Three-dimensional point cloud data polynomial fitting method, system, device and storage medium

Abstract

The present invention belongs to the field of mathematics and computer image processing, and specifically provides a three-dimensional point cloud data polynomial fitting method, system, device and storage medium, wherein the polynomial fitting method first determines the range of the three-dimensional point cloud data to be fitted, and then uses the least squares method to obtain the polynomial of each fitting grid; the grid polynomial includes x Axis direction connection grid polynomial, y Axial direction connection grid polynomial and circumferential direction connection grid polynomial are used to realize each fitting grid x Axis direction, y Since the present invention takes into account both the least squares polynomial solution accuracy and the block fitting accuracy, and solves the continuity problem of block fitting, it can establish high-precision three-dimensional surface polynomials based on three-dimensional point cloud data, guiding related production research.

Description

Technical Field

[0001] The present invention belongs to the field of mathematics and computer image processing, and in particular relates to a three-dimensional point cloud data polynomial fitting method, system, device and storage medium. Background Art

[0002] In the fields of mathematics and computer image processing, 3D point cloud data fitting is a commonly used method for data analysis and image generation. Polynomial fitting of 3D point cloud data, as one of these methods, has broad application prospects.

[0003] First, polynomial fitting of 3D point cloud data involves finding a polynomial function to approximate the surface defined by a set of 3D point cloud data. This polynomial function can be a quadratic, cubic, or higher-order polynomial. By fitting discrete data points, a continuous surface model can be obtained, which can be used for data analysis, visualization, modeling, and other aspects.

[0004] Secondly, the algorithm for polynomial fitting of 3D point cloud data is based on the least squares method. This method calculates a fitting polynomial function with the minimum sum of squared errors to best fit the surface data points. During the fitting process, polynomial functions of different degrees can be selected and parameters adjusted appropriately to achieve a better fit.

[0005] Finally, in practical applications, polynomial fitting of 3D point cloud data is widely used in areas such as surface reconstruction, CAD / CAM manufacturing, and remote sensing data analysis. For example, in surface reconstruction, we can fit a surface based on point cloud data to restore the original object's shape. In CAD / CAM manufacturing, we can use polynomial fitting of 3D point cloud data to generate part models, facilitating subsequent processing and manufacturing. In remote sensing analysis, we can use 3D point cloud data fitting to extract ground shape for use in geographic information systems, among other applications.

[0006] In general, polynomial fitting of 3D point clouds is an important data analysis and image processing method with broad application value. However, existing techniques struggle to simultaneously ensure accuracy, speed, and continuity in 3D point cloud polynomial fitting, failing to meet the precision requirements of various fields, such as surface reconstruction, CAD / CAM manufacturing, and remote sensing data analysis. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a three-dimensional point cloud data polynomial fitting method, system, device and storage medium, aiming to establish a polynomial that can accurately reflect the characteristics of three-dimensional point cloud data.

[0008] To solve the above technical problems, the technical solution adopted by the present invention is: a polynomial fitting method for three-dimensional point cloud data, comprising the following steps:

[0009] Step 1: Determine the variables of the three-dimensional point cloud data: determine the independent variables and dependent variables of the three-dimensional point cloud data polynomial to be fitted respectively;

[0010] Step 2: Determine the range of the independent variable of the 3D point cloud data: Project the 3D point cloud data to be fitted onto the 2D plane formed by the independent variable, and connect the projection boundary points to obtain the range of the independent variable;

[0011] The fitting grid is started from the first grid close to the origin and moves towards x Axis direction and y Get every other grid in the axis direction;

[0012] described x The mesh is connected along the axis x Axis direction, the grid between the two fitted grids;

[0013] described y The mesh is connected along the axis y Axis direction, the grid between the two fitted grids;

[0014] The circumferentially connected grid is the grid of the four fitting grid centers;

[0015] Step 4: Determine the fitting range of the grid polynomial;

[0016] Step 5: Calculate the fitted grid polynomial: according to the fitting range of the fitted grid polynomial, use the least square method to solve each fitted grid polynomial;

[0017] Step 6: x Calculation of mesh polynomials in the axial direction: x The axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. x The weight is determined by the principle that the distance in the axial direction is inversely proportional to the distance between the two fitting grids. x The principle of inversely proportional distance in the axial direction: the greater the distance, the smaller the weight;

[0018] Step 7 y Calculation of mesh polynomials in the axial direction: y The axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. y The weight is determined by the principle that the distance in the axial direction is inversely proportional to the distance between the two fitting grids. y The principle of inversely proportional distance in the axial direction, the greater the distance, the smaller the weight;

[0019] Step 8. Calculation of circumferential mesh polynomial: The circumferential mesh polynomial is generated by dynamically weighting the four adjacent fitting mesh polynomials. The weights are calculated based on the distance from the four fitting meshes. x axis, y The weight is determined by the principle of inversely proportional to the distance in the axial direction, and the weight is determined by the distance of the four fitting grids. x axis, y The principle of inversely proportional distance in the axial direction is that the greater the distance, the smaller the weight.

