CN117408943B - Orthodontic archwire error evaluation method based on curve fitting method - Google Patents

Abstract

The invention discloses an orthodontic archwire error evaluation method based on a curve fitting method, which relates to the technical field of orthodontic archwire evaluation, and aims at an orthodontic archwire curve which is bent in the directions of space x, y and z, and proper evaluation indexes and methods are selected to evaluate the error between the actual and theoretical orthodontic archwire curves with large curvature, wherein the technical key points are as follows: the theoretical orthodontic archwire and the actual orthodontic archwire are transformed to proper positions through spatial positions; an actual orthodontic archwire curve and a theoretical orthodontic archwire curve are projected; calculating and judging the average curvature between the theoretical and actual orthodontic archwire curves after projection; after projection, theoretical and actual orthodontic archwire curve information point data are introduced and evaluation parameters are set; judging whether fitting errors among actual and theoretical orthodontic archwire projection curves meet requirements or not; judging whether the absolute value of the average absolute value slope difference between the projection curves of the actual and theoretical orthodontic archwires meets the requirement or not; according to the invention, for the large-curvature orthodontic archwire curve, the information points are inserted into the theoretical and actual orthodontic archwire curve projection curves, the fitting degree between the theoretical and actual orthodontic archwire curves is described by utilizing the limited information points, the bending effect of the actual orthodontic archwire curve is reflected, and the spatial relationship between the theoretical and actual orthodontic archwire curves is evaluated with higher precision.

Description

Orthodontic archwire error evaluation method based on curve fitting method

Technical Field

The invention relates to an orthodontic archwire error evaluation method based on a curve fitting method, and belongs to the technical field of orthodontic archwire evaluation.

Background

The misjaw deformity presents higher incidence and is the third largest oral disease; in modern stomatology, fixed correction is a common and effective orthodontic treatment means, and bending of orthodontic archwires is a key of fixed correction technology; the traditional orthodontic archwire basically depends on manual bending, and the bending precision and the bending efficiency are difficult to ensure; in recent years, the consumption level of people and the awareness degree of oral diseases are improved, and the demands of orthodontic archwires are greatly increased; with the development of automation technology, the bending method of the arch wire in the orthodontic appliance starts to transition from the direction of the robot orthodontic arch wire with low cost, high efficiency, high precision and automation; however, whether manual or robotic, the assessment of the accuracy of orthodontic archwires is still dependent on the practitioner; the method does not use the guidance of the quantization parameters, is seriously dependent on the experience of doctors, and prevents the further development of orthodontic archwires to a certain extent;

In addition, the individuation characteristics of the distribution information of the bending points on the orthodontic archwire curve are considered, and the relative positions of the relative adjacent bending points on the orthodontic archwire curve and the transition curve between the adjacent bending points are embodied by the bending degree; when the orthodontic archwire curve is bent in the x, y and z directions and the curve curvature between adjacent bending points is large; the existing evaluation method does not quantitatively evaluate the curve with larger curvature between two bending points, the error of the existing method is larger when evaluating the curve of the orthodontic archwire with larger curvature, and no method can determine the error magnitude of the curve between the bending points of the orthodontic archwire through a quantization index so as to accurately evaluate the error of the prepared orthodontic archwire; in summary, a method for precisely and quantitatively evaluating the bending effect of an orthodontic arch wire with a curve with larger curvature between bending points is needed in the technical field of the bending evaluation of the orthodontic arch wire at present.

Disclosure of Invention

Aiming at the problems, the invention provides an orthodontic archwire error evaluation method based on a curve fitting method, solves the problem that a high-precision evaluation method aiming at an orthodontic archwire curve with larger curvature is lacking in the technical field of the current orthodontic archwire evaluation, and realizes the quantitative description of the error value of the whole curve of the orthodontic archwire.

An orthodontic archwire error evaluation method based on a curve fitting method comprises the following specific implementation processes:

Step one, theoretical and practical orthodontic archwire curve space position transformation and bending point data importing:

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 calculated and input, wherein a theoretical orthodontic archwire curve bending point information set P′_T＝{^Tp′₁,^Tp'₂,^Tp'₃,...,^Tp′_i,...,^Tp'_n},^Tp′_i＝(^Tx′_i,^Ty′_i,^Tz′_i) is used as position information of an ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the value range of i is more than or equal to 1 and less than or equal to n, wherein: ^Tx′_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ty′_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Tz′_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the 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 the midpoint of a connecting line between p _f,p_s and p _f and is ^T degrees', and the theoretical orthodontic archwire curve is subjected to spatial transformation: the point ^T o' is coincided with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p _s of the theoretical orthodontic archwire curve is positioned on a negative y-axis half axis, the right end point p _f of the theoretical orthodontic archwire curve is positioned on a positive y-axis half axis, and the theoretical orthodontic archwire curve and the x-axis do not have an intersection point; the theoretical orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the theoretical orthodontic archwire curve and the x axis are intersected, the spatial position information of the theoretical orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, a theoretical orthodontic archwire curve bending point information set P_T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_i,...,^Tp_n},^Tp_i＝(^Tx_i,^Ty_i,^Tz_i) in the final spatial position after rotation is calculated and input as the position information of the ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final spatial position after rotation, wherein: ^Tx_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w at a final spatial position after rotation is given, ^Ty_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation, and ^Tz_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation;

calculating and inputting an actual orthodontic archwire curve with n bending points according to the theoretical orthodontic archwire curve, wherein the actual orthodontic archwire curve bending point information set P′_R＝{^Rp′₁,^Rp'₂,^Rp'₃,…,^Rp′_i,…,^Rp'_n},^Rp′_i＝(^Rx′_i,^Ry′_i,^Rz′_i) is the position information of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the method comprises the following steps of: ^Rx′_i The method comprises the steps that the x-axis coordinate of an ith bending point of an actual orthodontic archwire curve relative to a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ry′_i is the y-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Rz′_i is the z-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the 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, the midpoint of a connecting line between p '_f is ^R degrees', and the actual orthodontic archwire curve is subjected to spatial transformation: the point ^R o ' is overlapped with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p ' _s of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis, the right end point p ' _f of the actual orthodontic archwire curve is positioned on the positive half axis of the y axis, and the actual orthodontic archwire curve and the x axis have no intersection point; the actual orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the intersection point of the actual orthodontic archwire curve and the x axis appears, the position information of the final space position of the actual orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, the set actual orthodontic archwire curve bending point information set P_R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_i,…,^Rp_n},^Rp_i＝(^Rx_i,^Ry_i,^Rz_i) is calculated and input as the position information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final space position after rotation, wherein: ^Rx_i The method comprises the steps that an x-axis coordinate of an ith bending point of an actual orthodontic archwire curve in a final space position after rotation relative to a three-dimensional orthodontic archwire error calibration coordinate system w is ^Ry_i, a y-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is ^Rz_i, and a z-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is provided;

step two, the conversion of the curve projection, bending points and characteristic points of the actual and theoretical orthodontic archwires:

