Mixed parameterization method for B spline curve interpolation based on supervised learning

Abstract

The invention discloses a mixed parameterization method for B spline interpolation based on supervised learning, and the method comprises the steps: sequentially selecting four continuous local data points for a group of given ordered data points, and calculating the geometric distribution characteristics of the four continuous local data points; selecting a local optimal parameterization method for the four data points based on geometric distribution characteristics according to a trained classifier, and calculating local parameters by using the selected local optimal parameterization method; and solving the problem of interval distribution and fitting of adjacent parameters of the global parameters and the local parameters by using a least square method, and generating a final global parameter result. The global parameters generated by the method can better adapt to geometric distribution of different data points, and the classifier, the interpolation curve evaluation index and the local optimal parameterization method can be replaced as required, so that the method has good expansibility and compatibility.

Description

Technical Field

[0001] The invention relates to the field of computer-aided geometric design, and in particular to a hybrid parameterization method for B-spline curve interpolation based on supervised learning. Background Art

[0002] In the field of computer-aided geometric design, B-spline is widely used in curve and surface modeling due to its good properties such as intuitiveness, locality, smoothness, geometric invariance, etc. The interpolation of B-spline curve is one of the basic algorithms. Given a set of ordered data points, the parameters are first determined according to the distribution of the data points, and then the node vectors are calculated using the uniform method or the average method. Finally, the control points are inversely solved by solving a set of linear equations to obtain a B-spline interpolation curve passing through all the data points. In this process, the parameters have a great influence on the shape of the final interpolation curve.

[0003] At present, many parameterization methods have been proposed. The simplest one is the Uniform method, which is to select parameters uniformly. Lim et al. proposed a Universal method. They found that the larger the value on the diagonal of the interpolation matrix, the more natural and smooth the interpolation curve. Therefore, they first uniformly determined the node vectors, and then used the parameters corresponding to the maximum value of each B-spline basis function as the corresponding parameter results. This method is simple to calculate and the generated parameters have affine invariance, but like the Uniform method, this method does not consider the geometric distribution characteristics of the data points. Therefore, these two methods are more suitable for uniformly distributed data points. For unevenly distributed data points, these two methods are prone to produce poor interpolation curves.

[0004] Based on the estimation of arc length by chord length, the Chord method was proposed. It calculates parameters by the ratio of the length of each chord segment of the line connecting data points to the total chord length. The Chord method often produces better interpolation curve results than the Uniform method and the Universal method. However, due to the deviation of the chord length estimation of arc length, its interpolation curve may deviate from the data points at the corners. Foley et al. proposed an improved chord length method (abbreviated as Foley method). They used the Nielsen matrix to calculate the chord length, thereby ensuring the affine invariance of the chord length calculation, and adjusted the chord length calculation result by introducing the angle of adjacent line segments in the line connecting data points, thereby generating a more natural interpolation curve. Xu et al. constructed an interpolation arc based on the arc length and the angle of adjacent line segments, and then used the arc length instead of the chord length for parameterized calculation. Although Foley and Xu both improved the arc length estimation in different ways, their interpolation curves still produced large swings like the Chord method.

[0005] For a car that is turning, the centripetal force is proportional to the square of the angular velocity. Based on this observation, Lee et al. proposed the Centripetal method. They used a power function of the chord length to calculate the parameters, and the exponential term was usually set to 0.5. In most cases, the interpolation curve of the Centripetal method is better than the Uniform method and the Chord method, but because the exponential term takes a fixed value, the results may deteriorate for data points with large changes in chord length. Fang et al. proposed an improved Centripetal method (abbreviated as Fang method), in which they estimated a measured circle of the final curve at each data point, and then used the power function of the sum of the arc of the measured circle and the chord length to calculate the parameters. Since this method takes into account the angle information of adjacent line segments in the line connecting the data points, the interpolation curve results have smaller swings than the Centripetal method, but this method is not suitable for collinear data points. Belta et al. proposed a dynamic exponential Centripetal method, in which they dynamically adjusted the exponent according to the chord length so that the interpolation curve could better fit the data point distribution. However, the quality of the interpolation curve depends largely on the initial value setting of the exponent.

