CN117217992B - Tooth preparation track interpolation precision evaluation method based on curvature fluctuation rate and step error judgment - Google Patents

Abstract

The invention discloses a tooth preparation track interpolation precision evaluation method based on curvature fluctuation rate and step error judgment, which relates to the technical field of tooth preparation track precision evaluation. The invention verifies the curvature fluctuation rate among the interpolation points of the tooth preparation track in advance, and then judges and corrects the step error, thereby avoiding unnecessary subsequent calculation, improving the evaluation efficiency of the interpolation precision of the tooth preparation track and realizing the efficient quantitative evaluation of the interpolation precision of the tooth preparation track.

Description

A method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment

Technical Field

The patent of this invention relates to a method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment, and belongs to the technical field of tooth preparation trajectory accuracy evaluation.

Background Art

Dental caries is an important cause of tooth defects, which seriously affects people's oral health; oral restoration is an important means of treating tooth defects, and tooth preparation is a necessary treatment link in the restoration process, which refers to the operation process in which doctors quantitatively remove the teeth in the carious area and form the expected three-dimensional shape. In traditional clinical applications, tooth preparation needs to rely on the doctor's manual operation and combine rich clinical experience to make a large number of repeated fine adjustments to the carious teeth. However, the current imbalance between doctors and patients cannot meet the current huge demand for tooth preparation; although with the continuous innovation of automation and robotics technology, the introduction of robots and auxiliary software to replace or assist doctors in completing tooth preparation has begun to transition from traditional manual tooth preparation to high-precision, automated, and digital processing methods, so there is an urgent need for an evaluation method for the interpolation accuracy of tooth preparation trajectories that is adapted to it.

In addition, considering the personalized characteristics of curvature fluctuation of the tooth preparation trajectory, for example, the curvature between the interpolation points on the patient's personalized tooth preparation trajectory varies greatly, resulting in a large curvature fluctuation rate in the tooth preparation trajectory, which in turn causes a large error in the arch height of the curve between individual interpolation points, resulting in a large error in the interpolation step length on the tooth preparation trajectory, resulting in poor interpolation accuracy of the patient's personalized tooth preparation trajectory. When evaluating the accuracy of such tooth preparation trajectories, there is currently no method that can determine the interpolation accuracy of such tooth preparation trajectories through indicators; the lack of such methods has resulted in the inability to obtain targeted guidance and improvement directions for the accuracy evaluation of tooth preparation trajectories, limiting the development of tooth preparation trajectory interpolation methods; in summary, the current technical field of interpolation accuracy evaluation of tooth preparation trajectories urgently needs a method that can accurately and quantitatively evaluate the interpolation accuracy of such tooth preparation trajectories.

Summary of the invention

In response to the above problems, the present invention proposes a method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment, which solves the problem that there is a lack of interpolation accuracy evaluation methods for tooth preparation trajectory with large curvature fluctuation rate and step error in the current field of tooth preparation trajectory interpolation accuracy evaluation. During the tooth preparation trajectory evaluation process, the curvature fluctuation rate of the tooth preparation trajectory is pre-verified, and then the step error is corrected, thereby achieving efficient quantitative evaluation of the interpolation accuracy of the tooth preparation trajectory.

A tooth preparation trajectory interpolation accuracy evaluation method based on curvature fluctuation rate and step error judgment, the specific implementation process of the method is as follows:

Step 1: Import tooth preparation trajectory data and calculate interpolation points of tooth preparation trajectory:

The doctor's clinical tooth preparation model is scanned to obtain a standardized tooth preparation model. The tooth model is processed by reverse engineering software to obtain discrete points of the tooth preparation trajectory of the relevant teeth. The discrete points are inversely calculated by introducing NURBS curves to obtain a discrete point information set A = {R ₁ , R ₂ , R ₃ , ..., R _j , ..., R _m } of m tooth preparation trajectories, where R _j = {P ^j , ω ^j , U ^j } is the discrete point information set of the j-th tooth preparation trajectory, where the value range of j is 1≤j≤m. is the control point information set of the jth tooth preparation trajectory, where the value range of i is 1≤i≤n, is the control point position information set of the i-th discrete point of the j-th tooth preparation trajectory, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system, is the weight factor information set of the control points of the j-th tooth preparation trajectory, is the weight factor of the ith control point of the jth tooth preparation trajectory, is the node vector information set of the discrete points of the j-th tooth preparation trajectory, is the node vector of the ith discrete point of the jth tooth preparation trajectory. The fourth-order Runge-Kutta method is used to calculate the node vector of the ith discrete point of the jth tooth preparation trajectory. Perform calculations and define Regulation in Calculated by high-order backward difference method, it is specified , t is the interpolation period of tooth preparation trajectory;