[0020] In a preferred solution, the number of independent variables is 2 and the number of dependent variables is 1.

[0021] In the preferred solution, in step four, when the number of three-dimensional point cloud data falling into the fitting grid is less than the number of fitting polynomial variables, the fitting range needs to be extended based on the fitting grid; when the number of three-dimensional point cloud data falling into the fitting grid is greater than the number of fitting polynomial variables, the fitting grid range is directly selected as the fitting range.

[0022] In a preferred solution, in step 5, the least squares method is used to solve the calculation expression of each fitting grid polynomial as follows:

[0023] ;

[0024] in, The coordinates are ( m , n )’s fitting grid polynomial corresponding to the fitting grid; B is the basis function vector; C is the coefficient vector; m for x Axis direction index; n for y Axis direction index.

[0025] In the preferred embodiment, in step six, x The calculation formula of the axial connection grid polynomial is:

[0026] ;

[0027] Split the above formula and combine similar terms to get:

[0028] ;

[0029] Substituting the corresponding fitting grid polynomial into the above formula, we can obtain x The mesh polynomial in the axial direction is:

[0030] ;

[0031] in, The coordinates are ( m , n )of x Axis direction connection grid polynomial; x is the horizontal axis value; For coordinates The fitting grid polynomial corresponding to the fitting grid of ;

[0032] In the preferred embodiment, in step seven, y The calculation formula of the axial connection grid polynomial is:

[0033] ;

[0034] Split the above formula and combine similar terms to get:

[0035]

[0036] Substitute the corresponding fitting grid polynomial into the above formula to obtain y The mesh polynomial in the axial direction is:

[0037]

[0038] in, for y The mesh polynomial in the axial direction; y is the vertical coordinate value; The coordinates are The fitting mesh polynomial corresponding to the fitting mesh of .

[0039] In a preferred solution, in step eight, the calculation formula of the circumferential connection grid polynomial is:

[0040] ;

[0041] Split the above formula and combine similar terms to get:

[0042] ;

[0043] Will y Substitute the axial direction fitting grid polynomial into the above formula to obtain:

[0044] ;

[0045] Substituting the fitted grid polynomial into the above formula, the circumferential connection grid polynomial is obtained as follows:

[0046] ;

[0047] in, is the circumferential mesh polynomial.

[0048] The present invention also provides a three-dimensional point cloud data polynomial fitting system, comprising:

[0049] 3D point cloud data variable determination module: used to respectively determine the independent variables and dependent variables of the 3D point cloud data polynomial to be fitted;

[0050] Independent variable range determination module: used to project the three-dimensional point cloud data to be fitted onto the two-dimensional plane formed by the independent variable, and connect the projection boundary points to obtain the independent variable range;

[0051] Data grid division module: used to divide the two-dimensional plane formed by the independent variable into grids according to the range and polynomial fitting accuracy, and obtain the fitting grid, x Axis direction connection grid, y Axial connection grid and circumferential connection grid;

[0052] Grid polynomial fitting range determination module: used for determining the grid polynomial fitting range;

[0053] Polynomial calculation module: used to fit grid polynomials, x Axis direction connection grid polynomial, y Calculation of axial mesh polynomials and circumferential mesh polynomials.

[0054] The present invention also provides a three-dimensional point cloud data polynomial fitting device, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the above-mentioned three-dimensional point cloud data polynomial fitting method when executing the computer program.

[0055] The present invention also provides a storage medium capable of storing a three-dimensional point cloud data polynomial fitting program, which can implement the above-mentioned three-dimensional point cloud data polynomial fitting method when the program is read and executed by a computer.

[0056] The present invention provides a three-dimensional point cloud data polynomial fitting method, system, device and storage medium, which have the following beneficial effects:

[0057] 1. In step 3 of the present invention, when dividing the grid, the number of data points falling within each fitting grid is taken into account. This fully utilizes every data point in the three-dimensional point cloud, maximizes the fitting accuracy of each fitting grid, and ensures that the local characteristics of the three-dimensional point cloud polynomial are reflected by block fitting of the three-dimensional point cloud data.