Defining a characteristic parameter j as a positive integer and containing 0, j epsilon [0, n+1]; specifically, when j e [1, n ], j=i;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Tz_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,…,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve to project the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j1,^Tz_j+1) of the feature point on the theoretical orthodontic archwire curve, thereby obtaining a theoretical projection curve The theoretical orthodontic archwire curve is positioned at the projection point/> of two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF^z of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-xy plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF^z in the o-xy projection plane;

Projecting a theoretical orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning a coordinate ^Tx_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents that the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j+1,^Tz_j+1) of the theoretical orthodontic archwire feature point, thereby obtaining a theoretical projection curve Projection points/>, of theoretical orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF^x of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-yz plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF^x in the o-yz projection plane;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ty_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to be 0; assuming that the intersection point of the theoretical orthodontic curve and the o-xz plane is ^Tp_c＝(^Tx_c,^Ty_c,^Tz_c)＝(0,^Ty_c,^Tz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the theoretical feature point represents the theoretical orthodontic archwire curve left end point p _s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀); when j epsilon [1, k-1], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); when j=n+1, the theoretical feature point represents a theoretical orthodontic archwire curve right end point p _f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1); projecting theoretical orthodontic archwire characteristic points located in o-xz negative planes to o-xz planes, and locating the projected characteristic points AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^TF^y-; projecting theoretical orthodontic archwire characteristic points located in an o-xz frontal plane to an o-xz plane, wherein the theoretical orthodontic archwire characteristic points are located in projection characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^TF^y+; ^T x is taken as the independent variable of the theoretical orthodontic archwire curve ^TF^y- and the theoretical orthodontic archwire curve ^TF^y+ in the o-xz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Rz_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the characteristic point on the actual orthodontic archwire curve, to obtain an actual projection curve The actual orthodontic archwire curve is positioned at the projection point/>, of two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^z of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on an o-xy plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^z in the o-xy projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning the coordinate ^Rx_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the actual orthodontic archwire characteristic point, to obtain an actual projection curve Projection points/>, of actual orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^x of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on the o-yz plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^x in the o-yz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ry_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; assuming that the intersection point of the actual orthodontic curve and the o-xz plane is ^Rp_c＝(^Rx_c,^Ry_c,^Rz_c)＝(0,^Ry_c,^Rz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the actual feature point represents the actual orthodontic archwire curve left end point p _s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀); when j epsilon [1, k-1], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); when j=n+1, the actual feature point represents the actual orthodontic archwire curve right end point p _f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1); projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz negative plane to the o-xz plane, and positioning the characteristic points of the projection AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^RF^y-; projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz frontal plane to the o-xz plane, and positioning the characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^RF^y+; ^R x is taken as the independent variable of the actual orthodontic archwire curve ^RF^y- and the actual orthodontic archwire curve ^RF^y+ in the o-xz projection plane;

Step three, calculating and judging average curvature between the projected theory and actual orthodontic archwire curves:

On the o-xy projection plane, the theoretical projection curve And theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-yz projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-xz negative projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection pointsAnd/>The distance between them is/>Theoretical projection curve/>Is of the curvature ofExpressed as/>Actual projection curve/>And the actual projection point/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection pointAnd/>The distance between them is/>Actual projection curve/>Is of the curvature ofExpressed as/>The average curvature between the projected theory and the actual orthodontic is/>Represented as

Theoretical projection curve on o-xz orthographic projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Calculation of The lower limit of (3) is defined as C _min; calculation/> The lower limit of (3) is defined as C _min; calculation/> And/>The lower limit of (3) is defined as C _min;

Defining a counting parameter t, wherein t is the number of curve segments of theoretical and actual projection curves, the average curvature of which is larger than the minimum average curvature C _min, and the initial value of t is 0;

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Hold true, or/>Hold true, or/>If true, t=t+1, and jump to step three b);

If it is Does not hold, and/>Does not hold, and/>If not, jumping to the step three b); specifically, if the result is not present, the same jump is made to step three b), which is aimed atA section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not true, continuing to judge the average curvature of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step three a);

if j+1 > n is true, judging whether the counting parameter t is more than or equal to 1 is true, and if so, jumping to the fourth step; if not, outputting that the curve segment with overlarge curvature does not exist in the orthodontic archwire curve, and performing precision evaluation by a curve fitting method is not needed;

step four, introducing actual orthodontic archwire curve information point data and fitting parameters after projection theory:

There is n+1 section of theoretical curve projection of orthodontic archwire on o-xy projection plane, for theoretical projection curve It is at projection point/>, of theoretical feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Specifically expressed as/>Theoretical orthodontic archwire projection curve/>The average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Expressed as/>Actual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1 sections of theoretical curve projections of orthodontic archwires exist on o-yz projection surface, and theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireFitting deviation between

The difference is expressed asSpecifically expressed as/>Theoretical orthodontic archwire projection curveThe average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Expressed as/>Actual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

K-1 segment of theoretical curve projection of orthodontic archwire exists on o-xz negative projection surface, and for theoretical projection curveIt is at the projection point/>, of the actual feature pointAnd/>(J E [0, k-2 ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe actual curve projection of the k-1 section orthodontic archwire exists on the o-xy negative projection surface, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown asTheoretical orthodontic archwire projection curve/>The average absolute value slope of (a) isExpressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1-k sections of theoretical curve projections of orthodontic archwires exist on o-xz orthographic projection plane, and the theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>(J E [ k, n ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe projection of the actual curve of the n+1-k section orthodontic archwire exists on the o-xy orthographic projection plane, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1 between the independent variables ^Ry_j and ^Ry_j+1, in which m information points are uniformly inserted, is expressed asDefining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown as

Theoretical orthodontic archwire projection curve/>The average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

Calculation ofAnd/> The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/> The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/>Calculation/>And/> And/>The upper limit of (1) is defined as (R ²)_max,/>)And/>The upper limit of (3) is defined as (K) _max;

step five, judging whether projection curve fitting deviation of the projection on the o-xy plane, the projection on the o-yz plane and the projection on the o-xz negative or positive plane meets the set requirements:

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step five b); /(I)

If it isNot true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting that the actual orthodontic archwire does not meet the set requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

If j+1 > n is not true, continuing to judge the fitting deviation of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step five a);

if j+1 > n is true, all curves are judged to be finished, and the step six is skipped;

Step six, judging whether the absolute value of the average absolute value slope difference of the projection curves projected on the o-xy plane, the o-yz plane and the o-xz negative or positive plane meets the set requirement:

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step six b);

If it is Not true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting an orthodontic archwire curve which does not meet the set requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not established, continuously judging the absolute value of the average absolute value slope difference of the projection curve of the next section of orthodontic archwire curve If the setting requirement is met, j=j+1 is skipped to step six);

if j+1 > n is true, all curves are evaluated, the error of each section of curve of the actual orthodontic archwire curve is within the allowable range, the orthodontic archwire evaluation is finished, and the output orthodontic archwire curve meets the set requirement.