Define the tooth preparation trajectory expression, represented by Q _j (u), and define the j-th tooth preparation trajectory expression as is about the node vector By substituting the parameters P ^j , ω ^j , and U ^j in the j-th tooth preparation trajectory discrete point information set R _j = {P ^j , ω ^j , U ^j } into the tooth preparation trajectory expression Q _j (u), the n interpolation point information set of the j-th tooth preparation trajectory is obtained. is the position information of the i-th interpolation point of the j-th tooth preparation trajectory, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the ith interpolation point of the jth tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system;

Step 2: Setting the actual step length between interpolation points of tooth preparation trajectory:

Define the actual step length between the interpolation points of the jth tooth preparation trajectory, using the symbol express, is a description of the actual step length of the j-th tooth preparation trajectory, by calculating the i-th interpolation point of the j-th tooth preparation trajectory and the i-1th interpolation point The actual step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is determined by the spatial distance between them.

Step 3: Setting the arch height error and curvature fluctuation rate between adjacent interpolation points of tooth preparation trajectory:

Define the arch height error between adjacent interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a quantitative description of the fluctuation degree of tooth preparation trajectory. The tooth preparation trajectory interpolation point is specified at At the i-th interpolation point of the j-th tooth preparation trajectory, the curvature radius Obtain an osculating circle, approximate the curve between adjacent interpolation points of the tooth preparation trajectory as an arc, and define the interpolation points after the approximate arc as The curvature radius of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is specified. Indicates the jth tooth preparation trajectory at the i-th node vector The first-order derivative at , Indicates the jth tooth preparation trajectory at the i-th node vector The second-order derivative at , specifies the maximum height error of the j-th tooth preparation trajectory as (h ^j ) _max ; Since the height error of the tooth preparation trajectory will change with the fluctuation of the curve curvature, the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory is defined, and the symbol is express, It is a quantitative description of the stability of tooth preparation trajectory. It is stipulated that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is expressed as The value range of i is 2≤i≤n. It represents the curvature deviation between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies represents the curvature of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies The upper limit index of the curvature fluctuation rate between adjacent interpolation points of j tooth preparation trajectories is specified as

Step 4: Evaluation of the curvature fluctuation rate of adjacent interpolation points of tooth preparation trajectory:

according to The calculation formula is used to calculate the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory, and the Is it established?

Specifically:

if If it is established, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is within the allowable range, and jump to step 5;

if If it is not true, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory exceeds the allowable range, and the output is that this tooth preparation trajectory is not suitable for this evaluation method, and the actual tooth preparation trajectory accuracy evaluation ends;

Step 5: Setting the theoretical step length between interpolation points of tooth preparation trajectory:

Define the theoretical step length between interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a description of the theoretical step length of the j-th tooth preparation trajectory. It stipulates that the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as It represents the height error between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory. Determine the constraint step size, specify represents the maximum constraint step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory determined by the maximum arch height error (h ^j ) _max , and specifies

Step 6. Setting and evaluating the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the tooth preparation trajectory:

The relative error between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory is defined as ^rj (i), ^which is a quantitative description of the stability of the interpolation point step length of the tooth preparation trajectory. The relative error between the actual step length and the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as The maximum value of the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th adjacent interpolation point of the j-th tooth preparation trajectory is specified as r ^j (i) _max , and the interval (0, r _j (i) _max ) is the tolerance range of the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the ^j -th tooth preparation trajectory; the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th interpolation point of the j-th tooth preparation trajectory is calculated according to the calculation formula of r j (i), and it is determined whether r ^j (i) ≤ r ^j (i) _max holds.

