is true or not,
the method comprises the following steps:
if delta is less than or equal to delta max If the actual orthodontic archwire curve end distance error is within the allowable range, the step III is skipped;
if delta is less than or equal to delta max If the error is not satisfied, the actual orthodontic archwire curve end distance error exceeds the allowable range, and the actual orthodontic archwire curve end distance error is output to exceed the allowable range, and the orthodontic archwire evaluation is finished;
Calculating complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending point of theoretical orthodontic arch wire by using symbol C r Representation, C r Is the comprehensive quantity of the bending difficulty degree of the theoretical orthodontic arch wire bending pointThe 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 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 on the theoretical orthodontic archwire curve, and is stipulated-> 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; />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 theoretical 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 straight line distance is regulatedRepresents 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 density of the theoretical orthodontic archwire, T ρ max for the maximum value of the curve bending point density of the theoretical orthodontic archwire, prescribe +.>The upper limit value of +.>A represents the number of parameters considered in calculating complexity;
step four, verifying the normalized bending point density of the theoretical orthodontic archwire curve:
according to the formulaCalculating normalized bending point density of ith bending point on theoretical orthodontic archwire curve, namely +.>Represents the 1 st bending point on the theoretical orthodontic archwire curve T p 1 Is taken out by comparisonMaximum value of +.>For condition->The verification is performed such that,
the method comprises the following steps:
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 n The maximum normalized bending point density within the predetermined value is not more than the set normalized bending point density upper limit value +.>The normalized bending point density of each bending point on the theoretical orthodontic archwire curve is less than or equal to the upper limit value +.>At this time a=1, +>Jumping to a fifth step;
if it isIf the evaluation method is not applicable to the orthodontic archwire curve, outputting the orthodontic archwire error rate evaluation ending;
Setting an actual orthodontic archwire curve bending point weighted curvature error rate, an actual orthodontic archwire curve bending point weighted line error rate and an actual orthodontic archwire curve bending point average offset error rate:
defining weighted curvature error rate of actual orthodontic archwire curve bending point by using symbolsIndicating a weighted curvature error rate +.>For the quantitative description of the error between the curvature of a theoretical orthodontic arch wire curve bending point and the curvature of an actual orthodontic arch wire curve bending point corresponding to the theoretical orthodontic arch wire curve bending point, the weighted curvature error of the ith bending point of the actual orthodontic arch wire curve is specified as +>ie c The curvature error rate of the ith bending point of the actual orthodontic archwire curve is expressed, and the regulation is carried out T K i Representing the curvature of the ith bending point of the theoretical orthodontic archwire curve, R K i representing the curvature of the ith bending point of the actual orthodontic archwire curve, and prescribing the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve>The upper limit value of +.>Defining the weighted line error rate of the curve bending point of the actual orthodontic archwire, and using the symbol +.>Indicating a weighted line error rate +.>For 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, the weighted line error rate of the ith bending point of the actual orthodontic archwire curve is specified to be expressed as i e d Line error rate representing the ith bending point of the actual orthodontic archwire curve, prescribing +.>Specifying the actual orthodontic archwire curve bending point weighted line error rate +.>The upper limit of +.>Defining weighted average bias error rate of actual orthodontic archwire curve bending point by using symbol +.>Indicating a weighted average bias error rate +.>For the quantitative description of the included angle between the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between the 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, the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve is specified to be expressed as i e a Mean offset error rate of the ith bending point of the actual orthodontic archwire curve, stipulate +.>Wherein the method comprises the steps of i e α Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle with the ith bending point of the actual orthodontic archwire curve R α i Error rate between, stipulate-> i e β Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle with the ith bending point of the actual orthodontic archwire curve R β i Error rate between, stipulate-> i e γ Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle with the ith bending point of the actual orthodontic archwire curve R γ i Error rate between, prescribeDefining weighted average bias error rate of actual orthodontic archwire curve bending point>The upper limit of +.>
Step six, evaluating the error rate of the actual orthodontic archwire curve:
according to the formulaCalculating the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve according to the formula +.>Calculating the weighted line error rate of the ith bending point of the actual orthodontic archwire curve according to the formulaCalculating a weighted average bias error rate of an ith bending point of an actual orthodontic archwire curve, wherein the initial value of i is i=1; />
