阅读说明：本技术 一种正畸弓丝弯制规划等半径圆域划分半径确定方法 (Method for determining equal-radius circular domain division radius of orthodontic arch wire bending planning ) 是由 姜金刚 吴殿昊 郭亚峰 张永德 左晖 曾阳 于 2020-06-01 设计创作，主要内容包括：本发明公开了一种正畸弓丝弯制规划等半径圆域划分半径确定方法,它涉及正畸弓丝弯制技术领域,本发明根据患者的个性化正畸弓丝曲线,基于正畸弓丝曲线弯制点信息集、弯制点的机器人弯制信息集,结合机器人弯制正畸弓丝的运动特点,建立一种正畸弓丝弯制规划等半径圆域划分半径确定方法。技术要点为：等半径确定圆域划分数据导入及正畸弓丝曲线转换；计算等半径确定圆域初始试划分个数；试划分等半径确定圆域；以圆域限制参数为限制条件,寻找最佳试划分个数；输出合理等半径圆域划分半径r<Sub>equal</Sub>。本发明通过改变试划分个数,确定合理等半径圆域的划分半径值,提高了等半径圆域划分的效率,进而提高正畸弓丝弯制规划的效率,避免了机器人弯制正畸弓丝过程中出现干涉及弯制复杂的问题。(The invention discloses a method for determining the radius of an equal-radius circular area in orthodontic arch wire bending planning, which relates to the technical field of orthodontic arch wire bending. The technical points are as follows: determining circle domain division data import and orthodontic arch wire curve conversion by equal radius; calculating equal radius to determine the initial trial division number of the circular domain; trying to divide the equal radius to determine a circular domain; searching the optimal trial division number by taking the circular domain limiting parameter as a limiting condition; output reasonable equal radius circular domain dividing radius r equal . The invention determines the dividing radius value of the reasonable equal-radius circular domain by changing the number of trial division, improves the dividing efficiency of the equal-radius circular domain and further improves the positive radiusThe efficiency of the bending planning of the orthodontic arch wire avoids the problems of interference and complex bending in the process of bending the orthodontic arch wire by the robot.)

1. The method for determining the radius division of the equal-radius circular domain in the orthodontic arch wire bending planning is characterized by comprising the following steps of: the method comprises the following concrete implementation processes:

step one, determining circle domain division data import and orthodontic arch wire curve conversion by equal radius:

according to the orthodontic arch wire curve with i bending points of a patient, calculating and inputting an orthodontic arch wire curve bending point information set T ═ T₁，t₂，t₃，...，t_i}，t_i＝(x_i，y_i，z_i) ' coordinates of each orthodontic archwire curve bending point, at each bending point t_iThe upper robot executes different bending movements, and each orthodontic arch wire curve bending point t_iAll correspond to a bending information unit r of a bending point robot_iThe bending information set of the robot for inputting the bending points is R ═ R₁，r₂，r₃，...，r_i}，r_i＝(x_i，y_i，z_i，α_i) ' denotes the coordinates of the bending point and the bending angle of the robot at the time of bending the point, α_iActing on bending points t for the robot_iAn upper bending angle;

centralizing the information of the individualized orthodontic arch wire curve forming control point into the coordinate t of each bending point_i＝(x_i，y_i，z_i) ' z in_iAssigned a value of 0, i.e. z_iObtaining an orthodontic arch wire curve conversion plane orthodontic arch wire curve T' which is equal to 0;

step two, calculating equal radiuses to determine the number of initial trial division of the circular domain:

according toPre-calculating the bending point angular distance ratio of all i bending points on the orthodontic arch wire curve, wherein the bending point angular distance ratio of the jth bending point is regulatedE_jIs a quantitative description of the bending complexity of the jth bending point, α_jTo act on the bending point t_jThe bending angle of the part is formed,indicating action at bending point t_jAt a bending distance, i.e. bending point t_j-1And t_jLength of the curved section therebetween, in particular, due to the first bending point t₁Without bending, the bending point t is specified₁Bending point-angular distance ratio E of₁Is equal to 0, according toPre-calculating the unit circle bending point density of all i bending points on the orthodontic arch wire curve, wherein the unit circle bending point density of the jth bending point is regulatedUnit is one/mm²，Is aligned with the jth bending point on the distorted arch wire curve in the unit circle area a₀Quantitative description of internal density, the value 1 in the formula represents only one bending point in the unit circle domain, l_jIndicates the bending point t_jLinear distance between bending points nearest thereto, unit circle region a₀Showing that the arch wire is arbitrary on the curve of the orthodontic arch wireA bending point t_jCentered at a point l_jIncluding only one bending point t_jJ is equal to or greater than 1 and equal to or less than i, according to ∑ E₁+E₂+...+E_iPerforming cumulative summation on the i bending point angular distance ratios which are pre-calculated, wherein ∑ E represents the cumulative sum of the angular distance ratios according toCumulatively summing the pre-calculated i unit circle domain bending point densities, wherein ∑ rho⁰Expressing the density accumulation sum of the bending points of the unit circular domain; firstly, n equal-radius determined circular areas are divided on a curve of the plane orthodontic arch wire in an experimental mode, and the initial value of n is n ═ max { [ i/Q { [_max]，[∑E/(∑E)_max],[∑ρ⁰/ρ_max]Is (b) } +1, in which [ i/Q_max]Represents the pair formula i/Q_maxRounding of the calculated result, Q_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nNumber of inner circle bending pointsUpper limit value required, in particular, Q_maxNumber of bending points in round area of 5Is a radius ofEqual radius of (a) determines the circular area a_nThe number of bending points in the inner part, [ ∑ E/(∑ E)_max]Represents a pair formula ∑ E/(∑ E)_maxRounding of the calculated result (∑ E)_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nInner circle bending point angular distance ratio andthe required upper limit value of the number of the main chain,represents the n-th constant radius determined circle area a on the curve of the orthodontic arch wire_nInside ofThe sum of the bending point angular-distance ratios of the bending points, i.e. the circle area a determined by the equal radius_nIs divided intoQuantitative description of the whole bending complexity of each bending point, and determining a circular domain a when the radius is equal_nThe inner bending points are respectively When it is prescribedq represents a circle area a determined on the curve of the orthodontic arch wire at equal radius_nThe number of all bending points in the previously generated n-1 circular fields, i.e.[∑ρ⁰/ρ_max]Expression pair ∑ ρ⁰/ρ_maxRounding of the calculated result, ρ_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nInner circle bending point densityRequired upper limit value, circle bending point densityIs a circular domain a_nInner partA bending point having a radius ofThe degree of compactness in the circular domain of (1) is specifiedDensity of bending points in circular areaUnit of (2) is one/mm²，Determining a circular area a for the nth equal radius on the curve of the plane orthodontic arch wire_nRadius value of (a), bending point angular pitch ratio E, unit circle region bending point density ρ mentioned in this order⁰Number of bending points in circleRatio of angular distance of bending points in circular areaDensity of bending points in circular areaThe five parameters are collectively called as equal-radius determined circle domain limiting parameters, and the step III is skipped;

step three, trying to divide and determining a circular domain by equal radius:

at the first bending point t₁Starting from the last bending point t_iN +1 points are selected as circular domain forming points on the curve segment of the plane orthodontic arch wire as the terminal point, and the first circular domain forming point is a bending point t₁The point where the last circle domain forming point is the bending point t_iThe length of n straight line segments connecting each circle region forming point and adjacent circle region forming points is equal to stipulateN straight line segments swept by horizontal rightward vectors in clockwise direction are used in sequenceIndicate and existWhereinRepresenting straight line segmentsTo bend the point t by dividing the equal radius circle₁Taking the circle domain forming point as the starting point to perform in sequence Is taken as the center of a circle, toN equal radius determination circle domains are generated as radii, the boundary line of each equal radius determination circle domain passes through two circle domain forming points, and the boundary lines of two adjacent equal radius determination circle domains intersect at a common circle domain forming point, namely the n-1 th equal radius determination circle domain a_n-1The right circular domain forming point is just the nth constant-radius determined circular domain a_nForming point of left circle region, defining equal radius to determine circle region a_nThe curved segment of the plane orthodontic arch wire which is intersected by the boundary line of the circular area is provided with a bending point_nDividing, when the point of a circle domain forming point shared by the boundary lines of two equal-radius determined circle domains is just one bending point on the curve of the orthodontic arch wire, the bending point of the intersection point is divided by the previous equal-radius determined circle domain, if the n-1 th equal-radius determined circle domain a_n-1And a firstn equal radius determination circle areas a_nThe point where the common circular domain forming point is located is exactly the bending point t_jBending point t_jIs equally radiussed to determine a circular area a_n-1After the division is finished, the trial division of n equal-radius determined circular domains is carried out, and then the step four is skipped;