Specifically:

If r ^j (i) ≤ ^{r j} (i) _max holds true, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory falls within the allowable tolerance range, and the corresponding interpolation point is a valid tooth preparation trajectory interpolation point, and jump to step eight;

If r ^j (i) ≤ ^{r j} (i) _max does not hold, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between the adjacent interpolation points of the j-th tooth preparation trajectory exceeds the allowable constraint range, and the interpolation points of the actual tooth preparation trajectory need to be corrected accordingly, and jump to step seven;

Step 7: Setting the correction parameters of the tooth preparation trajectory node vector:

The correction parameters of the tooth preparation trajectory node vector are defined as Regulation It is expressed as the theoretical step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, It is represented as the actual step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and defines the node vector of the i-th interpolation point of the j-th tooth preparation trajectory after correction. Regulation represents the node vector of the i-1th interpolation point of the jth tooth preparation trajectory, It is represented as the node vector of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and jumps to step 1;

Step 8: Determine whether the interpolation accuracy of tooth preparation trajectory has been evaluated:

a) Determine whether the number n of interpolation points of the i-th and j-th tooth preparation trajectories is equal,

Specifically:

If i=n is not true, it means that the interpolation accuracy evaluation has not been performed on all interpolation points on the j-th tooth preparation trajectory, then let i=i+1, and jump to step 1 to continue to evaluate the accuracy of the interpolation points on the tooth preparation trajectory;

If i=n, it means that the interpolation accuracy evaluation of all interpolation points on the j-th tooth preparation trajectory is completed, the interpolation accuracy evaluation of the j-th tooth preparation trajectory is output, and the process jumps to step eight b);

b) Determine whether j is equal to the number m of all tooth preparation trajectories,

Specifically:

If j=m is not true, it means that the interpolation accuracy evaluation has not been performed on all tooth preparation trajectories, then let j=j+1, and jump to step 1 to continue to evaluate the accuracy of the tooth preparation trajectory;

If j=m, it means that the interpolation accuracy evaluation of all tooth preparation trajectories is completed, and the relative errors of the curvature fluctuation rate and step length between adjacent interpolation points of all tooth preparation trajectories are within the allowable range, then the loop is exited and the interpolation accuracy evaluation of all tooth preparation trajectories is completed.

The beneficial effects of the present invention are:

1. Aiming at the special situation that the curvature fluctuation rate of adjacent interpolation points of tooth preparation trajectory is large, the present invention proposes the curvature fluctuation rate between adjacent interpolation points of the jth tooth preparation trajectory: concept and set The upper limit value is Taking into account the problem of large curvature fluctuation rate between adjacent interpolation points of the dental preparation trajectory, the arch height error of the dental preparation trajectory will be greatly affected during the interpolation process, and large errors are likely to occur during the interpolation of the dental preparation trajectory; the curvature fluctuation rate of adjacent interpolation points is an indicator reflecting the contour accuracy of the dental preparation trajectory. Therefore, the present invention first evaluates the curvature fluctuation rate of adjacent interpolation points of the dental preparation trajectory to complete the quantitative evaluation of the contour accuracy of adjacent interpolation points of the dental preparation trajectory; when the curvature fluctuation rate between adjacent interpolation points of the dental preparation trajectory exceeds the permitted range, there is no need to evaluate the subsequent interpolation step length of the dental preparation trajectory, thereby simplifying the evaluation steps.

2. The present invention proposes a theoretical step length between interpolation points of the tooth preparation trajectory, which is Setting method; Due to certain errors and uncertainties in the tooth preparation process, there is a certain difference between the theoretical step length and the actual step length; Determined Constrained Step Size and maximum bow height error Determine the maximum constrained step size It can ensure the stability and consistency of the entire interpolation result of the tooth preparation trajectory and avoid the unexpected situation of excessive step length during the interpolation process.