a) Evaluation of weighted curvature error rate of actual orthodontic archwire curve bending point
According to the formulaThe calculated weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve is judged +.>Whether it is true or not,
the method comprises the following steps:
if it isIf the error rate of the weighted curvature of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six b);
if it isIf the error rate exceeds the allowable range, outputting that the error rate exceeds the allowable range, and ending the orthodontic archwire evaluation;
b) Evaluation of error rate of actual orthodontic archwire curve bending point weighted line
According to the formulaThe calculated line error rate of the ith bending point of the actual orthodontic archwire curve is judgedWhether it is true or not,
the method comprises the following steps:
if it isIf the weighted line error rate of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six) is carried out;
if it isIf the error rate of the weighted line of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, outputting that the error rate of the weighted line of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, and ending the orthodontic archwire evaluation;
c) Evaluation of weighted average bias error rate of actual orthodontic archwire bending point
According to the formulaThe average bias error rate of the ith bending point of the calculated actual orthodontic archwire curve is judged +.>Whether it is true or not,
the method comprises the following steps:
if it isThe method includes the steps that (1) the weighted average bias error rate of the ith bending point of an actual orthodontic archwire curve is in an allowable range, and the step (seven) is skipped;
if it isIf the error rate exceeds the allowable range, outputting that the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, and ending the orthodontic archwire evaluation;
Step seven, judging whether the actual orthodontic archwire curve bending point is 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 actual orthodontic archwire curve bending points are not evaluated, making i=i+1, namely, indicating that the next actual orthodontic archwire curve bending point is evaluated, and jumping to the step six a);
if i=n is true, it is indicated that all actual orthodontic archwire curve bending points have been evaluated, and the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are within the allowable range, then the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are output to be within the allowable range, and the orthodontic archwire evaluation is ended.
Implementation example 2: as shown in fig. 4, in the process of evaluating the error rate of the orthodontic archwire based on the angle-to-distance ratio of the normalized bending points on an actual orthodontic archwire curve containing n=16 bending points, the initial value of i is i=1, and the upper limit value delta of the end distance error of the actual orthodontic archwire curve is set max =4, calculating the end distance error delta=2.4 of the actual orthodontic archwire curve, and verifying that the end distance error delta is less than or equal to delta of the actual orthodontic archwire curve max If true, jumping to the third step; setting the upper limit value of the normalized bending point density of the theoretical orthodontic archwire curve bending pointThe maximum value +.A. is obtained by calculating the normalized bending point density of 16 bending points of the actual orthodontic archwire curve and comparing>Judging whether the density of the bending points of the actual orthodontic archwire curve exists>The evaluation method is applicable to the actual orthodontic archwire curve; setting the upper limit of the weighted curvature error rate of the actual orthodontic archwire curve bending point>Upper limit of weighted line error rate +.>Upper limit of weighted average bias error rate +.>Calculating the 1 st bending point of the theoretical orthodontic archwire curve according to the formula for calculating the complexity value of the bending point of the theoretical orthodontic archwire curve in the third step T p 1 Complexity of (2) 1 C r =0.41, calculating the 1 st bending point of the actual orthodontic archwire curve according to the fifth step R p 1 Is a weighted curvature error rate>Weighted line error rate +.>And weighted average bias error rate +.>And jumps to step six a) to determine +.>If true, jump to step six b) determine +.>If true, jump to step six c) determine +.>The weighted curvature error rate +_of the first bending point of the actual orthodontic archwire curve is true>Weighted line error rate +.>And weighted average bias error rate +. >If the values are within the allowable range, jumping to the step seven, and verifying that 1=16 is not established at the moment through the step seven, which means that all the bending points of the actual orthodontic archwire curve are not evaluated at the moment, so that i=i+1 is jumped to the step six) to evaluate the 2 nd bending point of the actual orthodontic archwire curve, and by repeating the step, the evaluation of the subsequent bending points of the actual orthodontic archwire curve can be completed, and the bending points of the actual orthodontic archwire curve are assumed R p 2 , R p 3 , R p 4 , R p 5 , R p 6 , R p 7 , R p 8 The weighted curvature error rate, the weighted line error rate, and the weighted average offset error rate are all within the allowable range, but the 9 th bending point of the actual orthodontic archwire curve exists The weighted average offset error rate of the 9 th bending point of the actual orthodontic archwire curve exceeds the upper limit, the weighted average offset error rate of the 9 th bending point of the actual orthodontic archwire curve is output to be overlarge, the subsequent actual orthodontic archwire bending points are not evaluated, and the orthodontic archwire evaluation is finished.