The beneficial effects of the invention are as follows:

1. The invention aims at theoretical and actual orthodontic archwire error evaluation, and the actual orthodontic archwire curve and the theoretical orthodontic archwire curve are projected to an o-xy plane, an o-yz plane and a negative plane and a positive plane of the o-xz by using a dimension-reducing mapping method; the positive plane and the negative plane of the o-xz plane of the orthodontic archwire curve are considered to be projected, so that the space state of the orthodontic archwire curve can be correctly mapped.

2. Aiming at theoretical and actual orthodontic archwire error evaluation, m equidistantly-divided information points are respectively inserted between bending points of two adjacent theoretical and actual orthodontic archwire projections according to the distance in independent variable dimension; each information point has corresponding theoretical and practical function values of orthodontic archwire curve projection, and the characteristic reflected on the curve is that m information points exist on the curve of two adjacent bending points; the information points can be used for more accurately mapping the space state of the orthodontic archwire curve; the absolute value of the difference between the fitting deviation and the average absolute value slope of the theoretical and actual orthodontic archwire curves introduced by the invention is a representation of the fitting degree of the theoretical and actual orthodontic archwire curves; the absolute value of the average absolute value slope difference can represent the deviation of the magnitude of the orthodontic force, and the absolute value of the average absolute value slope difference and the fitting deviation can reflect the deviation of the direction of the orthodontic force.

3. Compared with the invention patent of the inventor, namely an orthodontic archwire error evaluation method based on a contour dimension reduction method, firstly, the invention is different from the invention in that the projection of theoretical and actual orthodontic archwires Qu Xianxiang o-xz plane is unidirectional, and the projection of the invention comprises positive and negative directions; the method is characterized in that the fitting degree between an actual orthodontic archwire curve and a theoretical orthodontic archwire curve is quantitatively described by a double-line position distance in a mathematical method, namely a two-dimensional archwire double-line position distance, aiming at the area of a closed area formed between the projected intersection points between the theoretical orthodontic archwire and the actual orthodontic archwire, so that the bending effect of the orthodontic archwire is evaluated; the invention utilizes the idea of function fitting, introduces fitting deviation to evaluate the deviation of a theoretical orthodontic archwire curve and an actual orthodontic archwire curve, and the method is realized on the basis that m information points are introduced on a transition curve between two bending points.

4. Compared with an invention patent 'an orthodontic wire error evaluation method based on a space equidistant dividing plane' declared by the inventor on the same day, although the two methods are equally divided on a theoretical orthodontic wire curve and an actual orthodontic wire curve, the equidistant dividing of 'an orthodontic wire error evaluation method based on a space equidistant dividing plane' is realized by inserting equidistant planes on the universe independent variables y of the theoretical and actual orthodontic wire curves, the fitting degree judgment of the theoretical and actual orthodontic wire curves is carried out on the basis of a three-dimensional space, and the fitting degree of the theoretical and actual orthodontic wire curves is realized according to the offset between theoretical intersection points and actual intersection points, vectors between adjacent theoretical intersection points and the offset angles of x, y and z of a coordinate system; the equidistant segmentation of the orthodontic archwire curve is realized in the positive and negative directions of projection of the actual orthodontic archwire Qu Xianxiang o-xy plane, o-yz plane and o-xz plane, and the equidistant segmentation process is performed for the distances on different independent variables of the projection curve of the theoretical and actual orthodontic archwire; the judgment of the fitting degree of the theoretical and actual orthodontic archwire curves is realized through the deviation equation and the absolute value of the slope.

5. Compared with an invention patent 'an orthodontic archwire error evaluation method based on bending point curvature and dimension-reduction angular distance deviation domain' which is declared by the inventor on the same day, although the two methods use a dimension-reduction projection method, the 'an orthodontic archwire error evaluation method based on bending point curvature and dimension-reduction angular distance deviation domain' aims at the situation that the curvature of a curve between two bending points is smaller, and the concept of the angular distance deviation domain S _i-1,i provided by the method of the patent can ensure that the maximum deviation meets the upper limit; the patent aims at the orthodontic archwire curve with larger curvature, and the geometric characteristics of the orthodontic archwire curve with large curvature are restored with higher precision by utilizing the idea of infinitesimal; 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.

6. The invention patent of the inventor, namely an orthodontic archwire error evaluation method based on a contour dimension reduction method, aims at an orthodontic archwire curve which is bent in the directions of x, y and z; the invention patent of the inventor, namely an orthodontic archwire error evaluation method based on a weight ratio method, aims at an orthodontic archwire curve with relatively smaller complexity of a bending point; the invention patent of the inventor, namely an orthodontic archwire error evaluation method based on a complexity distinguishing method, aims at an orthodontic archwire curve with relatively large complexity of a bending point; the inventor's invention patent of the invention, an orthodontic archwire evaluation method based on space translation sub-coordinate system trigrams judgment, evaluates the bending point error of an orthodontic archwire curve; the invention patent of the inventor, namely an orthodontic archwire error evaluation method based on residual square sum interval division, aims at an orthodontic archwire curve with smaller adjacent bending point angular distance ratio difference; the invention patent of the inventor, namely an orthodontic archwire evaluation method based on coplanar equiangular vectors, aims at an orthodontic archwire curve with smaller angular distance ratio difference between adjacent bending points; the inventor's invention patent ' an orthodontic archwire bending point error evaluation method based on vector collineation ' aims at an orthodontic archwire curve with a bending point sensitive to directional deviation; the invention aims at the orthodontic archwire curve with larger curvature among the bending points.

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 evaluation method based on a curve fitting method;

FIG. 2 is a schematic view of a projected plane of an actual orthodontic archwire curve versus a theoretical orthodontic archwire curve;

FIG. 3 is any two-segment plot of the projection of an actual orthodontic archwire curve versus a theoretical orthodontic archwire curve on o-xy;

Fig. 4 is a schematic diagram of m=5 inserted information points on each segment of theoretical and actual orthodontic archwire curve;

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.