[0006] Zhang et al. proposed a parametric method with quadratic interpolation accuracy (abbreviated as ZCM method). According to the properties of quadratic polynomial curves, they proposed a quadratic interpolation method to calculate local parameters, and then calculated global parameters with quadratic accuracy by solving a least squares problem. However, this method focuses more on the accuracy of the interpolation curve and ignores the influence of the geometric distribution of data points on the interpolation curve.

[0007] In general, the Uniform method and the Universal method are more suitable for uniformly distributed data points. The Foley method and the Xu method are improved Chord methods. Although they take into account the chord length and the angle information of adjacent line segments, they may still have large swings like the chord length method. Fang's method has smaller swings for data points with sudden changes in distribution compared with the interpolation curves generated by other methods, but it is not suitable for collinear data points. The ZCM method pays more attention to the accuracy of the interpolation curve rather than the shape of the interpolation curve. Each method has its own advantages and disadvantages. In actual use, it is often necessary to select a suitable method according to the task. No method can be applied to all data point distribution situations. This leads to two questions: 1. How to select a suitable parameterization method based on the geometric distribution of data points; 2. Is there a parameterization method that can obtain parameterization results that fit the data point distribution under different data point distributions. Summary of the invention

[0008] In view of the shortcomings of the prior art, the present invention proposes a hybrid parameterization method for B-spline curve interpolation based on supervised learning, which first selects four consecutive data points in sequence for a given set of data points to calculate their geometric features, then uses a supervised classifier to select an optimal local parameterization method based on the features, and uses the parameterization method to calculate local parameters. Finally, the local parameters are combined using the least squares method to generate global parameters. The goal of the combination is to make the ratio of the interval between two adjacent parameters at each intermediate data point as consistent as possible globally and locally, so that the global parameters can better fit the data point distribution to obtain a high-quality interpolation curve.

[0009] The present invention is implemented by the following technical scheme: a hybrid parameterization method for B-spline curve interpolation based on supervised learning, comprising the following steps:

[0010] (1) For a set of two-dimensional ordered data points that need to be interpolated by B-spline, four consecutive data points are selected locally;

[0011] (2) Using the pre-trained classifier to select the optimal local parameterization method according to the geometric distribution characteristics of every four data points, and then using the selected parameterization method to calculate the local parameters;

[0012] (3) According to the correspondence between data points and local parameters, the proportional relationship between adjacent parameter intervals is calculated, and the local parameters are merged using the least squares method to generate the final global parameters.

[0013] Furthermore, the pre-trained classifier in step (2) is obtained by adjusting the classifier parameters by using the grid search method. The geometric features of each set of data points and their corresponding method labels together constitute the training data of the classifier. The XgBoost classifier is trained based on the training data generated previously. For a given set of data points Select four consecutive data points in sequence Use the trained XgBoost classifier to select an optimal parameterization method for each set of data points based on the geometric features mentioned above, and use this method to calculate the local parameters in For each data point A global parameter t needs to be calculated i Correspondingly, these global parameters are strictly monotonically increasing; the distance between two adjacent parameters is defined as x i =t i+1 -t i ,0≤i≤n-1,n≥3; the positional relationship between each intermediate parameter and its two adjacent parameters in the global parameters is defined as dg i =x i-1 / (x i-1 +xi ),1≤i≤n-1, similarly, the positional relationship between each intermediate parameter and its two adjacent parameters in the local parameters is defined as dl i ,1≤i≤n-1.

[0014] Furthermore, in step (2), the selection of the optimal parameterization method for the local four-point data using a pre-trained classifier is based on the representation of turtle geometry to randomly generate a training data set consisting of four two-dimensional ordered data points as a group; the pre-trained classifier randomly generates original data based on turtle geometry, each group of data has four two-dimensional data points, and based on the evaluation index of Fang below, an optimal parameterization method is selected from the three methods of Foley, Fang, and Universal for each group of data as the method label for each group of data, and then the geometric distribution characteristics and labels of the data points are combined as training data, and finally the classifier is trained using the XgBoost classifier.