step four, searching the optimal trial division number:

respectively calculating n equal-radius determined circle domain bending points generated in the third stepObtaining a circle bending point number setThe number of n circular domain bending points in the circular domain bending point number set Q is arranged in descending order, the maximum number of the circular domain bending points is taken out and recorded as Q_amAccording to the required upper limit value Q of the number of the bending points of the circular area_maxWhen Q is not present, the judgment is made as to whether Q is present_am≤5，

The method specifically comprises the following steps:

if Q is_amIf the number is not more than 5, the upper limit value Q of the number of bending points which do not conform to the circle domain exists in the generated n equal-radius determined circle domains_maxIf the required circular domain is known that the n value is not the optimal trial division number, the radius of the circular domain is changed by changing the number of the circular domains, the radius of the circular domain is determined by trial division again, and the like, so that n is equal to n +1, namely, one more circular domain is added on the basis of the division number when the radius of the circular domain is determined by trial division at the next time, and then the step three is skipped;

if Q is_amIf the number of the generated n equal-radius determined circle domains is less than or equal to 5, the generated n equal-radius determined circle domains all accord with the upper limit value Q of the number of the bending points of the circle domains_maxAccording to further requirements ofCalculating n equal radii generated in the third step to determine the circular domain bending point density of the circular domainObtaining a density set of round bending pointsThe n circular domain bending point densities in the circular domain bending point density set P are arranged in a descending order, and the maximum circular domain bending point density is taken out and recorded as rho_amAccording toCalculating the sum of angular distance ratios of the circle bending points of the n equal-radius determined circle regions generated in the third stepObtaining the angle-distance ratio and the collection of the bending points of the circleArranging the angle-distance ratios of the bending points of the circle region and the n angle-distance ratios of the bending points of the circle region in the set M in descending order, taking out the largest sum of the angle-distance ratios of the bending points of the circle region, and recording as (∑ E)_amAccording to the required upper limit value rho of the density of the round bending points_maxThe bending point-angular distance ratio and the upper limit value of the harmony circle region (∑ E)_maxAt Q_amJudging whether rho exists or not under the condition that no more than 5 is satisfied_am≤ρ_maxAnd (∑ E)_am≤(∑E)_max，

The method specifically comprises the following steps:

if ρ_am≤ρ_maxTrue and (∑ E)_am≤(∑E)_maxIf yes, the n equal-radius determined circular domains generated in the third step all meet the upper limit value rho of the density of the bending points of the circular domains_maxThe bending point-angular distance ratio and the upper limit value of the harmony circle region (∑ E)_maxAll the equal-radius determining circular domains meet the dividing requirement, and the n value is just the optimal dividing number, namely the n equal-radius determining circular domains a are called₁、a₂、…、a_nAll are reasonable equal-radius circular areas, and the step five is skipped;

if ρ_am≤ρ_maxFalse or (∑ E)_am≤(∑E)_maxIf this is not true, three cases are known: rho_am≤ρ_maxTrue and true (∑ E)_am≤(∑E)_maxDissatisfaction, rho_am≤ρ_maxNot stand and (∑ E)_am≤(∑E)_maxIs established, ρ_am≤ρ_maxFalse and (∑ E)_am≤(∑E)_maxIf any of the three conditions occurs, the existence of n equal-radius circle regions generated in the step three is not in accordance with the upper limit value rho of the bending point density of the circle region_maxOr the ratio of the bending point to the angular distance in the circle and the upper limit value (∑ E)_maxIf the required circular domain is known that the n value is not the optimal trial division number, the radius of the circular domain is changed by changing the number of the circular domains, the radius of the circular domain is determined by trial division again, and the like, so that n is equal to n +1, namely, one more circular domain is added on the basis of the division number when the radius of the circular domain is determined by trial division at the next time, and then the step three is skipped;

step five, outputting reasonable equal-radius circular domain dividing radius

Obtaining the dividing radiuses of n reasonable equal-radius circular domains and n reasonable equal-radius circular domains with the same length output in the fourth step, wherein the dividing radius values are sequentiallyOrder toThen r is_equalNamely, the orthodontic arch wire curve is divided into n reasonable equal-radius circular areas with general dividing radius, and the dividing radius r of the reasonable equal-radius circular areas is output_equalAnd the routine is ended.