Example 1: as shown in fig. 1, 2, 3 and 4, the following technical solutions are adopted in this embodiment: an orthodontic archwire error evaluation method based on a curve fitting method comprises the following specific implementation processes:

Step one, theoretical and practical orthodontic archwire curve space position transformation and bending point data importing:

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 calculated and input, wherein a theoretical orthodontic archwire curve bending point information set P′_T＝{^Tp′₁,^Tp'₂,^Tp'₃,...,^Tp′_i,...,^Tp'_n},^Tp′_i＝(^Tx′_i,^Ty′_i,^Tz′_i) is used as position information of an ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the value range of i is more than or equal to 1 and less than or equal to n, wherein: ^Tx′_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ty′_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Tz′_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the 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 the midpoint of a connecting line between p _f,p_s and p _f and is ^T degrees', and the theoretical orthodontic archwire curve is subjected to spatial transformation: the point ^T o' is coincided with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p _s of the theoretical orthodontic archwire curve is positioned on a negative y-axis half axis, the right end point p _f of the theoretical orthodontic archwire curve is positioned on a positive y-axis half axis, and the theoretical orthodontic archwire curve and the x-axis do not have an intersection point; the theoretical orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the theoretical orthodontic archwire curve and the x axis are intersected, the spatial position information of the theoretical orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, a theoretical orthodontic archwire curve bending point information set P_T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_i,...,^Tp_n},^Tp_i＝(^Tx_i,^Ty_i,^Tz_i) in the final spatial position after rotation is calculated and input as the position information of the ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final spatial position after rotation, wherein: ^Tx_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w at a final spatial position after rotation is given, ^Ty_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation, and ^Tz_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation;

calculating and inputting an actual orthodontic archwire curve with n bending points according to the theoretical orthodontic archwire curve, wherein the actual orthodontic archwire curve bending point information set P′_R＝{^Rp′₁,^Rp'₂,^Rp'₃,…,^Rp′_i,…,^Rp'_n},^Rp′_i＝(^Rx′_i,^Ry′_i,^Rz′_i) is the position information of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the method comprises the following steps of: ^Rx′_i The method comprises the steps that the x-axis coordinate of an ith bending point of an actual orthodontic archwire curve relative to a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ry′_i is the y-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Rz′_i is the z-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the 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, the midpoint of a connecting line between p '_f is ^R degrees', and the actual orthodontic archwire curve is subjected to spatial transformation: the point ^R o ' is overlapped with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p ' _s of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis, the right end point p ' _f of the actual orthodontic archwire curve is positioned on the positive half axis of the y axis, and the actual orthodontic archwire curve and the x axis have no intersection point; the actual orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the intersection point of the actual orthodontic archwire curve and the x axis appears, the position information of the final space position of the actual orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, the set actual orthodontic archwire curve bending point information set P_R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_i,…,^Rp_n},^Rp_i＝(^Rx_i,^Ry_i,^Rz_i) is calculated and input as the position information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final space position after rotation, wherein: ^Rx_i The method comprises the steps that an x-axis coordinate of an ith bending point of an actual orthodontic archwire curve in a final space position after rotation relative to a three-dimensional orthodontic archwire error calibration coordinate system w is ^Ry_i, a y-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is ^Rz_i, and a z-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is provided;

step two, the conversion of the curve projection, bending points and characteristic points of the actual and theoretical orthodontic archwires:

Defining a characteristic parameter j as a positive integer and containing 0, j epsilon [0, n+1]; specifically, when j e [1, n ], j=i;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Tz_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,…,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve to project the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j1,^Tz_j+1) of the feature point on the theoretical orthodontic archwire curve, thereby obtaining a theoretical projection curve The theoretical orthodontic archwire curve is positioned at the projection point/> of two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF^z of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-xy plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF^z in the o-xy projection plane;

Projecting a theoretical orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning a coordinate ^Tx_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents that the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j+1,^Tz_j+1) of the theoretical orthodontic archwire feature point, thereby obtaining a theoretical projection curve Projection points/>, of theoretical orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF^x of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-yz plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF^x in the o-yz projection plane;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ty_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to be 0; assuming that the intersection point of the theoretical orthodontic curve and the o-xz plane is ^Tp_c＝(^Tx_c,^Ty_c,^Tz_c)＝(0,^Ty_c,^Tz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the theoretical feature point represents the theoretical orthodontic archwire curve left end point p _s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀); when j epsilon [1, k-1], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); when j=n+1, the theoretical feature point represents a theoretical orthodontic archwire curve right end point p _f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1); projecting theoretical orthodontic archwire characteristic points located in o-xz negative planes to o-xz planes, and locating the projected characteristic points AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^TF^y-; projecting theoretical orthodontic archwire characteristic points located in an o-xz frontal plane to an o-xz plane, wherein the theoretical orthodontic archwire characteristic points are located in projection characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^TF^y+; ^T x is taken as the independent variable of the theoretical orthodontic archwire curve ^TF^y- and the theoretical orthodontic archwire curve ^TF^y+ in the o-xz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Rz_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the characteristic point on the actual orthodontic archwire curve, to obtain an actual projection curve The actual orthodontic archwire curve is positioned at the projection point/>, of two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^z of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on an o-xy plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^z in the o-xy projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning the coordinate ^Rx_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the actual orthodontic archwire characteristic point, to obtain an actual projection curve Projection points/>, of actual orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^x of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on the o-yz plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^x in the o-yz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ry_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; assuming that the intersection point of the actual orthodontic curve and the o-xz plane is ^Rp_c＝(^Rx_c,^Ry_c,^Rz_c)＝(0,^Ry_c,^Rz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the actual feature point represents the actual orthodontic archwire curve left end point p _s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀); when j epsilon [1, k-1], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); when j=n+1, the actual feature point represents the actual orthodontic archwire curve right end point p _f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1); projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz negative plane to the o-xz plane, and positioning the characteristic points of the projection AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^RF^y-; projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz frontal plane to the o-xz plane, and positioning the characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^RF^y+; ^R x is taken as the independent variable of the actual orthodontic archwire curve ^RF^y- and the actual orthodontic archwire curve ^RF^y+ in the o-xz projection plane; /(I)

Step three, calculating and judging average curvature between the projected theory and actual orthodontic archwire curves:

On the o-xy projection plane, the theoretical projection curve And theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-yz projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-xz negative projection planeAnd theoretical projection points/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection pointsAnd/>The distance between them is/>Theoretical projection curve/>Is of the curvature ofExpressed as/>Actual projection curve/>And the actual projection point/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection pointAnd/>The distance between them is/>Actual projection curve/>Is of the curvature ofExpressed as/>The average curvature between the projected theory and the actual orthodontic is/>Represented as