[0058] 2. In step 4 of the present invention, when determining the fitting range, the situation where the data points within the fitting grid are used for fitting anomalies is taken into consideration, and the data points around the fitting grid play an important supporting role in fitting the polynomial.

[0059] 3. In step 5 of the present invention, the least square method is used when fitting each fitting grid, thereby ensuring the fitting accuracy of each fitting polynomial from a mathematical principle.

[0060] 4. Steps 6, 7, and 8 of the present invention use the inverse distance weighted method to perform weighted summation on the fitting polynomials of each part, thereby ensuring the overall continuity of the three-dimensional point cloud data polynomial and playing the role of smoothly connecting the fitting surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The present invention will be further described below with reference to the accompanying drawings and examples:

[0062] Figure 1 is a flow chart of a polynomial fitting method for three-dimensional point cloud data provided by an embodiment of the present invention;

[0063] Figure 2 is the independent variable range of the three-dimensional point cloud data provided by the embodiment of the present invention;

[0064] Figure 3 Schematic diagram of grid division in the polynomial fitting method for three-dimensional point cloud data provided by an embodiment of the present invention;

[0065] Figure 4 This is a graph of polynomial fitting results of three-dimensional point cloud data provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0067] Combine Figures 1 to 4 The specific embodiments of the present invention are described in further detail.

[0068] like Figure 1 As shown, a polynomial fitting method for three-dimensional point cloud data includes the following steps:

[0069] Step 1: Determine the variables of the three-dimensional point cloud data: Determine the independent variables and dependent variables of the three-dimensional point cloud data polynomial to be fitted, with two independent variables and one dependent variable.

[0070] Step 2: Determine the range of the independent variable of the 3D point cloud data: Project the 3D point cloud data to be fitted onto the 2D plane formed by the independent variable, and connect the projection boundary points to obtain the range of the independent variable;

[0071] Step 3: Grid division of 3D point cloud data: Divide the 2D plane formed by the independent variable into grids according to the range and polynomial fitting accuracy to obtain the fitting grid, xAxis direction connection grid, y Axial connection grid and circumferential connection grid;

[0072] The fitting grid is started from the first grid close to the origin and moves towards x Axis direction and y The data is obtained at every grid in the axial direction. When the required polynomial fitting accuracy is relatively high, the fitting grid can be divided as densely as possible, and it is ensured that the data points falling within each fitting grid meet the data volume requirements of the least squares fitting. That is, when the fitting polynomial has n variables, n+1 data points are usually required for fitting.

[0073] described x The mesh is connected along the axis x Axis direction, the grid between the two fitted grids;

[0074] described y The mesh is connected along the axis y Axis direction, the grid between the two fitted grids;

[0075] The circumferentially connected grid is the grid of the four fitting grid centers;

[0076] Step 4. Determine the fitting range of the grid polynomial: By default, the fitting range of the grid polynomial is the fitting grid range. However, when abnormal fitting results occur when using data points within the fitting grid, extend the boundary of the fitting grid outward until the fitting effect meets the requirements.

[0077] Step 4. Determine the fitting range of the fitting grid polynomial: When the number of 3D point cloud data falling into the fitting grid is less than the number of fitting polynomial variables, the fitting range needs to be extended based on the fitting grid to meet the data volume requirements of the least squares fitting; when the number of 3D point cloud data falling into the fitting grid is greater than the number of fitting polynomial variables, directly select the fitting grid range as the fitting range.

[0078] Step 5: Calculate the fitted grid polynomial: according to the fitting range of the fitted grid polynomial, use the least square method to solve each fitted grid polynomial;

[0079] Step 6: x Calculation of mesh polynomials in the axial direction: x The axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. x It is determined based on the principle that the distance in the axial direction is inversely proportional to the distance;

[0080] Step 7 y Calculation of mesh polynomials in the axial direction: yThe axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. y It is determined based on the principle that the distance in the axial direction is inversely proportional to the distance;

[0081] Step 8. Calculation of circumferential mesh polynomial: The circumferential mesh polynomial is generated by dynamically weighting the four adjacent fitting mesh polynomials. The weights are calculated based on the distance from the four fitting meshes. x axis, y It is determined based on the principle that the distance in the axial direction is inversely proportional.

[0082] Example:

[0083] This embodiment solves the problem of polynomial fitting of turbine flow characteristics. The specific operation steps are as follows:

[0084] (1) Determination of 3D point cloud data variables

[0085] In the polynomial fitting problem of turbine flow characteristics, the independent variable is the unit speed and guide vane opening y , the dependent variable is unit flow .