3. The present invention is directed to a method for determining the step length error between interpolation points on a tooth preparation trajectory, proposes the concept of the relative error r ^j (i) between the actual step length and the theoretical step length between the interpolation points of the j-th tooth preparation trajectory, and sets an upper limit value r ^j (i) _max of r ^j (i), thereby realizing a quantitative description of the evaluation of the interpolation step length of the tooth preparation trajectory. When evaluating the interpolation step length of the tooth preparation trajectory, it is necessary to consider the relative error between the actual step length of the tooth preparation trajectory and the theoretical step length of the tooth preparation trajectory. When the relative error of the step length between the interpolation points of the tooth preparation trajectory exceeds the permissible range, the step length needs to be corrected to ensure the accuracy of the tooth preparation trajectory.

4. In order to solve the problem of excessive step error between interpolation points on tooth preparation trajectory, the present invention proposes correction parameters for node vectors of tooth preparation trajectory. The quantitative description of the interpolation step length correction of the tooth preparation trajectory is realized; the correction equation for the node vector of adjacent interpolation points of the tooth preparation trajectory is proposed: The node vectors of adjacent interpolation points of the tooth preparation trajectory are corrected; when the relative error of the interpolation step exceeds the permitted range, it will cause problems with the accuracy of the actual tooth preparation trajectory. The node vectors of adjacent interpolation points of the tooth preparation trajectory are corrected, and new interpolation points of the tooth preparation trajectory are recalculated to ensure the reliability of the tooth preparation trajectory interpolation.

BRIEF DESCRIPTION OF THE DRAWINGS

For ease of explanation, the present invention is described in detail with reference to the following specific implementations and accompanying drawings.

FIG1 is a flow chart of a method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment;

Fig. 2 is a schematic diagram of the entire tooth preparation trajectory;

FIG3 is a schematic diagram of the j-th tooth preparation trajectory;

FIG4 is a schematic diagram of the interpolation points and the curvature radius after the curve between adjacent interpolation points of the j-th tooth preparation trajectory is approximated to a circular arc;

FIG5 is a schematic diagram of the actual step length between adjacent interpolation points of the j-th tooth preparation trajectory and the constrained step length determined by the arch height error;

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is described below through the specific embodiments shown in the accompanying drawings, but it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concepts of the present invention.

Implementation Example 1: As shown in FIG. 1 , FIG. 2 , FIG. 3 , FIG. 4 , and FIG. 5 , this specific implementation adopts the following technical solution: a method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment, and the specific implementation process of the method is as follows:

Step 1: Import tooth preparation trajectory data and calculate interpolation points of tooth preparation trajectory:

The doctor's clinical tooth preparation model is scanned to obtain a standardized tooth preparation model. The tooth model is processed by reverse engineering software to obtain discrete points of the tooth preparation trajectory of the relevant teeth. The discrete points are inversely calculated by introducing NURBS curves to obtain a discrete point information set A = {R ₁ , R ₂ , R ₃ , ..., R _j , ..., R _m } of m tooth preparation trajectories, where R _j = {P ^j , ω ^j , U ^j } is the discrete point information set of the j-th tooth preparation trajectory, where the value range of j is 1≤j≤m. is the control point information set of the jth tooth preparation trajectory, where the value range of i is 1≤i≤n, is the control point position information set of the i-th discrete point of the j-th tooth preparation trajectory, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system, is the weight factor information set of the control points of the j-th tooth preparation trajectory, is the weight factor of the ith control point of the jth tooth preparation trajectory, is the node vector information set of the discrete points of the j-th tooth preparation trajectory, is the node vector of the ith discrete point of the jth tooth preparation trajectory. The fourth-order Runge-Kutta method is used to calculate the node vector of the ith discrete point of the jth tooth preparation trajectory. Perform calculations and define Regulation in Calculated by high-order backward difference method, it is specified t is the interpolation cycle of tooth preparation trajectory;

Define the tooth preparation trajectory expression, represented by Q _j (u), and define the j-th tooth preparation trajectory expression as is about the node vector By substituting the parameters P ^j , ω ^j , and U ^j in the j-th tooth preparation trajectory discrete point information set R _j = {P ^j , ω ^j , U ^j } into the tooth preparation trajectory expression Q _j (u), the n interpolation point information set of the j-th tooth preparation trajectory is obtained. is the position information of the i-th interpolation point of the j-th tooth preparation trajectory, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the ith interpolation point of the jth tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system;

Step 2: Setting the actual step length between interpolation points of tooth preparation trajectory:

Define the actual step length between the interpolation points of the jth tooth preparation trajectory, using the symbol express, is a description of the actual step length of the j-th tooth preparation trajectory, by calculating the i-th interpolation point of the j-th tooth preparation trajectory and the i-1th interpolation point The actual step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is determined by the spatial distance between them.