Implementation example 3: as shown in fig. 5, in the process of evaluating the error rate of the orthodontic archwire based on the angle-to-distance ratio of the normalized bending points on an actual orthodontic archwire curve containing n=16 bending points, the initial value of i is i=1, and the upper limit value delta of the end distance error of the actual orthodontic archwire curve is set max =4, calculating the end distance error delta=3.2 of the actual orthodontic archwire curve, and verifying that the end distance error delta is less than or equal to delta of the actual orthodontic archwire curve max Setting the upper limit value of the normalized bending point density of the theoretical orthodontic archwire curve bending pointThe maximum value +.A. is obtained by calculating the normalized bending point density of 16 bending points of the actual orthodontic archwire curve and comparing>By judging the density of the bending points of the actual orthodontic archwire curve>The evaluation method is applicable to the actual orthodontic archwire curve; setting the upper limit of the weighted curvature error rate of the actual orthodontic archwire curve bending point>Upper limit of weighted line error rate +.>Upper limit of weighted average bias error rateCalculating the 1 st bending point of the theoretical orthodontic archwire curve according to the formula for calculating the complexity value of the bending point of the theoretical orthodontic archwire curve in the third step T p 1 Complexity of (2) 1 C r =0.66, calculating the 1 st bending point of the actual orthodontic archwire curve according to the fifth step R p 1 Is a weighted curvature error rate>Weighted line error rate +.>And weighted average bias error rateAnd jumps to step six a) to determine +.>If true, jump to step six b) determine +.>If true, jump to step six c) determine +.>Is true, i.e. the weighted curvature error rate of the first bending point of the actual orthodontic archwire curve +. >Weighted line error rate +.>And weighted average bias error rate/>If the values are within the allowable range, jumping to the step seven, verifying that 1=16 is not established at the moment through the step seven, and indicating that all bending points of the actual orthodontic archwire curve are not evaluated at the moment, so that i=i+1 is jumped to the step six) to evaluate the 2 nd bending point of the actual orthodontic archwire curve, and repeating the step to complete evaluation of the bending point of the subsequent actual orthodontic archwire curve and obtain the bending point of the subsequent actual orthodontic archwire curve through calculation R p 2 , R p 3 , R p 4 , R p 5 , R p 6 , R p 7 , R p 8 , R p 9 , R p 10 , R p 11 , R p 12 , R p 13 , R p 14 , R p 15 , R p 16 If the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate do not exceed the upper limit value, the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of the actual orthodontic archwire curve bending point are all within the allowable range, and the orthodontic archwire evaluation is finished. />

Claims (1)

1. An orthodontic archwire error rate evaluation method based on normalized bending point angular distance ratio 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 ) 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 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 ) Is the ith bending point phase of the theoretical orthodontic archwire curve in the final poseFor the position information of the three-dimensional orthodontic archwire error calibration coordinate system w, 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 bending point information set by using an actual orthodontic archwire curve with n bending points manufactured according to a theoretical orthodontic archwire curve R P'＝{ R p' 1 , R p' 2 , R p' 3 ,..., R p' i ,..., R p' n }， R p' i ＝( R α' i , R β' i , R γ' i , R d' i ) The pose information of the coordinate system w is marked for the ith bending point of the actual orthodontic archwire curve relative to the error of the three-dimensional orthodontic archwire, R α' i An included angle formed by the connecting line between the ith bending point of the actual orthodontic archwire curve and the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w and the x axis, R β' i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a y axis, R γ' i an included angle formed by a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w and a z-axis, R d' i calibrating the length of a connecting line between an ith bending point of an actual orthodontic archwire curve and an origin o of a three-dimensional orthodontic archwire error calibration coordinate system w; actual orthodontic archwire curveThe left end point is p' s The right end point of the actual orthodontic archwire curve is p' f ，p' s And p' f The midpoint of the connecting line between the two is R o', spatially transforming the actual orthodontic archwire curve: let the dot R o ' coincides with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, and the left end point p ' of the actual archwire curve ' s The right end point p 'of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis' f The method comprises the steps that an actual orthodontic archwire curve is located on a y-axis positive half shaft, no intersection point exists between the actual orthodontic archwire curve and an x-axis positive half shaft, the actual orthodontic archwire curve is rotated clockwise along the y-axis positive direction until the intersection point occurs between the actual orthodontic archwire curve and the x-axis positive half shaft, the pose of the actual orthodontic archwire curve after spatial transformation is set as the final pose in a three-dimensional orthodontic archwire error calibration coordinate system w, and an actual orthodontic archwire curve bending point information set under the final pose is calculated and input R P＝{ R p 1 , R p 2 , R p 3 ,..., R p i ,..., R p n }， R p i ＝( R α i , R β i , R γ i , R d i ) The pose information of the coordinate system w is marked for the ith bending point of the actual orthodontic archwire curve in the final pose relative to the error of the three-dimensional orthodontic archwire, R α i 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, R β i 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, R γ i 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, R d i calibrating the length of 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;