Technical Field

The invention relates to a method for determining the equal-radius circular domain dividing radius of orthodontic arch wire bending planning, and belongs to the technical field of orthodontic arch wire bending.

Background

The malocclusion deformity is the third major oral disease endangering human health, has higher morbidity, and in modern oral medicine, the fixed correction is a common and effective orthodontic treatment means, while the bending of an orthodontic arch wire is the key of the fixed correction technology.

In the process of bending the personalized orthodontic arch wire by the robot, interference may occur between the personalized orthodontic arch wire and the robot bending paw, namely the personalized orthodontic arch wire collides with the robot bending paw, and after the interference occurs, the bending precision of the personalized orthodontic arch wire is greatly influenced, so that the correction effect is influenced, and the bent personalized arch wire cannot be applied to clinical treatment; research shows that in the process of forward bending the individual orthodontic arch wire, the forward bending is to bend the unbent orthodontic arch wire into a complex formed arch wire, interference is often caused by unreasonable bending sequence of forming control points, the reasonable bending sequence of the forming control points can effectively avoid the occurrence of interference, and the obtaining of the reasonable bending sequence of the forming control points is a necessary premise for realizing digital bending of the orthodontic arch wire.

For the research of the dividing field of the orthodontic arch wire bending planning, an equal-radius circular domain dividing method is proposed in an invention patent, which is granted by the inventor and has the publication number of CN107647925B, namely a circular domain dividing method for the orthodontic arch wire bending planning, and the equal-radius circular domain dividing method is used for dividing the regions of an orthodontic arch wire curve and finally sequencing each region to obtain the bending sequence of a final bending point The bending complexity is too large, namely the individuation characteristics of distribution information of bending points on an orthodontic arch wire curve are not fully considered in the divided intervals, so that the idle stroke invalid action or the mutual interference action in the bending process of the bending robot cannot be effectively avoided, the maximization of the advantages of the bending robot is not favorably exerted, and the bending efficiency cannot be obviously improved.

Disclosure of Invention

Aiming at the problems, the invention provides a method for determining the radius division of equal-radius circular areas for the bending planning of an orthodontic arch wire, which solves the problem that the prior art for bending the orthodontic arch wire lacks a method for determining the radius division of the equal-radius circular areas for planning the bending sequence of the orthodontic arch wire, provides reasonable circular area limiting parameters in the process of determining the radius division of the equal-radius circular areas, quantitatively restricts the intensity of bending points divided by the equal-radius circular areas and the bending complexity, obtains a series of reasonable equal-radius circular areas which accord with the personalized characteristics of distribution information of the bending points on an orthodontic arch wire curve, finally obtains the division radius which is universal for the equal-radius circular areas, and provides convenience for the method for dividing the equal-radius circular areas for planning the bending sequence of the orthodontic arch wire, thereby improving the efficiency of the bending planning of the orthodontic arch wire, exerting the maximization of the advantages of a bending robot and ensuring the normal operation of the bending process of the orthodontic arch wire, the problem of interference in the process of bending the orthodontic arch wire by the robot is avoided.

The above purpose is mainly achieved through the following scheme: a method for determining the radius of an equal-radius circular domain in orthodontic arch wire bending planning concretely comprises the following steps:

step one, determining circle domain division data import and orthodontic arch wire curve conversion by equal radius:

according to the number of patientsCalculating and inputting an orthodontic arch wire curve of the bending point, and calculating and inputting an orthodontic arch wire curve bending point information set T ═ T₁，t₂，t₃，...，t_i}，t_i＝(x_i，y_i，z_i) ' coordinates of each orthodontic archwire curve bending point, at each bending point t_iThe upper robot executes different bending movements, and each orthodontic arch wire curve bending point t_iAll correspond to a bending information unit r of a bending point robot_iThe bending information set of the robot for inputting the bending points is R ═ R₁，r₂，r₃，...，r_i}，r_i＝(x_i，y_i，z_i，α_i) ' denotes the coordinates of the bending point and the bending angle of the robot at the time of bending the point, α_iActing on bending points t for the robot_iAn upper bending angle;