Step 3: Setting the arch height error and curvature fluctuation rate between adjacent interpolation points of tooth preparation trajectory:

Define the arch height error between adjacent interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a quantitative description of the fluctuation degree of tooth preparation trajectory. The tooth preparation trajectory interpolation point is specified at At the i-th interpolation point of the j-th tooth preparation trajectory, the curvature radius Obtain an osculating circle, approximate the curve between adjacent interpolation points of the tooth preparation trajectory as an arc, and define the interpolation points after the approximate arc as The curvature radius of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is specified. Indicates the jth tooth preparation trajectory at the i-th node vector The first-order derivative at , Indicates the jth tooth preparation trajectory at the i-th node vector The second-order derivative at , specifies the maximum height error of the j-th tooth preparation trajectory as (h ^j ) _max ; Since the height error of the tooth preparation trajectory will change with the fluctuation of the curve curvature, the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory is defined, and the symbol is express, It is a quantitative description of the stability of tooth preparation trajectory. It is stipulated that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is expressed as The value range of i is 2≤i≤n. It represents the curvature deviation between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies represents the curvature of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies The upper limit index of the curvature fluctuation rate between adjacent interpolation points of j tooth preparation trajectories is specified as

Step 4: Evaluation of the curvature fluctuation rate of adjacent interpolation points of tooth preparation trajectory:

according to The calculation formula is used to calculate the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory, and the Is it established?

Specifically:

if If it is established, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is within the allowable range, and jump to step 5;

if If it is not true, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory exceeds the allowable range, and the output is that this tooth preparation trajectory is not suitable for this evaluation method, and the actual tooth preparation trajectory accuracy evaluation ends;

Step 5: Setting the theoretical step length between interpolation points of tooth preparation trajectory:

Define the theoretical step length between interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a description of the theoretical step length of the j-th tooth preparation trajectory. It stipulates that the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as It represents the height error between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory. Determine the constraint step size, specify represents the maximum constraint step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory determined by the maximum arch height error (h ^j ) _max , and specifies

Step 6. Setting and evaluating the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the tooth preparation trajectory:

The relative error between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory is defined as ^rj (i), ^which is a quantitative description of the stability of the interpolation point step length of the tooth preparation trajectory. The relative error between the actual step length and the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as The maximum value of the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th adjacent interpolation point of the j-th tooth preparation trajectory is specified as r ^j (i) _max , and the interval (0, r _j (i) _max ) is the tolerance range of the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the ^j -th tooth preparation trajectory; the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th interpolation point of the j-th tooth preparation trajectory is calculated according to the calculation formula of r j (i), and it is determined whether r ^j (i) ≤ r ^j (i) _max holds.

Specifically:

If r ^j (i) ≤ ^{r j} (i) _max holds true, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory falls within the allowable tolerance range, and the corresponding interpolation point is a valid tooth preparation trajectory interpolation point, and jump to step eight;

If r ^j (i) ≤ ^{r j} (i) _max does not hold, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between the adjacent interpolation points of the j-th tooth preparation trajectory exceeds the allowable constraint range, and the interpolation points of the actual tooth preparation trajectory need to be corrected accordingly, and jump to step seven;

Step 7: Setting the correction parameters of the tooth preparation trajectory node vector:

The correction parameters of the tooth preparation trajectory node vector are defined as Regulation It is expressed as the theoretical step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, It is represented as the actual step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and defines the node vector of the i-th interpolation point of the j-th tooth preparation trajectory after correction. Regulation represents the node vector of the i-1th interpolation point of the jth tooth preparation trajectory, It is represented as the node vector of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and jumps to step 1;