[0086] (2) Determination of the range of independent variables of 3D point cloud data

[0087] Project the three-dimensional point cloud data of the turbine flow characteristic onto the two-dimensional plane formed by the unit speed and the guide vane opening, as shown in the following example: Figure 2 As shown, the independent variable The range of is [63.9,83.1], the independent variable y The range is [9.95,42.04].

[0088] (3) 3D point cloud data grid division

[0089] like Figure 3 As shown, the independent variable The interval is divided into 3 equal parts, with coordinates of [63.9, 70.3, 76.7, 83.1], and the independent variable y The interval is divided into 7 equal parts, with coordinates of [9.95, 14.5, 19, 23.5, 28.5, 33, 37.5, 42.04], and the independent variable and y The coordinates of the two-dimensional plane are divided into 21 parts, and the grid coordinates are ( m , n ), , . m and n When both are odd numbers, the grid is a fitted grid. m is an even number, nThe grid when is an odd number is x Axis direction connection grid. m is an odd number, n The grid when is an even number is y Axis direction connection grid. m and n When the numbers are even, the grids are connected circumferentially.

[0090] (4) Determination of the fitting range of the fitting grid polynomial

[0091] Since the number of 3D point cloud data that falls into each fitting grid is small, select The fitting range is , y The fitting range is .

[0092] (5) Fitting grid polynomial calculation

[0093] Select basis functions according to the fitting grid polynomial fitting range , the fitting grid polynomial coefficient matrix A1 is calculated using the least squares method as shown in Table 1.

[0094] Table 1 Fitting grid polynomial coefficient matrix A1

[0095]

[0096] (6) x Axial mesh polynomial calculation

[0097] According to the fitted grid polynomial, the inverse distance weighted method can be used to calculate x The coefficient matrices of the axial connection grid polynomials are divided into A2 and A3, as shown in Tables 2 and 3.

[0098] Table 2 x Coefficient matrix A2 of the axial mesh polynomial

[0099] A2 A2{1,:} A2{:,1} [2527.32;-62.59;27.01;0.16;0.38;-0.07] A2{:,2} [3300.65;-75.68;4.12;1.07;0.33;-1.16] A2{:,3} [964.51;-6.95;0.32;0.82;-0.14;-0.56] A2{:,4} [-2419.60;33.26;106.79;-1.36;0.13;0.12]

[0100] Table 3 x Coefficient matrix A3 of the axial mesh polynomial

[0101] A3 A3{1,:} A3{:,1} [-29.31;0.70;0.42;-0.01;0;0.01] A3{:,2} [-38.02;0.84;0.63;-0.01;0;0.010] A3{:,3} [-4.37;-0.11;0.56;-0.01;0;0] A3{:,4} [25.20;-0.44;-0.42;0.02;0;-0.01]

[0102] (7) y Axial mesh polynomial calculation

[0103] According to the fitted grid polynomial, the inverse distance weighted method can be used to calculate y The coefficient matrices of the axial connection grid polynomials are divided into A4 and A5, as shown in Tables 4 and 5.

[0104] Table 4 y Coefficient matrix A4 of the axial mesh polynomial

[0105] A4 A4{1,:} A4{2,:} A4{:,1} [717.89;-16.72;31.70;1.21;-0.03;-2.61] [1137.98;-25.10;23.34;1.44;-0.01;-2.78] A4{:,2} [1895.79;-40.02;-2.95;1.67;0;-1.79] [810.20;-7.60;-4.31;1.49;-0.21;-1.43] A4{:,3} [-8487.85;107.27;300.84;-0.99;-0.52;-2.85] [-10006.27;125.15;348.36;-2.33;-0.30;-2.20]

[0106] Table 5 y Coefficient matrix A5 of the axial mesh polynomial

[0107] A5 A5{1,:} A5{2,:} A5{:,1} [-22.94;0.39;1.42;-0.09;0.01;0.15] [-35.10;0.60;1.72;-0.10;0.01;0.16] A5{:,2} [-53.43;1.03;1.96;-0.06;0;0.05] [-6.45;-0.31;1.86;-0.05;0.01;0.03] A5{:,3} [243.41;-3.28;-6.87;0.03;0.01;0.06] [284.70;-3.74;-8.24;0.07;0.01;0.04]

[0108] (8) Calculation of circumferential mesh polynomials

[0109] according to x The axial direction connection grid polynomial, according to the inverse distance weighted method, the coefficient matrices of the circumferential connection grid polynomial are A6, A7, A8 and A9, as shown in Tables 6 to 9. The fitting results of the three-dimensional point cloud data are as follows: Figure 4 .