[0015] Specifically, the turtle geometry-based representation randomly generates four two-dimensional ordered data points, and the generation method is as follows: the coordinates of the first data point of each group of data points are set to (a, b), the values ​​of a and b can be randomly selected, and an initial direction is randomly selected; the direction of the next line segment is obtained by rotating a certain angle according to the direction of the previous line segment, and the angle is randomly selected from [-5 / 6Pi, 5 / 6Pi], and the positive and negative angles correspond to clockwise and counterclockwise rotations respectively; the length of each line segment can be randomly selected within a given length range, and the range of the length is related to the distance between adjacent data points to be interpolated in actual use; for each group of data points, the present invention selects the first line segment from three factors: the data point coordinates, the chord length, and the angle between the lines connecting the adjacent data points. The geometric distribution of data points is analyzed from the perspective of feature analysis; to prevent the influence of different coordinates on the classifier, the coordinates of each group of data points are normalized to [0, 1]; the ratio of each chord length to the average chord length and the coefficient of variation of the three chord lengths are used to reflect the change and distribution of the chord length; the difference in the angles between adjacent line segments and the absolute value of the difference are used to reflect the inflection of the line connecting the data points; according to the evaluation indicators mentioned above, the optimal method is selected from the three methods of Foley, Fang and Universal as its method label for each group of data points; the geometric features of each group of data points and their corresponding method labels together constitute the training data of the classifier, where the input is the geometric features and the output is the method label.

[0016] Specifically, the geometric distribution features of the local four points are designed as follows: the coordinates of each group of data points are normalized to [0, 1]; the ratio of each chord length to the average chord length and the coefficient of variation of the three chord lengths are used to reflect the change and distribution of the chord lengths; the difference in the angles of adjacent line segments and the absolute value of the difference are used to reflect the inflection of the line connecting the data points.

[0017] Furthermore, the evaluation index based on Fang below selects an optimal parameterization method from the three methods of Foley, Fang, and Universal for each group of data as the method label of each group of data, specifically: the index for judging the quality of the interpolation curve can be used to judge the quality of the global or local interpolation curve; the parameterization result is proportional to the interpolation curve result; its expression is as follows:

[0018]

[0019] Where K i are two adjacent data points P i and P i+1 The maximum curvature on the curve segment, D i The height of the i-th segment is defined as follows:

[0020]

[0021] Where C(t) is the interpolation curve, L i YesP i and P i+1 The connection between.

[0022] Specifically, in step (3), the data points are divided into four situations according to the number of local parameters corresponding to each data point: situation (A) is 1 parameter, situation (B) is 2 parameters, situation (C) is 3 parameters, and situation (D) is 4 parameters; then the proportional relationship between the local adjacent parameter intervals is calculated respectively, and finally the least squares method is used to make the proportional relationship between the global adjacent parameter intervals and the proportional relationship between the local adjacent parameter intervals as consistent as possible, so as to obtain the global parameters.

[0023] Specifically, the data points in the situation (A) correspond to only one endpoint local parameter; the data points in the situation (B) correspond to one endpoint local parameter and one intermediate local parameter; the data points in the situation (C) correspond to one endpoint local parameter and two intermediate local parameters; the data points in the situation (D) correspond to two endpoint local parameters and two intermediate local parameters.

[0024] Compared with the existing methods, the beneficial effects of the present invention are as follows: by utilizing the technical content of the present invention, the interpolation curve generated by the present invention is more consistent with the data point distribution, has smaller swings and fewer cusps and self-intersections. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic diagram for explaining the overall process of the hybrid parameterization method for B-spline curve interpolation based on supervised learning of the present invention;

[0026] Figure 2 Schematic diagram of a method for generating training data based on turtle geometry representation in the present invention;

[0027] Figure 3 A schematic diagram of the index for judging the quality of the B-spline interpolation curve used in the present invention;

[0028] Figure 4 It is a schematic diagram of the corresponding relationship between data points and local parameters in the present invention;

[0029] Figure 5 A comparison chart of the results of the embodiment of the present invention and the existing method under a set of data points;

[0030] Figure 6 It is a comparison chart of the results of the embodiment of the present invention and the existing method under another set of data points. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described below in conjunction with embodiments and accompanying drawings.