centralizing the information of the individualized orthodontic arch wire curve forming control point into the coordinate t of each bending point_i＝(x_i，y_i，z_i) ' z in_iAssigned a value of 0, i.e. z_iObtaining an orthodontic arch wire curve conversion plane orthodontic arch wire curve T' which is equal to 0;

step two, calculating equal radiuses to determine the initial pre-division number of the circular domain:

according toPre-calculating the bending point angular distance ratio of all i bending points on the orthodontic arch wire curve, wherein the bending point angular distance ratio of the jth bending point is regulatedE_jIs a quantitative description of the bending complexity of the jth bending point, α_jTo act on the bending point t_jThe bending angle of the part is formed,indicating action at bending point t_jAt a bending distance, i.e. bending point t_j-1And t_jLength of the curved section therebetween, in particular, due to the first bending point t₁Without bending, the bending point t is specified₁Bending point-angular distance ratio E of₁Is equal to 0, according toPre-calculating the unit circle bending point density of all i bending points on the orthodontic arch wire curve, wherein the unit circle bending point density of the jth bending point is regulatedUnit is one/mm²，Is aligned with the jth bending point on the distorted arch wire curve in the unit circle area a₀Quantitative description of internal density, the value 1 in the formula represents only one bending point in the unit circle domain, l_jIndicates the bending point t_jLinear distance between bending points nearest thereto, unit circle region a₀Showing any one bending point t on the curve of the orthodontic arch wire_jCentered at a point l_jIncluding only one bending point t_jJ is equal to or greater than 1 and equal to or less than i, according to ∑ E₁+E₂+...+E_iPerforming cumulative summation on the i bending point angular distance ratios which are pre-calculated, wherein ∑ E represents the cumulative sum of the angular distance ratios according toAccumulating and summing the pre-calculated i unit circle domain bending point densities,∑ p therein⁰Expressing the density accumulation sum of the bending points of the unit circular domain; firstly, trying to divide n equal-radius determined circular areas on a curve of the plane orthodontic arch wire, wherein the initial value of n isWherein [ i/Q_max]Represents the pair formula i/Q_maxRounding of the calculated result, Q_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nNumber of inner circle bending pointsUpper limit value required, in particular, Q_maxNumber of bending points in round area of 5Is a radius ofEqual radius of (a) determines the circular area a_nThe number of bending points in the inner part, [ ∑ E/(∑ E)_max]Represents a pair formula ∑ E/(∑ E)_maxRounding of the calculated result (∑ E)_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nInner circle bending point angular distance ratio andthe required upper limit value of the number of the main chain,represents the n-th constant radius determined circle area a on the curve of the orthodontic arch wire_nInside ofThe sum of the bending point angular-distance ratios of the bending points, i.e. the circle area a determined by the equal radius_nIs divided intoWith integral bending complexity of individual bending pointsQuantization description, determining the circular field a when the radius is equal_nThe inner bending points are respectively When it is prescribedq represents a circle area a determined on the curve of the orthodontic arch wire at equal radius_nThe number of all bending points in the previously generated n-1 circular fields, i.e.[∑ρ⁰/ρ_max]Expression pair ∑ ρ⁰/ρ_maxRounding of the calculated result, ρ_maxRepresents any one equal-radius determined circular area a to be divided on the curve of the plane orthodontic arch wire_nInner circle bending point densityRequired upper limit value, circle bending point densityIs a circular domain a_nInner partA bending point having a radius ofThe degree of compactness in the circular domain of (1) is specifiedDensity of bending points in circular areaUnit of (2) is one/mm²，Determining a circular area a for the nth equal radius on the curve of the plane orthodontic arch wire_nRadius value of (a), bending point angular pitch ratio E, unit circle region bending point density ρ mentioned in this order⁰Number of bending points in circleRatio of angular distance of bending points in circular areaDensity of bending points in circular areaThe five parameters are collectively called as equal-radius determined circle domain limiting parameters, and the step III is skipped;