Step 8: Determine whether the interpolation accuracy of tooth preparation trajectory has been evaluated:

a) Determine whether the number n of interpolation points of the i-th and j-th tooth preparation trajectories is equal,

Specifically:

If i=n is not true, it means that the interpolation accuracy evaluation has not been performed on all interpolation points on the j-th tooth preparation trajectory, then let i=i+1, and jump to step 1 to continue to evaluate the accuracy of the interpolation points on the tooth preparation trajectory;

If i=n, it means that the interpolation accuracy evaluation of all interpolation points on the j-th tooth preparation trajectory is completed, the interpolation accuracy evaluation of the j-th tooth preparation trajectory is output, and the process jumps to step eight b);

b) Determine whether j is equal to the number m of all tooth preparation trajectories,

Specifically:

If j=m is not true, it means that the interpolation accuracy evaluation has not been performed on all tooth preparation trajectories, then let j=j+1, and jump to step 1 to continue to evaluate the accuracy of the tooth preparation trajectory;

If j=m, it means that the interpolation accuracy evaluation of all tooth preparation trajectories is completed, and the relative errors of the curvature fluctuation rate and step length between adjacent interpolation points of all tooth preparation trajectories are within the allowable range, then the loop is exited and the interpolation accuracy evaluation of all tooth preparation trajectories is completed.

Implementation Example 2: As shown in FIG3, FIG4, and FIG5, in the process of performing a tooth preparation trajectory interpolation accuracy evaluation method based on curvature fluctuation rate and step error judgment on the j-th tooth preparation trajectory containing n=27 interpolation points, the initial value of i is i=1, and the upper limit value of the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory is specified to be The maximum arch height error of the j-th tooth preparation trajectory is specified as (h ^j ) _max = 0.1 mm, and the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory is specified as r ^j (i) _max = 0.5 mm; according to step 1, the tooth preparation trajectory data is imported, and the i-th interpolation point of the j-th tooth preparation trajectory is calculated. Calculate the actual step length between the i-th interpolation points of the j-th tooth preparation trajectory according to the formula in step 2 According to the formula in step 3, calculate the curvature deviation between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory. The curvature deviation of the adjacent interpolation points of the actual tooth preparation trajectory Then calculate the curvature fluctuation rate between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory The arch height error between the i-th interpolation points of the j-th tooth preparation trajectory is calculated by the formula Jump to step 4 to evaluate the curvature fluctuation rate of adjacent interpolation points of tooth preparation trajectory. The curvature fluctuation rate between the current adjacent interpolation points of the j-th tooth preparation trajectory calculated in step 3 is less than the upper limit value, and the process jumps to step 5 to perform the theoretical step length between the i-th interpolation points of the j-th tooth preparation trajectory. The interpolation step length under the bow height error constraint is calculated by the formula and the constrained step length determined under the maximum bow height error By comparison Jump to step 6 to calculate and evaluate the relative error between the actual step length and the theoretical step length between the ith interpolation point of the jth tooth preparation trajectory. Calculate the relative error r ^j (i) between the actual step length and the theoretical step length between the ith interpolation point of the jth tooth preparation trajectory by the formula. By comparing r ^j (i) ≤ ^{r j} (i) _max , it is obtained that the relative error of the interpolation step length of the 13th, 14th, 15th, and 16th interpolation points calculated according to the formula in step 6 is greater than the upper limit value, then jump to step 7 to correct the node vector of the tooth preparation trajectory, and calculate the correction coefficient by the formula And the corrected node vector Jump to step 1, and complete the above steps again to evaluate the interpolation accuracy of the tooth preparation trajectory. If the relative errors of the step lengths of the interpolation points except the 13th, 14th, 15th, and 16th interpolation points are all less than the upper limit, then jump to step 8a), set i=i+1 and jump to step 1 to evaluate the curvature fluctuation rate and step length error of subsequent interpolation points. Through the loop, it is calculated that the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory with 27 interpolation points and the relative error between the actual step length and the theoretical step length are less than the corresponding upper limit, then the interpolation accuracy evaluation of the j-th tooth preparation trajectory is output and ended.