step two, calculating and judging the actual orthodontic archwire curve end distance error:
the curve end distance error of the actual orthodontic archwire is defined, and is represented by a symbol delta, and delta= |is regulated T a- R a|， T a represents the left endpoint p of the theoretical orthodontic archwire curve s And theoretical orthodontic archwire curve right end point p f The straight-line distance between the two, R a represents the left endpoint p 'of the curve of the actual orthodontic archwire' s And the right end point p 'of the actual orthodontic archwire' f The distance between the two is defined as delta, and the upper limit value of the end distance error delta is defined as delta max Judging delta is less than or equal to delta max Whether it is true or not,
the method comprises the following steps:
if delta is less than or equal to delta max If the actual orthodontic archwire curve end distance error is within the allowable range, the step III is skipped;
if delta is less than or equal to delta max If the error is not satisfied, the error of the curve end distance of the actual orthodontic archwire exceeds the allowable range, and the error of the curve end distance of the actual orthodontic archwire is output to exceed the allowable range, and the error rate evaluation of the orthodontic archwire is finished;
calculating complexity of a theoretical orthodontic arch wire curve bending point:
defining the complexity of curve bending point of theoretical orthodontic arch wire by using symbol C r Representation, C r Is the comprehensive quantitative description of the bending difficulty of the theoretical orthodontic archwire bending point, 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 of the ith bending point of the theoretical orthodontic archwire curve is represented, the angle-to-distance ratio of the bending point is a quantitative description of the bending complexity of a single bending point on the orthodontic archwire curve,provision of-> 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; />Normalized bending point density representing the ith bending point of a theoretical orthodontic archwire curve, provision 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 straight line distance is regulated 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 for the maximum value of the curve bending point density of the theoretical orthodontic archwire, prescribe +.>The upper limit value of +.>A represents the number of parameters considered in calculating complexity;
step four, verifying the normalized bending point density of the theoretical orthodontic archwire curve:
according to the formulaCalculating normalized bending point density of ith bending point on 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 densities of +.>Maximum value of +.>For condition->The verification is performed such that,
the method comprises the following steps:
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 n The maximum normalized bending point density within the predetermined value is not more than the set normalized bending point density upper limit value +.>The normalized bending point density of each bending point on the theoretical orthodontic archwire curve is less than or equal to the upper limit value +.>At this time a=1, +>Jumping to a fifth step;
if it isIf the evaluation method is not applicable to the orthodontic archwire curve, outputting the orthodontic archwire error rate evaluation ending;
setting an actual orthodontic archwire curve bending point weighted curvature error rate, an actual orthodontic archwire curve bending point weighted line error rate and an actual orthodontic archwire curve bending point average offset error rate:
defining weighted curvature error rate of actual orthodontic archwire curve bending point by using symbolsIndicating a weighted curvature error rate +.>For the quantitative description of the error between the curvature of a theoretical orthodontic arch wire curve bending point and the curvature of an actual orthodontic arch wire curve bending point corresponding to the theoretical orthodontic arch wire curve bending point, the weighted curvature error of the ith bending point of the actual orthodontic arch wire curve is specified as +> i e c Representing the ith bend of the actual orthodontic archwire curveError rate of curvature of point, stipulation- > T K i Representing the curvature of the ith bending point of the theoretical orthodontic archwire curve, R K i representing the curvature of the ith bending point of the actual orthodontic archwire curve, and prescribing the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve>The upper limit value of +.>Defining the weighted line error rate of the curve bending point of the actual orthodontic archwire, and using the symbol +.>Indicating a weighted line error rate +.>For 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, the weighted line error rate of the ith bending point of the actual orthodontic archwire curve is specified to be expressed as> i e d Line error rate representing the ith bending point of the actual orthodontic archwire curve, prescribing +.>Specifying the actual orthodontic archwire curve bending point weighted line error rate +.>The upper limit of +.>Defining weighted average bias error rate of actual orthodontic archwire curve bending point by using symbol +.>Indicating a weighted average bias error rate +.