Theoretical projection curve on o-xz orthographic projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection pointsAnd/>The distance between them is/>Theoretical projection curve/>Is of the curvature ofExpressed as/>Actual projection curve/>And the actual projection point/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection pointAnd/>The distance between them is/>Actual projection curve/>Is of the curvature ofExpressed as/>The average curvature between the projected theory and the actual orthodontic is/>Represented as

Calculation of The lower limit of (3) is defined as C _min; calculation/> The lower limit of (3) is defined as C _min; calculation/> And/>The lower limit of (3) is defined as C _min;

Defining a counting parameter t, wherein t is the number of curve segments of theoretical and actual projection curves, the average curvature of which is larger than the minimum average curvature C _min, and the initial value of t is 0;

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Hold true, or/>Hold true, or/>If true, t=t+1, and jump to step three b);

If it is Does not hold, and/>Does not hold, and/>If not, jumping to the step three b); specifically, if the result is not present, the same jump is made to step three b), which is aimed atA section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not true, continuing to judge the average curvature of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step three a);

if j+1 > n is true, judging whether the counting parameter t is more than or equal to 1 is true, and if so, jumping to the fourth step; if not, outputting that the curve segment with overlarge curvature does not exist in the orthodontic archwire curve, and performing precision evaluation by a curve fitting method is not needed;

step four, introducing actual orthodontic archwire curve information point data and fitting parameters after projection theory:

There is n+1 section of theoretical curve projection of orthodontic archwire on o-xy projection plane, for theoretical projection curve It is at projection point/>, of theoretical feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Specifically expressed as/>Theoretical orthodontic archwire projection curveThe average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1 sections of theoretical curve projections of orthodontic archwires exist on o-yz projection surface, and theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Specifically expressed as/>Theoretical orthodontic archwire projection curve/>The average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Expressed as/>Actual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

K-1 segment of theoretical curve projection of orthodontic archwire exists on o-xz negative projection surface, and for theoretical projection curveIt is at the projection point/>, of the actual feature pointAnd/>(J E [0, k-2 ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe actual curve projection of the k-1 section orthodontic archwire exists on the o-xy negative projection surface, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown asTheoretical orthodontic archwire projection curve/>The average absolute value slope of (a) isExpressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1-k sections of theoretical curve projections of orthodontic archwires exist on o-xz orthographic projection plane, and the theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>(J E [ k, n ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe projection of the actual curve of the n+1-k section orthodontic archwire exists on the o-xy orthographic projection plane, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1 between the independent variables ^Ry_j and ^Ry_j+1, in which m information points are uniformly inserted, is expressed asDefining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown asTheoretical orthodontic archwire projection curve/>The average absolute value slope of (a) isExpressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

Calculation ofAnd/> The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/> The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/>Calculation/>And/> And/>The upper limit of (1) is defined as (R ²)_max,/>)And/>The upper limit of (3) is defined as (K) _max;

step five, judging whether projection curve fitting deviation of the projection on the o-xy plane, the projection on the o-yz plane and the projection on the o-xz negative or positive plane meets the set requirements:

a) Judging Whether it is true or not,

The method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step five b);

If it is Not true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting that the actual orthodontic archwire does not meet the set requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

If j+1 > n is not true, continuing to judge the fitting deviation of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step five a);

if j+1 > n is true, all curves are judged to be finished, and the step six is skipped;

Step six, judging whether the absolute value of the average absolute value slope difference of the projection curves projected on the o-xy plane, the o-yz plane and the o-xz negative or positive plane meets the set requirement:

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step six b);

If it is Not true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting an orthodontic archwire curve which does not meet the set requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not established, continuously judging the absolute value of the average absolute value slope difference of the projection curve of the next section of orthodontic archwire curve If the setting requirement is met, j=j+1 is skipped to step six);

If j+1 > n is established, all curves are evaluated, the error of each section of curve of the actual orthodontic archwire curve is within the allowable range, the output orthodontic archwire curve meets the set requirement, and the orthodontic archwire evaluation is finished.

Implementation example 2: as shown in fig. 2, 3 and 4, the present embodiment takes an orthodontic archwire curve with 16 bending points as an example, and inputs a theoretical orthodontic archwire curve bending point information set P′_T＝{^Tp′₁,^Tp'₂,^Tp'₃,...,^Tp′₁₆}, to input a theoretical orthodontic archwire curve bending point P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp₁₆ at a final spatial position after rotation; inputting an actual orthodontic archwire curve bending point information set P′_R＝{^Rp′₁,^Rp'₂,^Rp'₃,...,^Rp′₁₆},, and inputting a theoretical orthodontic archwire curve bending point P _R＝{^Rp₁,^Rp₂,^Rp₃,...,^Rp₁₆ in a final spatial position after rotation; the characteristic points are marked as j, are 16 points comprising 2 points at the head and the tail of the orthodontic archwire curve and bending points, and are 18 points in total; the theoretical and actual orthodontic archwire space curves are respectively directed to an o-xy plane, an o-yz plane,Projection, assuming that the intersection points of theoretical and practical orthodontic archwire curves and o-xz surfaces are between the 8 th and 9 th characteristic points, obtaining the projection curve equation of the theoretical orthodontic archwire as ^TF^z、^TF^x,/>The projection curve equation of the actual orthodontic archwire is ^RF^z、^RF^x,/>

The theoretical and actual average curvature of the curve segment of the orthodontic archwire in the third step, o-xy projection plane isThe fitting deviation of the theory of the o-yz projection surface and the actual orthodontic archwire curve segment is as follows: The fitting deviation of the theory of the o-xz negative projection surface and the actual orthodontic archwire curve segment is as follows: the fitting deviation of the theory of the o-xz orthographic projection surface and the actual orthodontic archwire curve segment is as follows: judging whether the average curvature between theoretical and actual orthodontic archwire curves meets the requirement or not, and judging/> Whether or not it is true, if so, j=j+1, and judgingIf the set of average curvatures between the theoretical and actual orthodontic archwire curves of the 17 sections meet the set requirements, the step is repeated, and if the set of average curvatures is met, the step is skipped to the step four, and the assumption is met; /(I)