[0032] Example

[0033] See also Figure 1 In this embodiment, the hybrid parameterization method for B-spline curve interpolation based on supervised learning includes the following steps:

[0034] First, a classifier is trained to select the local optimal parameterization method. The index used in the present invention to judge the quality of the interpolation curve is proposed by Fang's paper and is used to judge the quality of the global or local interpolation curve. The better the parameterization result, the better the interpolation curve result. Figure 2 As shown, its definition is as follows:

[0035]

[0036] Where K i are two adjacent data points P i and P i+1 The maximum curvature on the curve segment, D i The height of the i-th segment is defined as follows:

[0037]

[0038] Where C(t) is the interpolation curve, L i YesP i and P i+1 The connection between.

[0039] Since there is no public dataset, the present invention randomly generates a training dataset consisting of four two-dimensional ordered data points as a group based on the representation of turtle geometry, such as Figure 3As shown, the generation method is as follows: the coordinates of the first data point of each group of data points are set to (5,5) and an initial direction is randomly selected; the direction of the next line segment is obtained by rotating a certain angle based on the direction of the previous line segment, and the angle is randomly selected from [-5 / 6Pi, 5 / 6Pi], and the positive and negative angles correspond to clockwise and counterclockwise rotations respectively; the length of each line segment is randomly selected between [2,20]. For each group of data points, the present invention performs feature analysis of the geometric distribution of data points from three aspects: data point coordinates, chord length, and the angle between adjacent data points. In order to prevent the influence of different coordinates on the classifier, the coordinates of each group of data points are normalized to [0, 1]; the ratio of each chord length to the average chord length and the coefficient of variation of the three chord lengths are used to reflect the change and distribution of the chord length; the difference in the angle between adjacent line segments and the absolute value of the difference are used to reflect the inflection of the data point connection line. According to the above-mentioned evaluation index, for each group of data points, the best method is selected from the three methods of Foley, Fang and Universal (Foley is the method proposed by Foley et al. in the paper "Knot selection for parametricspline interpolation" in 1989; Fang is the method proposed by Jing-Jing Fang et al. in the paper "Animproved parameterization method for b-spline curve and surfaceinterpolation" in 2013; Universal is the method proposed by Lim et al. in the paper "A universalparametrization in b-spline curve and surface interpolation" in 1999) as its method label. The geometric features of each group of data points and their corresponding method labels together constitute the training data of the classifier, wherein the input is the geometric features and the output is the method label. XgBoost is used as the classifier in the present invention due to its advantages of high training accuracy and fast training speed. The classifier parameters are adjusted by using the grid search method, and the XgBoost classifier is trained based on the training data generated above.

[0040] For a given set of data points Select four consecutive data points in sequence Use the trained XgBoost classifier to select an optimal parameterization method for each set of data points based on the geometric features mentioned above, and use this method to calculate the local parameters in For each data point A global parameter t needs to be calculated iCorrespondingly, these global parameters are strictly monotonically increasing. The distance between two adjacent parameters is defined as x i =t i+1 -t i ,0≤i≤n-1,n≥3. The positional relationship between each intermediate parameter and its two adjacent parameters in the global parameters is defined as dg i =x i-1 / (x i-1 +x i ),1≤i≤n-1, similarly, the positional relationship between each intermediate parameter and its two adjacent parameters in the local parameters is defined as dl i ,1≤i≤n-1 to represent

[0041] The data points are divided into four types according to the number of local parameters corresponding to each data point: (A) 1, (B) 2, (C) 3, (D) 4, such as Figure 4 (a) is a diagram of a set of data points and their corresponding local parameters. The local parameters are represented by broken lines and are divided into four categories (A), (B), (C), and (D) according to the number of local parameters corresponding to each data point. Figure 4 (b) is a schematic diagram of the corresponding relationship between the local parameters of data points of types (A) and (B). Figure 4 (c) is a schematic diagram of the local parameters corresponding to the data points of type (C). Figure 4 (d) is a schematic diagram of the local parameter correspondence of data points of type (D). The data points in case (A) correspond to only one endpoint local parameter; the data points in case (B) correspond to one endpoint local parameter and one intermediate local parameter; the data points in case (C) correspond to one endpoint local parameter and two intermediate local parameters; the data points in case (D) correspond to two endpoint local parameters and two intermediate local parameters. For cases (B)(C)(D), the dl i The calculation is as follows: Figure 4 As shown in (b), for the data point (B1) in case (B), For data point (B2), like Figure 4 (c) and Figure 4 As shown in (d), for cases (C) and (D),