step three, trying to divide and determining a circular domain by equal radius:

at the first bending point t₁Starting from the last bending point t_iN +1 points are selected as circular domain forming points on the curve segment of the plane orthodontic arch wire as the terminal point, and the first circular domain forming point is a bending point t₁The point where the last circle domain forming point is the bending point t_iThe points are located so that the length of n straight line segments obtained by connecting each circle domain forming point with the adjacent circle domain forming points is equal, and n straight line segments scanned by the horizontal right vector in the clockwise direction are specified to be sequentially usedIndicate and existWhereinRepresenting straight line segmentsTo bend the point t by dividing the equal radius circle₁Taking the circle domain forming point as the starting point to perform in sequence Is taken as the center of a circle, toN equal radius determination circle domains are generated as radii, the boundary line of each equal radius determination circle domain passes through two circle domain forming points, and the boundary lines of two adjacent equal radius determination circle domains intersect at a common circle domain forming point, namely the n-1 th equal radius determination circle domain a_n-1The right circular domain forming point is just the nth constant-radius determined circular domain a_nForming point of left circle region, defining equal radius to determine circle region a_nThe curved segment of the plane orthodontic arch wire which is intersected by the boundary line of the circular area is provided with a bending point_nDividing, when the point of a circle domain forming point shared by the boundary lines of two equal-radius determined circle domains is just one bending point on the curve of the orthodontic arch wire, the bending point of the intersection point is divided by the previous equal-radius determined circle domain, if the n-1 th equal-radius determined circle domain a_n-1Determining a circle area a with the nth equal radius_nThe point where the common circular domain forming point is located is exactly the bending point t_jBending point t_jIs equally radiussed to determine a circular area a_n-1After the division is finished, the trial division of n equal-radius determined circular domains is carried out, and then the step four is skipped;

step four, searching the optimal trial division number:

respectively calculating n equal-radius determined circle domain bending points generated in the third stepCan obtain the number set of the bending points of the circular domainThe number of n circular domain bending points in the circular domain bending point number set Q is arranged in descending order, and the largest circular domain bending point is taken outNumber, denoted as Q_amAccording to the required upper limit value Q of the number of the bending points of the circular area_maxWhen Q is not present, the judgment is made as to whether Q is present_am≤5，

The method specifically comprises the following steps:

if Q is_amIf the number is not more than 5, the upper limit value Q of the number of bending points which do not conform to the circle domain exists in the generated n equal-radius determined circle domains_maxIf the required circular domain is known that the n value is not the optimal trial division number, the radius of the circular domain is changed by changing the number of the circular domains, the radius of the circular domain is determined by trial division again, and the like, so that n is equal to n +1, namely, one more circular domain is added on the basis of the division number when the radius of the circular domain is determined by trial division at the next time, and then the step three is skipped;

if Q is_amIf the number of the generated n equal-radius determined circle domains is less than or equal to 5, the generated n equal-radius determined circle domains all accord with the upper limit value Q of the number of the bending points of the circle domains_maxAccording to further requirements ofCalculating n equal radii generated in the third step to determine the circular domain bending point density of the circular domainCan obtain a density set of round-domain bending pointsThe n circular domain bending point densities in the circular domain bending point density set P are arranged in a descending order, and the maximum circular domain bending point density is taken out and recorded as rho_amAccording toCalculating the sum of angular distance ratios of the circle bending points of the n equal-radius determined circle regions generated in the third stepCan obtain the angle-distance ratio and the collection of the bending points of the circular areaArranging the angle-distance ratios of the bending points of the circle region and the n angle-distance ratios of the bending points of the circle region in the set M in descending order, taking out the largest sum of the angle-distance ratios of the bending points of the circle region, and recording as (∑ E)_amAccording to the required upper limit value rho of the density of the round bending points_maxThe bending point-angular distance ratio and the upper limit value of the harmony circle region (∑ E)_maxAt Q_amJudging whether rho exists or not under the condition that no more than 5 is satisfied_am≤ρ_maxAnd (∑ E)_am≤(∑E)_maxThe method specifically comprises the following steps:

if ρ_am≤ρ_maxTrue and (∑ E)_am≤(∑E)_maxIf yes, the n equal-radius determined circular domains generated in the third step all meet the upper limit value rho of the density of the bending points of the circular domains_maxThe bending point-angular distance ratio and the upper limit value of the harmony circle region (∑ E)_maxAll the equal-radius determining circular domains meet the dividing requirement, and the n value is just the optimal dividing number, namely the n equal-radius determining circular domains a are called₁、a₂、…、a_nAll are reasonable equal-radius circular areas, and the step five is skipped;

if ρ_am≤ρ_maxFalse or (∑ E)_am≤(∑E)_maxIf this is not true, three cases are known: rho_am≤ρ_maxTrue and true (∑ E)_am≤(∑E)_maxDissatisfaction, rho_am≤ρ_maxNot stand and (∑ E)_am≤(∑E)_maxIs established, ρ_am≤ρ_maxFalse and (∑ E)_am≤(∑E)_maxIf any of the three conditions occurs, the existence of n equal-radius circle regions generated in the step three is not in accordance with the upper limit value rho of the bending point density of the circle region_maxOr the ratio of the bending point to the angular distance in the circle and the upper limit value (∑ E)_maxIf the required circular domain is known that the n value is not the optimal trial division number, the radius of the circular domain is changed by changing the number of the circular domains, the radius of the circular domain is determined by trial division again, and the like, so that n is equal to n +1, namely, one more circular domain is added on the basis of the division number when the radius of the circular domain is determined by trial division at the next time, and then the step three is skipped;

step five, outputting reasonable equal-radius circular domain dividing radius

Obtaining the dividing radiuses of n reasonable equal-radius circular domains and n reasonable equal-radius circular domains with the same length output in the fourth step, wherein the dividing radius values are sequentiallyOrder toThen r is_equalNamely, the orthodontic arch wire curve can be divided into n reasonable equal-radius circular areas with general dividing radiuses, and the dividing radiuses r of the reasonable equal-radius circular areas are output_equalAnd the routine is ended.

The invention has the beneficial effects that:

1. aiming at the determination of the dividing radius of the circular domain with equal radius, the invention adopts five circular domain limiting parameters as the calculation basis of the dividing radius of the circular domain with equal radius, and mentions the number of bending points of the circular domainUnit circle domain bending point density rho⁰Bending point density of circular regionThe concept of (1) quantitatively describing the degree of closeness of bending points, and mentioning bending point angular distance ratio E and circular region bending point angular distance ratio sumThe concept of (1) is to quantitatively describe the bending complexity of a single bending point and the total bending complexity of bending points in a circular domain, firstly, the initial value of the number n of trial division is determined by adopting the limiting parameter of each circular domain, the trial division is carried out by taking the initial value of n as the starting point, instead of the trial division of the circular domain with equal radius by taking the initial value of n without basis as the starting point, and the speed of searching the optimal division number n is effectively improved; after generating equal radius to determine the circle domain, first using Q_maxPerforming bending point number constraint and reusing rho_max、(∑E)_maxUpper limit value pair of circular domain limiting parameterThe bending density and the bending difficulty are subjected to conditional constraint, and the calculation efficiency of the algorithm can be fully improved, namely Q is not satisfied_maxThe orthodontic arch wire can be fed back immediately when being limited by the conditions, and a plurality of reasonable equal-radius circular areas meeting the set requirements can be formed on one orthodontic arch wire curve through the upper limit limitation of the three, so that the dividing radius r of the equal-radius circular areas meeting the requirements can be obtained_equalThe dividing radius determined by the method is adopted for dividing the circular domain, a series of equal-radius circular domains which meet requirements and are reasonably planned can be generated at one time, the phenomena that the bending point density is too high and the bending complexity is too high in the divided circular domain are effectively avoided, and therefore the problem that the robot interferes in the bending process is avoided to the greatest extent.

2. According to the invention, the dividing radius is determined by changing the number of the trial division and adopting a method of trial division of the equal-radius circular domain, the number n of the circular domain division is taken as a central variable, and the change of the number n of the circular domain division can change the distribution condition of the forming points of the circular domain on the curve of the orthodontic arch wire, so that the change of the circle center and the radius of the circular domain is caused, namely, the position and the size of the circular domain with the equal radius can be uniquely determined as long as the number n of the circular domain division is determined, the calculation of the data of the divided circular domain by a system is facilitated, and the efficiency of determining the.