Step four, uniformly inserting 5 information points, namely m=5, into the orthodontic archwire projection curve between every two characteristic points according to independent variables; knowing the coordinate information of the information points, the absolute value of the fitting deviation and the average absolute value slope difference of the theoretical and actual orthodontic archwire curve segments of each projection surface can be calculated; the fitting deviation of the o-xy projection plane theory and the actual orthodontic archwire curve segment is as follows: the absolute value of the average absolute value slope difference between the o-xy projection surface theory and the actual orthodontic archwire curve segment is as follows: /(I) The fitting deviation of the theory of the o-yz projection surface and the actual orthodontic archwire curve segment is as follows: /(I)The absolute value of the average absolute value slope difference between the theory of the o-yz projection surface and the actual orthodontic archwire curve segment is as follows: /(I)The fitting deviation of the theory of the o-xz negative projection surface and the actual orthodontic archwire curve segment is as follows: /(I)The fitting deviation of the theory of the o-xz orthographic projection surface and the actual orthodontic archwire curve segment is as follows: The absolute value of the average absolute value slope difference between the theory of the o-yz negative projection surface and the actual orthodontic archwire curve segment is as follows: /(I) The absolute value of the average absolute value slope difference between the o-yz orthographic projection surface theory and the actual orthodontic archwire curve segment is as follows: /(I)The upper limit of the fitting deviation between the theoretical and the actual orthodontic archwire curve is regulated to be (R ²)_max, the upper limit of the absolute value of the average absolute value slope difference between the theoretical and the actual orthodontic archwire curve is regulated to be (K) _max, and the fifth step is to judge whether the fitting deviation between the theoretical and the actual orthodontic archwire curve meets the requirement or not, judge/>Whether or not it is true, if so, j=j+1, and judgingIf so, repeating the following steps to know that the fitting deviation between the theory of the 17-section orthodontic archwire curve and the actual orthodontic archwire curve meets the set requirement, and then jumping to the step six,

Judging whether the absolute value of the average absolute value slope difference between the theoretical and actual orthodontic archwire curves meets the requirement or notWhether or not it is true, if so, j=j+1, and judgingIf so, repeating the following steps to know that the absolute value of the average absolute value slope difference between the theoretical and actual orthodontic archwire curves of the 17 sections of orthodontic archwires meets the set requirements, and then finishing the evaluation of the actual orthodontic archwires.

/>

Claims (1)

1. An orthodontic archwire error evaluation method based on a curve fitting method is characterized by comprising the following steps of: the method comprises the following specific implementation processes:

Step one, theoretical and practical orthodontic archwire curve space position transformation and bending point data importing:

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 calculated and input, wherein a theoretical orthodontic archwire curve bending point information set P_T'＝{^Tp'₁,^Tp'₂,^Tp'₃,...,^Tp'_i,...,^Tp'_n},^Tp'_i＝(^Tx'_i,^Ty'_i,^Tz'_i) is used as position information of an ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the value range of i is more than or equal to 1 and less than or equal to n, wherein: ^Tx'_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ty'_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Tz'_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the 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 the midpoint of a connecting line between p _f,p_s and p _f and is ^T degrees', and the theoretical orthodontic archwire curve is subjected to spatial transformation: the point ^T o' is coincided with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p _s of the theoretical orthodontic archwire curve is positioned on a negative y-axis half axis, the right end point p _f of the theoretical orthodontic archwire curve is positioned on a positive y-axis half axis, and the theoretical orthodontic archwire curve and the x-axis do not have an intersection point; the theoretical orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the theoretical orthodontic archwire curve and the x axis are intersected, the spatial position information of the theoretical orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, a theoretical orthodontic archwire curve bending point information set P_T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_i,...,^Tp_n},^Tp_i＝(^Tx_i,^Ty_i,^Tz_i) in the final spatial position after rotation is calculated and input as the position information of the ith bending point of the theoretical orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final spatial position after rotation, wherein: ^Tx_i The method comprises the steps that the x-axis coordinate of the ith bending point of a theoretical orthodontic archwire curve in a three-dimensional orthodontic archwire error calibration coordinate system w at a final spatial position after rotation is given, ^Ty_i is the y-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation, and ^Tz_i is the z-axis coordinate of the ith bending point of the theoretical orthodontic archwire curve in the three-dimensional orthodontic archwire error calibration coordinate system w at the final spatial position after rotation;

Calculating and inputting an actual orthodontic archwire curve with n bending points according to the theoretical orthodontic archwire curve, wherein the actual orthodontic archwire curve bending point information set P'_R＝{^Rp'₁,^Rp'₂,^Rp'₃,…,^Rp'_i,…,^Rp'_n},^Rp'_i＝(^Rx'_i,^Ry'_i,^Rz'_i) is the position information of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and the method comprises the following steps of: ^Rx'_i The method comprises the steps that the x-axis coordinate of an ith bending point of an actual orthodontic archwire curve relative to a three-dimensional orthodontic archwire error calibration coordinate system w is obtained, ^Ry'_i is the y-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w, and ^Rz'_i is the z-axis coordinate of the ith bending point of the actual orthodontic archwire curve relative to the 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, the midpoint of a connecting line between p '_f is ^R degrees', and the actual orthodontic archwire curve is subjected to spatial transformation: the point ^R o ' is overlapped with the origin o of the three-dimensional orthodontic archwire error calibration coordinate system w, the left end point p ' _s of the actual orthodontic archwire curve is positioned on the negative half axis of the y axis, the right end point p ' _f of the actual orthodontic archwire curve is positioned on the positive half axis of the y axis, and the actual orthodontic archwire curve and the x axis have no intersection point; the actual orthodontic archwire curve is rotated clockwise along the positive direction of the y axis until the intersection point of the actual orthodontic archwire curve and the x axis appears, the position information of the final space position of the actual orthodontic archwire curve after rotation is set as the position information in the three-dimensional orthodontic archwire error calibration coordinate system w, the set actual orthodontic archwire curve bending point information set P_R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_i,…,^Rp_n},^Rp_i＝(^Rx_i,^Ry_i,^Rz_i) is calculated and input as the position information of the i-th bending point of the actual orthodontic archwire curve relative to the three-dimensional orthodontic archwire error calibration coordinate system w in the final space position after rotation, wherein: ^Rx_i The method comprises the steps that an x-axis coordinate of an ith bending point of an actual orthodontic archwire curve in a final space position after rotation relative to a three-dimensional orthodontic archwire error calibration coordinate system w is ^Ry_i, a y-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is ^Rz_i, and a z-axis coordinate of the ith bending point of the actual orthodontic archwire curve in the final space position after rotation relative to the three-dimensional orthodontic archwire error calibration coordinate system w is provided;

step two, the conversion of the curve projection, bending points and characteristic points of the actual and theoretical orthodontic archwires:

Defining a characteristic parameter j as a positive integer and containing 0, j epsilon [0, n+1]; specifically, when j e [1, n ], j=i;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Tz_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,…,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve to project the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j1,^Tz_j+1) of the feature point on the theoretical orthodontic archwire curve, thereby obtaining a theoretical projection curve The theoretical orthodontic archwire curve is positioned at the projection point/> of two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF^z of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-xy plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF^z in the o-xy projection plane;

Projecting a theoretical orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning a coordinate ^Tx_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to 0; when j epsilon [1, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); specifically, when j=0, the theoretical feature point represents the left end point p_s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀)＝(0,^Ty₀,0); of the theoretical orthodontic archwire curve, and when j=n+1, the theoretical feature point represents that the right end point p_f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1)＝(0,^Ty_n+1,0); of the theoretical orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j) and ^Tp_j+1＝(^Tx_j+1,^Ty_j+1,^Tz_j+1) of the theoretical orthodontic archwire feature point, thereby obtaining a theoretical projection curve Projection points/>, of theoretical orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar theoretical orthodontic archwire curve ^TF_x of the theoretical orthodontic archwire curve after the projection of the theoretical orthodontic archwire curve on an o-yz plane, and regarding ^T y as an independent variable of the theoretical orthodontic archwire curve ^TF_x in the o-yz projection plane;

Projecting the theoretical orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ty_i in each bending point ^Tp_i＝(^Tx_i,^Ty_i,^Tz_i in the theoretical orthodontic archwire curve bending point information set P _T＝{^Tp₁,^Tp₂,^Tp₃,...,^Tp_n) to be 0; assuming that the intersection point of the theoretical orthodontic curve and the o-xz plane is ^Tp_c＝(^Tx_c,^Ty_c,^Tz_c)＝(0,^Ty_c,^Tz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the theoretical feature point represents the theoretical orthodontic archwire curve left end point p _s＝^Tp₀＝(^Tx₀,^Ty₀,^Tz₀); when j epsilon [1, k-1], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the theoretical feature points coincide with the theoretical bending points, and the theoretical feature points can be expressed as ^Tp_j＝(^Tx_j,^Ty_j,^Tz_j); when j=n+1, the theoretical feature point represents a theoretical orthodontic archwire curve right end point p _f＝^Tp_n+1＝(^Tx_n+1,^Ty_n+1,^Tz_n+1); projecting theoretical orthodontic archwire characteristic points located in o-xz negative planes to o-xz planes, and locating the projected characteristic points AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^TF^y-; projecting theoretical orthodontic archwire characteristic points located in an o-xz frontal plane to an o-xz plane, wherein the theoretical orthodontic archwire characteristic points are located in projection characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the theoretical projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^TF^y+; ^T x is taken as the independent variable of the theoretical orthodontic archwire curve ^TF^y- and the theoretical orthodontic archwire curve ^TF^y+ in the o-xz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xy plane in the final pose, namely assigning the coordinate ^Rz_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-xy between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the characteristic point on the actual orthodontic archwire curve, to obtain an actual projection curve The actual orthodontic archwire curve is positioned at the projection point/>, of two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^z of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on an o-xy plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^z in the o-xy projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-yz plane in the final pose, namely assigning the coordinate ^Rx_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; when j is epsilon [1, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); specifically, when j=0, the actual characteristic point represents the left end point p_s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀)＝(0,^Ry₀,0); of the actual orthodontic archwire curve, and when j=n+1, the actual characteristic point represents that the right end point p_f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1)＝(0,^Ry_n+1,0); of the actual orthodontic archwire curve projects the orthodontic archwire Qu Xianxiang o-yz between the projection points ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j) and ^Rp_j+1＝(^Rx_j+1,^Ry_j+1,^Rz_j+1) of the actual orthodontic archwire characteristic point, to obtain an actual projection curve Projection points/>, of actual orthodontic archwire curve on two characteristic pointsAnd/>Between them; obtaining a planar actual orthodontic archwire curve ^RF^x of the actual orthodontic archwire curve after the projection of the actual orthodontic archwire curve on the o-yz plane, and regarding ^R y as an independent variable of the actual orthodontic archwire curve ^RF^x in the o-yz projection plane;

Projecting the actual orthodontic archwire Qu Xianxiang o-xz plane in the final pose, namely assigning the coordinate ^Ry_i in each bending point ^Rp_i＝(^Rx_i,^Ry_i,^Rz_i in the actual orthodontic archwire curve bending point information set P _R＝{^Rp₁,^Rp₂,^Rp₃,…,^Rp_n) to be 0; assuming that the intersection point of the actual orthodontic curve and the o-xz plane is ^Rp_c＝(^Rx_c,^Ry_c,^Rz_c)＝(0,^Ry_c,^Rz_c),, and the intersection point is positioned between the kth-1 and the kth characteristic point; the feature points lying in the o-xz negative plane are expressed as: when j=0, the actual feature point represents the actual orthodontic archwire curve left end point p _s＝^Rp₀＝(^Rx₀,^Ry₀,^Rz₀); when j epsilon [1, k-1], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); the feature points lying in the o-xz frontal plane are expressed as: when j epsilon [ k, n ], the actual characteristic point coincides with the actual bending point, and the actual characteristic point can be expressed as ^Rp_j＝(^Rx_j,^Ry_j,^Rz_j); when j=n+1, the actual feature point represents the actual orthodontic archwire curve right end point p _f＝^Rp_n+1＝(^Rx_n+1,^Ry_n+1,^Rz_n+1); projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz negative plane to the o-xz plane, and positioning the characteristic points of the projection AndThe projection curve between is noted as/>Wherein j is E [0, k-1], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz negative plane is recorded as ^RF^y-; projecting the characteristic points of the actual orthodontic archwire positioned in the o-xz frontal plane to the o-xz plane, and positioning the characteristic points/>And/>The projection curve between is noted as/>Wherein j is epsilon [ k, n ], and the actual projection curve of the whole orthodontic archwire obtained in the o-xz frontal plane is ^RF^y+; ^R x is taken as the independent variable of the actual orthodontic archwire curve ^RF^y- and the actual orthodontic archwire curve ^RF^y+ in the o-xz projection plane;

Step three, calculating and judging average curvature between the projected theory and actual orthodontic archwire curves:

On the o-xy projection plane, the theoretical projection curve And theoretical projection points/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>AndThe distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-yz projection planeAnd theoretical projection points/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>AndThe distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Theoretical projection curve on o-xz negative projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection pointsAnd/>The distance between them is/>Theoretical projection curve/>Is of the curvature ofExpressed as/>Actual projection curve/>And the actual projection point/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection pointAnd/>The distance between them is/>Actual projection curve/>Is of the curvature ofExpressed as/>The average curvature between the projected theory and the actual orthodontic is/>Represented as