[0042] In order to make the global parameters better fit the distribution of data points, the global parameters should fit the distribution of local parameters as much as possible, and the distribution of adjacent parameters should be as consistent as possible globally and locally, which can be expressed as follows:

[0043] dg i =dl i ,1≤i≤n-1;

[0044] Since the number of unknowns n exceeds the number of equations (n-1), the system of equations has infinite solutions. To solve this problem, let x0 = 1, x1 = 1, the number of equations exceeds the number of unknowns, and the linear equations become overdetermined. Then use the least squares method to minimize F(x1, x2, ..., x n-2 ), which is defined as follows:

[0045]

[0046] get Finally, let t0 = 0, recursively find the global parameters, and normalize them to [0, 1] to get the final result.

[0047] Figure 5 and Figure 6 This is a graph showing the processing results of two groups of data with different data point distributions in this embodiment, where Figure 5 (a) is a data point and its connection line, and the remaining sub-graphs are comparison diagrams of the results of the present invention and the existing methods, where the solid line is the result of the present invention (abbreviated as Hybrid), and the dotted line is the result of the comparison method. The legend above the sub-graph presents the quantitative results of the evaluation indicators; Figure 5 The data points in the left area have relatively gentle fluctuations, and the lines connecting the data points in the middle and right areas have sharp corners and large changes in chord length. Figure 6 The lines connecting the data points in the figure intersect with each other, and the length of each chord changes dramatically, with a U-shaped distribution on the left and a Z-shaped distribution on the right. Figure 5 and Figure 6 Figure (a) shows the data points and their connections. Figure 5 and Figure 6The dotted lines in other sub-figures in are the results obtained by the comparison methods. The comparison methods in this embodiment include the Uniform method (proposed by De Boor et al. in the book "A practical guide to splines" in 1978), the Chord Length method (proposed by De Boor et al. in the book "A practical guide to splines" in 1978), the Centripetal method (proposed by Lee et al. in the paper "Choosing nodes in parametric curve interpolation" published in 1989), the method proposed by Universal, Foley, Fang, Xu et al. (Xu: proposed by Xu et al. in the paper "An improved parameterized interpolation method based on modified chord length" published in 2022), and the method proposed by Zhang Caiming et al. (ZCM: proposed by Zhang Caiming et al. in the paper "A method for determining knots in parametric The solid line is the result obtained by using the hybrid parameterization method (abbreviated as Hybrid) for B-spline curve interpolation based on supervised learning in this embodiment, and the legend in the upper right corner of each sub-figure contains the abbreviation of the comparison method name (Uniform, Chord Length, Centripetal, Universal, Foley, Fang, Xu, ZCM) and the abbreviation of the method in this embodiment (Hybrid), as well as the quantitative results of the evaluation indicators and the data point legend.

[0048] Those skilled in the art will readily appreciate other embodiments of the present application after considering the description and practicing the contents disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The description and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the claims.

[0049] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A hybrid parameterization method for B-spline curve interpolation based on supervised learning, characterized in that: The following steps are involved: (1) For a set of two-dimensional ordered data points that need to be interpolated by B-spline, four consecutive data points are selected locally; (2) Using the pre-trained classifier to select the optimal local parameterization method according to the geometric distribution characteristics of every four data points, and then using the selected parameterization method to calculate the local parameters; (3) According to the correspondence between data points and local parameters, the proportional relationship between adjacent parameter intervals is calculated, and the local parameters are merged using the least squares method to generate the final global parameters.

2. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 1, characterized in that: The pre-trained classifier in step (2) is obtained by adjusting the classifier parameters by using the grid search method. The geometric features of each group of data points and their corresponding method labels together constitute the training data of the classifier. The XgBoost classifier is trained based on the training data generated previously. For a given set of data points Select four consecutive data points in sequence Use the trained XgBoost classifier to select an optimal parameterization method for each set of data points based on the geometric features mentioned above, and use this method to calculate the local parameters in For each data point A global parameter t needs to be calculated i Correspondingly, these global parameters are strictly monotonically increasing; the distance between two adjacent parameters is defined as x i =t i+1 -t i ,0≤i≤n-1,n≥3; the positional relationship between each intermediate parameter and its two adjacent parameters in the global parameters is defined as dg i =x i-1 / (x i-1 +x i ),1≤i≤n-1, similarly, the positional relationship between each intermediate parameter and its two adjacent parameters in the local parameters is defined as dl i ,1≤i≤n-1.

3. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 1, characterized in that: In step (2), the optimal parameterization method for the local four-point data is selected using a pre-trained classifier, and a training data set consisting of four two-dimensional ordered data points is randomly generated based on the representation of turtle geometry; the pre-trained classifier randomly generates original data based on turtle geometry, and each group of data has four two-dimensional data points. Based on the evaluation index of Fang below, an optimal parameterization method is selected from the three methods of Foley, Fang, and Universal for each group of data as the method label for each group of data, and then the geometric distribution characteristics and labels of the data points are combined as training data, and finally the classifier is trained using the XgBoost classifier.

4. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 3, characterized in that: The turtle geometry-based representation randomly generates four two-dimensional ordered data points, and the generation method is as follows: the coordinates of the first data point of each group of data points are set to (a, b), the values ​​of a and b can be randomly selected, and an initial direction is randomly selected; the direction of the next line segment is obtained by rotating a certain angle according to the direction of the previous line segment, and the angle is randomly selected from [-5 / 6Pi, 5 / 6Pi], and the positive and negative angles correspond to clockwise and counterclockwise rotations respectively; the length of each line segment can be randomly selected within a given length range, and the length range is related to the distance between adjacent data points to be interpolated in actual use; for each group of data points, the present invention selects the interpolated value from three aspects: data point coordinates, chord length, and the angle between adjacent data points Perform feature analysis on the geometric distribution of data points; to prevent the influence of different coordinates on the classifier, the coordinates of each group of data points are normalized to [0, 1]; the ratio of each chord length to the average chord length and the coefficient of variation of the three chord lengths are used to reflect the change and distribution of the chord length; the difference in the angles between adjacent line segments and the absolute value of the difference are used to reflect the inflection of the line connecting the data points; according to the evaluation indicators mentioned above, select the best method from the three methods of Foley, Fang and Universal as its method label for each group of data points; the geometric features of each group of data points and their corresponding method labels together constitute the training data of the classifier, where the input is the geometric features and the output is the method label.

5. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 3, characterized in that: The geometric distribution feature design of the local four points is as follows: the coordinates of each group of data points are normalized to [0, 1]; the ratio of each chord length to the average chord length and the coefficient of variation of the three chord lengths are used to reflect the change and distribution of the chord length; the difference in the angles of adjacent line segments and the absolute value of the difference are used to reflect the inflection of the line connecting the data points.

6. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 3, characterized in that: The evaluation index based on Fang below selects an optimal parameterization method from the three methods of Foley, Fang and Universal for each group of data as the method label of each group of data. Specifically, the index for judging the quality of the interpolation curve can be used to judge the quality of the global or local interpolation curve; the parameterization result is proportional to the interpolation curve result; its expression is as follows: Where K i are two adjacent data points P i and P i+1 The maximum curvature on the curve segment, D i The height of the i-th segment is defined as follows: Where C(t) is the interpolation curve, L i YesP i and P i+1 The connection between.

7. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 1, characterized in that: In the step (3), the data points are divided into four situations according to the number of local parameters corresponding to each data point: situation (A) is 1 parameter, situation (B) is 2 parameters, situation (C) is 3 parameters, and situation (D) is 4 parameters; then the proportional relationship between the local adjacent parameter intervals is calculated respectively, and finally the least squares method is used to make the proportional relationship between the global adjacent parameter intervals and the proportional relationship between the local adjacent parameter intervals as consistent as possible, so as to obtain the global parameters.

8. The hybrid parameterization method for B-spline curve interpolation based on supervised learning according to claim 6, characterized in that: The data points in the situation (A) correspond to only one endpoint local parameter; the data points in the situation (B) correspond to one endpoint local parameter and one intermediate local parameter; the data points in the situation (C) correspond to one endpoint local parameter and two intermediate local parameters; the data points in the situation (D) correspond to two endpoint local parameters and two intermediate local parameters.

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