Claims (1)

1. A method for evaluating the interpolation accuracy of tooth preparation trajectory based on curvature fluctuation rate and step error judgment, characterized in that: the specific implementation process of the method is: Step 1: Import tooth preparation trajectory data and calculate interpolation points of tooth preparation trajectory: The doctor's clinical tooth preparation model is scanned to obtain a standardized tooth preparation model. The tooth model is processed by reverse engineering software to obtain discrete points of the tooth preparation trajectory of the relevant teeth. The discrete points are inversely calculated by introducing NURBS curves to obtain a discrete point information set A = {R ₁ , R ₂ , R ₃ , ..., R _j , ..., R _m } of m tooth preparation trajectories, where R _j = {P ^j , ω ^j , U ^j } is the discrete point information set of the j-th tooth preparation trajectory, where the value range of j is 1≤j≤m. is the control point information set of the jth tooth preparation trajectory, where the value range of i is 1≤i≤n, is the control point position information set of the i-th discrete point of the j-th tooth preparation trajectory, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the control point of the i-th discrete point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system, is the weight factor information set of the control points of the j-th tooth preparation trajectory, is the weight factor of the ith control point of the jth tooth preparation trajectory, is the node vector information set of the discrete points of the j-th tooth preparation trajectory, is the node vector of the ith discrete point of the jth tooth preparation trajectory. The fourth-order Runge-Kutta method is used to calculate the node vector of the ith discrete point of the jth tooth preparation trajectory. Perform calculations and define Regulation in Calculated by high-order backward difference method, it is specified t is the interpolation cycle of tooth preparation trajectory; Define the tooth preparation trajectory expression, represented by Q _j (u), and define the j-th tooth preparation trajectory expression as is about the node vector By substituting the parameters P ^j , ω ^j , and U ^j in the j-th tooth preparation trajectory discrete point information set R _j = {P ^j , ω ^j , U ^j } into the tooth preparation trajectory expression Q _j (u), the n interpolation point information set of the j-th tooth preparation trajectory is obtained. is the position information of the i-th interpolation point of the j-th tooth preparation trajectory, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the x-axis in the three-dimensional coordinate system, is the value of the ith interpolation point of the jth tooth preparation trajectory on the y-axis in the three-dimensional coordinate system, is the value of the i-th interpolation point of the j-th tooth preparation trajectory on the z-axis in the three-dimensional coordinate system; Step 2: Setting the actual step length between interpolation points of tooth preparation trajectory: Define the actual step length between the interpolation points of the jth tooth preparation trajectory, using the symbol express, is a description of the actual step length of the j-th tooth preparation trajectory, by calculating the i-th interpolation point of the j-th tooth preparation trajectory and the i-1th interpolation point The actual step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is determined by the spatial distance between them. Step 3: Setting the arch height error and curvature fluctuation rate between adjacent interpolation points of tooth preparation trajectory: Define the arch height error between adjacent interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a quantitative description of the fluctuation degree of tooth preparation trajectory. The tooth preparation trajectory interpolation point is specified at At the i-th interpolation point of the j-th tooth preparation trajectory, the curvature radius Obtain an osculating circle, approximate the curve between adjacent interpolation points of the tooth preparation trajectory as an arc, and define the interpolation points after the approximate arc as The curvature radius of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is specified. Indicates the jth tooth preparation trajectory at the i-th node vector The first-order derivative at , Indicates the jth tooth preparation trajectory at the i-th node vector The second-order derivative at , specifies the maximum height error of the j-th tooth preparation trajectory as (h ^j ) _max ; Since the height error of the tooth preparation trajectory will change with the fluctuation of the curve curvature, the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory is defined, and the symbol is express, It is a quantitative description of the stability of tooth preparation trajectory. It is stipulated that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is expressed as The value range of i is 2≤i≤n. It represents the curvature deviation between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies represents the curvature of the curve between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory, and specifies The upper limit index of the curvature fluctuation rate between adjacent interpolation points of j tooth preparation trajectories is specified as Step 4: Evaluation of the curvature fluctuation rate of adjacent interpolation points of tooth preparation trajectory: according to The calculation formula is used to calculate the curvature fluctuation rate between adjacent interpolation points of the