3. In the invention, the dividing radius is determined by adopting the equal-radius circular domain trial dividing method, and in the process of determining the bending points by the equal-radius circular domain trial dividing method, the region to which each bending point belongs is strictly defined, so that the situation that the bending points are repeatedly divided by the same equal-radius determined circular domain can be avoided, the dividing radius of the equal-radius circular domain is ensured to be dividing data with absolute significance, and the rationality and the accuracy of the dividing radius determining method are improved.

4. Compared with the invention patent ' a determination method for dividing the radius of a plane equal-radius circular region based on the angle-distance ratio of the bending points of the orthodontic arch wire ', which is filed by the inventor on the same day ', the method provided by the invention does not require that the bending points of the personalized orthodontic arch wire curve meet the upper limit of the density of the bending points per unit in advanceCompared with the invention patent 'a method for determining the radius of a plane equal-radius circular region based on the density of bending points of an orthodontic arch wire', which is filed on the same day by the inventor, the method provided by the invention does not require that the bending points of the personalized orthodontic arch wire curve meet the upper limit constraint of the angular distance ratio of the bending points in advance, although the three methods all belong to a series of methods for determining the radius of the plane equal-radius circular region, and the determination of the radius is based on the thought of a trial and error method, the method adopts the density of the bending points of the circular region in the process of dividing the circular regionSum of bending point and angular distance ratio of sum circleIn conclusion, the method is not only suitable for individual orthodontic arch wire curves with special attributes, but also suitable for all orthodontic arch wire curves capable of adopting a plane dividing method, so that the method has general applicability and comprehensiveness in a series of methods for determining the plane equal-radius circular domain dividing radius in orthodontic arch wire bending planning.

5. Compared with the invention patent of CN107647925B granted by the inventor, namely a method for dividing the circular domain for the orthodontic arch wire bending planning, the invention patent of CN107647925B belongs to a method for dividing the circular domain with equal radius, the invention patent has the condition that the density of bending points in the divided circular domain interval is too large or too small, namely the generated circular domain interval does not fully consider the individual characteristics of distribution information of the bending points on the curve of the orthodontic arch wire, the orthodontic arch wire curve is divided only by an unboosted homogenization standard, and the proposed circular domain dividing process only divides the orthodontic arch wire curve by circular arcs to obtain areas, but not strictly divides the circular domain, but belongs to a method for determining the radius of the circular domain with equal radius, and also relates to the dividing process of the circular domain in the determining process, according to the used circular domain limiting parameters, the bending points of the divided circular domains are subjected to quantitative constraint of bending complexity and density, thereby causing the dividing radius of the equal-radius circular domain to change according with the regulation of the circular domain limiting parameters, finally obtaining the dividing radius of the reasonable equal-radius circular domain according with the individual characteristics of the distribution information of the bending points on the curve of the orthodontic arch wire, and dividing the circular domain by utilizing the determined dividing radius, can effectively avoid the situation that the intensity of bending points in each divided circle area is greatly different from the bending complexity, improves the uniformity of each area, the bending robot can not generate idle stroke invalid action or mutual interference action in the bending process, therefore, the advantage maximization of the bending robot can be exerted, the normal operation of the orthodontic arch wire bending process is ensured, the efficiency of orthodontic arch wire bending planning is improved, and the problem of interference in the process of bending the orthodontic arch wire by the robot is avoided.

Drawings

For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.

Fig. 1 is a flow chart of a method for determining the radius of an orthodontic arch wire bending plan equal radius circle domain partition;

fig. 2 is a schematic view of distribution of individual orthodontic arch wire bending points;

fig. 3 is a schematic view of an initial trial division of an individualized orthodontic archwire curve in a circle domain of equal radius;

fig. 4 is a schematic view of an individualized orthodontic archwire curve in which trial division is completed in equal radius circular areas;

Detailed Description

For the purposes of promoting a clear understanding of the objects, aspects and advantages of the invention, reference will now be made to the following description of the preferred embodiments illustrated in the accompanying drawings, with the understanding that the description is illustrative only and is not intended to limit the scope of the invention, and that the following description will omit descriptions of well-known structures and techniques in order to avoid unnecessarily obscuring the concepts of the invention.