>For the quantitative description of the included angle between the theoretical orthodontic archwire curve bending point and each coordinate axis of the three-dimensional orthodontic archwire error calibration coordinate system and the average error of the included angle between the 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, the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve is specified to be expressed as > i e a Mean offset error rate of the ith bending point of the actual orthodontic archwire curve, stipulate +.>Wherein the method comprises the steps of i e α Angle of ith bending point of theoretical orthodontic archwire curve T α i Angle with the ith bending point of the actual orthodontic archwire curve R α i Error rate between, stipulate-> i e β Angle of ith bending point of theoretical orthodontic archwire curve T β i Angle with the ith bending point of the actual orthodontic archwire curve R β i Error rate between, stipulate-> i e γ Angle of ith bending point of theoretical orthodontic archwire curve T γ i Angle with the ith bending point of the actual orthodontic archwire curve R γ i Error rate between, stipulate->Defining weighted average bias error rate of actual orthodontic archwire curve bending point>The upper limit of +.>
Step six, evaluating the error rate of the actual orthodontic archwire curve:
according to the formulaCalculating the weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve according to the formula +.>Calculating the weighted line error rate of the ith bending point of the actual orthodontic archwire curve according to the formula +.>Calculating a weighted average bias error rate of an ith bending point of an actual orthodontic archwire curve, wherein the initial value of i is i=1;
a) Evaluation of weighted curvature error rate of actual orthodontic archwire curve bending point
According to the formulaThe calculated weighted curvature error rate of the ith bending point of the actual orthodontic archwire curve is judged +. >Whether it is true or not,
the method comprises the following steps:
if it isIf the error rate of the weighted curvature of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six b);
if it isIf the error rate exceeds the allowable range, outputting that the error rate exceeds the allowable range, and ending the error rate evaluation of the orthodontic archwire;
b) Evaluation of error rate of actual orthodontic archwire curve bending point weighted line
According to the formulaThe calculated line error rate of the ith bending point of the actual orthodontic archwire curve is judgedWhether it is true or not,
the method comprises the following steps:
if it isIf the weighted line error rate of the ith bending point of the actual orthodontic archwire curve is within the allowable range, jumping to the step six) is carried out;
if it isFailure, indicating the weighted line error of the ith bending point of the actual orthodontic archwire curveOutputting the weighted line error rate of the ith bending point of the actual orthodontic archwire curve to exceed the allowable range, and ending the orthodontic archwire error rate evaluation;
c) Evaluation of weighted average bias error rate of actual orthodontic archwire curve bending point
According to the formula The average bias error rate of the ith bending point of the calculated actual orthodontic archwire curve is judged +.>Whether it is true or not,
the method comprises the following steps:
if it isThe method includes the steps that (1) the weighted average bias error rate of the ith bending point of an actual orthodontic archwire curve is in an allowable range, and the step (seven) is skipped;
if it isIf the error rate exceeds the allowable range, outputting that the weighted average offset error rate of the ith bending point of the actual orthodontic archwire curve exceeds the allowable range, and ending the orthodontic archwire error rate evaluation;
step seven, judging whether the actual orthodontic archwire curve bending point is 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 actual orthodontic archwire curve bending points are not evaluated, making i=i+1, namely, indicating that the next actual orthodontic archwire curve bending point is evaluated, and jumping to the step six a);
if i=n is true, it is indicated that all actual orthodontic archwire curve bending points have been evaluated, and the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are within the allowable range, then the weighted curvature error rate, the weighted line error rate and the weighted average offset error rate of all actual orthodontic archwire curve bending points are output to be within the allowable range, and the orthodontic archwire error rate evaluation is ended.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2008520350A (en) * 2004-11-17 2008-06-19 スリーエム イノベイティブ プロパティズ カンパニー Calculation of occlusion in 3-D virtual orthodontic system
KR20160082842A (en) * 2014-12-29 2016-07-11 한라대학교산학협력단 Method for calculating bending points and angles of orthodontic archwires using computer and program thereof
CN111588502A (en) * 2020-06-01 2020-08-28 哈尔滨理工大学 Orthodontic arch wire variable-radius circular domain dividing method based on bending point-angular distance ratio sum
CN114028006A (en) * 2021-09-24 2022-02-11 广州瑞通生物科技有限公司 Control method, equipment, medium and product of automatic arch wire bending device

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7240528B2 (en) * 2004-11-22 2007-07-10 Lingualcare, Inc. Method and device for shaping an orthodontic archwire

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2008520350A (en) * 2004-11-17 2008-06-19 スリーエム イノベイティブ プロパティズ カンパニー Calculation of occlusion in 3-D virtual orthodontic system
KR20160082842A (en) * 2014-12-29 2016-07-11 한라대학교산학협력단 Method for calculating bending points and angles of orthodontic archwires using computer and program thereof
CN111588502A (en) * 2020-06-01 2020-08-28 哈尔滨理工大学 Orthodontic arch wire variable-radius circular domain dividing method based on bending point-angular distance ratio sum
CN114028006A (en) * 2021-09-24 2022-02-11 广州瑞通生物科技有限公司 Control method, equipment, medium and product of automatic arch wire bending device

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