j-th tooth preparation trajectory, and the Is it established? Specifically: if If it is established, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory is within the allowable range, and jump to step 5; if If it is not true, it means that the curvature fluctuation rate between adjacent interpolation points of the jth actual tooth preparation trajectory exceeds the allowable range, and the output is that this tooth preparation trajectory is not suitable for this evaluation method, and the actual tooth preparation trajectory accuracy evaluation ends; Step 5: Setting the theoretical step length between interpolation points of tooth preparation trajectory: Define the theoretical step length between interpolation points of the jth tooth preparation trajectory, using the symbol express, It is a description of the theoretical step length of the j-th tooth preparation trajectory. It stipulates that the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as It represents the height error between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory. Determine the constraint step size, specify represents the maximum constraint step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory determined by the maximum arch height error (h ^j ) _max , and specifies Step 6. Setting and evaluating the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the tooth preparation trajectory: The relative error between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory is defined as ^rj (i), ^which is a quantitative description of the stability of the interpolation point step length of the tooth preparation trajectory. The relative error between the actual step length and the theoretical step length between the i-th interpolation point and the i-1-th interpolation point of the j-th tooth preparation trajectory is expressed as The maximum value of the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th adjacent interpolation point of the j-th tooth preparation trajectory is specified as r ^j (i) _max , and the interval (0, r _j (i) _max ) is the tolerance range of the relative error between the actual step length and the theoretical step length between adjacent interpolation points of the ^j -th tooth preparation trajectory; the relative error between the actual step length and the theoretical step length between the ith interpolation point and the i-1th interpolation point of the j-th tooth preparation trajectory is calculated according to the calculation formula of r j (i), and it is determined whether r ^j (i) ≤ r ^j (i) _max holds. Specifically: If r ^j (i) ≤ ^{r j} (i) _max holds true, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between adjacent interpolation points of the j-th tooth preparation trajectory falls within the allowable tolerance range, and the corresponding interpolation point is a valid tooth preparation trajectory interpolation point, and jump to step eight; If r ^j (i) ≤ ^{r j} (i) _max does not hold, it means that the relative error r ^j (i) between the actual step length and the theoretical step length between the adjacent interpolation points of the j-th tooth preparation trajectory exceeds the allowable constraint range, and the interpolation points of the actual tooth preparation trajectory need to be corrected accordingly, and jump to step seven; Step 7: Setting the correction parameters of the tooth preparation trajectory node vector: The correction parameters of the tooth preparation trajectory node vector are defined as Regulation It is expressed as the theoretical step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, It is represented as the actual step length of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and defines the node vector of the i-th interpolation point of the j-th tooth preparation trajectory after correction. Regulation represents the node vector of the i-1th interpolation point of the jth tooth preparation trajectory, It is represented as the node vector of the i-th interpolation point of the j-th tooth preparation trajectory that exceeds the allowed constraint range, and jumps to step 1; Step 8: Determine whether the interpolation accuracy of tooth preparation trajectory has been evaluated: a) Determine whether the number n of interpolation points of the i-th and j-th tooth preparation trajectories is equal, Specifically: If i=n is not true, it means that the interpolation accuracy evaluation has not been performed on all interpolation points on the j-th tooth preparation trajectory, then let i=i+1, and jump to step 1 to continue to evaluate the accuracy of the interpolation points on the tooth preparation trajectory; If i=n, it means that the interpolation accuracy evaluation of all interpolation points on the j-th tooth preparation trajectory is completed, the interpolation accuracy evaluation of the j-th tooth preparation trajectory is output, and the process jumps to step eight b); b) Determine whether j is equal to the number m of all tooth preparation trajectories, Specifically: If j=m is not true, it means that the interpolation accuracy evaluation has not been performed on all tooth preparation trajectories, then let j=j+1, and jump to step 1 to continue to evaluate the accuracy of the tooth preparation trajectory; If j=m, it means that the interpolation accuracy evaluation of all tooth preparation trajectories is completed, and the relative errors of the curvature fluctuation rate and step length between adjacent interpolation points of all tooth preparation trajectories are within the allowable range, then the loop is exited and the interpolation accuracy evaluation of all tooth preparation trajectories is completed.