Theoretical projection curve on o-xz orthographic projection planeAnd theoretical projection points/>AndThe area of the surrounding area between the connecting lines of (a) is/>In particular theoretical projection points/>And/>The distance between them is/>Theoretical projection curve/>Is/>Represented asActual projection curve/>And the actual projection point/>And/>The area of the surrounding area between the connecting lines of (a) is/>In particular the actual projection point/>And/>The distance between them is/>Actual projection curve/>Is/>Expressed as/>The average curvature between the projected theory and the actual orthodontic is/>Expressed as/>

Calculation ofj∈[0,n]，/>The lower limit of (3) is defined as C _min; calculation/>j∈[0,n]，/>The lower limit of (3) is defined as C _min; calculation/> And/>The lower limit of (3) is defined as C _min;

Defining a counting parameter t, wherein t is the number of curve segments of theoretical and actual projection curves, the average curvature of which is larger than the minimum average curvature C _min, and the initial value of t is 0;

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Hold true, or/>Hold true, or/>If true, t=t+1, and jump to step three b);

If it is Does not hold, and/>Does not hold, and/>If not, jumping to the step three b); specifically, if the result is not present, the same jump is made to step three b), which is directed to/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not true, continuing to judge the average curvature of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step three a);

if j+1 > n is true, judging whether the counting parameter t is more than or equal to 1 is true, and if so, jumping to the fourth step; if not, outputting that the curve segment with overlarge curvature does not exist in the orthodontic archwire curve, and performing precision evaluation by a curve fitting method is not needed;

step four, introducing actual orthodontic archwire curve information point data and fitting parameters after projection theory:

There is n+1 section of theoretical curve projection of orthodontic archwire on o-xy projection plane, for theoretical projection curve It is at projection point/>, of theoretical feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curveThe function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Specifically expressed as/>Theoretical orthodontic archwire projection curve/>The average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Expressed as/>Actual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1 sections of theoretical curve projections of orthodontic archwires exist on o-yz projection surface, and theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curveThe function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>N+1 sections of orthodontic archwire actual curves exist on the o-xy projection plane respectively, and the actual projection curves/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed as/>Corresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) -th information point is/>Theoretical orthodontic archwire projection curve/>, between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Specifically expressed as/>Theoretical orthodontic archwire projection curve/>The average absolute value slope of (2) is/>Expressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

K-1 segment of theoretical curve projection of orthodontic archwire exists on o-xz negative projection surface, and for theoretical projection curveIt is at the projection point/>, of the actual feature pointAnd/>(J E [0, k-2 ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe actual curve projection of the k-1 section orthodontic archwire exists on the o-xy negative projection surface, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1, where m information points are inserted uniformly between arguments ^Ry_j and ^Ry_j+1, is denoted/>Defining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown asTheoretical orthodontic archwire projection curve/>The average absolute value slope of (a) isExpressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

N+1-k sections of theoretical curve projections of orthodontic archwires exist on o-xz orthographic projection plane, and the theoretical projection curves are calculatedIt is at the projection point/>, of the actual feature pointAnd/>(J E [ k, n ]), the independent variable is ^T y; the distance between ^Ty_j and ^Ty_j+1, where m information points are inserted uniformly between arguments ^Ty_j and ^Ty_j+1, is denoted/>Defining the parameter a E [0, m+1] representing the a-th information point, the argument y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isThe projection of the actual curve of the n+1-k section orthodontic archwire exists on the o-xy orthographic projection plane, and the actual projection curve/>It is at the projection point/>, of the actual feature pointAnd/>The independent variable is ^R y; the distance between ^Ry_j and ^Ry_j+1 between the independent variables ^Ry_j and ^Ry_j+1, in which m information points are uniformly inserted, is expressed asDefining a parameter a E [0, m+1] representing the a-th information point, the y-coordinate value of the a-th information point can be expressed asCorresponding projection curve/>The function value is expressed as/>The y coordinate value of the (m+1) th information point isTheoretical orthodontic archwire projection curve between jth feature point and (j+1) th feature pointAnd the projection curve/>, of the actual orthodontic archwireThe fitting deviation between is expressed as/>Is specifically shown asTheoretical orthodontic archwire projection curve/>The average absolute value slope of (a) isExpressed as/>Likewise, the actual orthodontic archwire projection curve/>, between the jth feature point and the (j+1) th feature pointThe average absolute value slope of (2) is/>Represented asActual orthodontic archwire projection curve/>And theoretical orthodontic archwire projection curve/>The absolute value of the average absolute value slope difference of/>

Calculation ofAnd/>j∈[0,n]，/>The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/>j∈[0,n]，/>The upper limit of (1) is defined as (R ²)_max,/>)The upper limit of (3) is defined as (K) _max;

Calculation of And/>J is E [0, k-1]; calculation/>And/>j∈[k,n]；/>And/>The upper limit of (1) is defined as (R ²)_max,/>)And/>The upper limit of (3) is defined as (K) _max;

step five, judging whether projection curve fitting deviation of the projection on the o-xy plane, the projection on the o-yz plane and the projection on the o-xz negative or positive plane meets the set requirements:

a) Judging Whether or not it is:

the method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step five b);

If it is Not true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting that the actual orthodontic archwire does not meet the set requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

If j+1 > n is not true, continuing to judge the fitting deviation of the projection curve of the next orthodontic archwire curve If the setting requirement is met, j=j+1 is caused to jump to the step five a);

if j+1 > n is true, all curves are judged to be finished, and the step six is skipped;

Step six, judging whether the absolute value of the average absolute value slope difference of the projection curves projected on the o-xy plane, the o-yz plane and the o-xz negative or positive plane meets the set requirement:

a) Judging Whether it is true or not,

The method comprises the following steps:

If it is Is true/>Is true/>If true, jumping to the step six b); /(I)

If it isNot true, or/>Not true, or/>If not, finishing the evaluation of the orthodontic archwire, and outputting an orthodontic archwire curve which does not meet the expected precision requirement; specifically, if the result is not present, it is ignored, this is for/>A section of curve when j=k-1, which is ignored in (b);

b) Judging whether all the characteristic points are finished:

Judging whether j+1 > n is true or not,

The method comprises the following steps:

if j+1 > n is not established, continuously judging the absolute value of the average absolute value slope difference of the projection curve of the next section of orthodontic archwire curve If the setting requirement is met, j=j+1 is skipped to step six);

If j+1 > n is true, all curves are evaluated, the error of each section of curve of the actual orthodontic archwire curve is within the allowable range, the orthodontic archwire evaluation is finished, and the output orthodontic archwire curve is satisfied within the expected error range.