[0110] Table 6 Coefficient matrix A6 of circumferential mesh polynomial

[0111] A6 A6{1,:} A6{:,1} [5752.45;-117.19;-68.44;3.96;0.18;-4.61] A6{:,2} [-11114.37;348.43;-19.34;-0.47;-2.58;2.57] A6{:,3} [-26685.23;321.53;870.28;-17.02;2.09;4.94]

[0112] Table 7 Coefficient matrix A7 of circumferential mesh polynomial

[0113] A7 A7{1,:} A7{:,1} [-65.64;1.31;1.31;-0.04;0;0.03] A7{:,2} [169.62;-5.06;0.21;0.03;0.03;-0.06] A7{:,3} [237.25;-2.79;-7.42;0.21;-0.03;-0.10]

[0114] Table 8 Coefficient matrix A8 of circumferential mesh polynomial

[0115] A8 A8{1,:} A8{:,1} [-168.69;2.86;4.99;-0.20;0.01;0.24] A8{:,2} [509.60;-14.99;0.83;0.05;0.10;-0.13] A8{:,3} [738.20;-8.77;-23.23;0.48;-0.06;-0.15]

[0116] Table 9 Coefficient matrix A9 of circumferential mesh polynomial

[0117] A9 A9{1,:} A9{:,1} [1.90;-0.03;-0.05;0;0;0] A9{:,2} [-7.34;0.21;0.01;0;0;0] A9{:,3} [-6.45;0.07;0.21;-0.01;0;0]

[0118] The embodiment of the present invention provides a three-dimensional point cloud data polynomial fitting system, comprising: a three-dimensional point cloud data variable determination module, a three-dimensional point cloud data independent variable range determination module, a three-dimensional point cloud data grid division module, a fitting grid polynomial fitting range determination module, a fitting grid polynomial calculation module, x Axis direction connection grid polynomial calculation module, y Axial direction connection grid polynomial calculation module, circumferential direction connection grid polynomial calculation module.

[0119] 3D point cloud data variable determination module: used to respectively determine the independent variables and dependent variables of the 3D point cloud data polynomial to be fitted, where there are 2 independent variables and 1 dependent variable.

[0120] Independent variable range determination module: used to project the three-dimensional point cloud data to be fitted onto the two-dimensional plane formed by the independent variable, and connect the projection boundary points to obtain the independent variable range.

[0121] Data grid division module: used to divide the two-dimensional plane formed by the independent variable into grids according to the range and polynomial fitting accuracy, and obtain the fitting grid, x Axis direction connection grid, y Axial connection grid and circumferential connection grid.

[0122] Fitting grid polynomial fitting range determination module: When the 3D point cloud data falls into the fitting grid less, the fitting range needs to be expanded outside the fitting grid to ensure sufficient fitting data; when the 3D point cloud data falls into the fitting grid more, the fitting grid range can be directly selected as the fitting range.

[0123] Polynomial calculation module: used to fit grid polynomials, x Axis direction connection grid polynomial, y Calculation of axial mesh polynomials and circumferential mesh polynomials.

[0124] The present invention also provides a three-dimensional point cloud data polynomial fitting device, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the above-mentioned three-dimensional point cloud data polynomial fitting method when executing the computer program.

[0125] The present invention also provides a storage medium capable of storing a three-dimensional point cloud data polynomial fitting program, which can implement the above-mentioned three-dimensional point cloud data polynomial fitting method when the program is read and executed by a computer.

[0126] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A three-dimensional point cloud data polynomial fitting method for polynomial fitting of turbine flow characteristics, characterized in that: The following steps are involved: Step 1: Determine the variables of the 3D point cloud data: Determine the independent variables and dependent variables of the 3D point cloud data polynomial to be fitted. In the polynomial fitting problem of the turbine flow characteristic, the independent variable is the unit speed. and guide vane opening y , the dependent variable is unit flow ; Step 2: Determine the range of the independent variable of the 3D point cloud data: Project the 3D point cloud data to be fitted onto the 2D plane formed by the independent variable, and connect the projection boundary points to obtain the range of the independent variable; Step 3: Grid division of 3D point cloud data: Grid the 2D plane formed by the independent variables to obtain the fitted grid, x Axis direction connection grid, y Axial connection grid and circumferential connection grid; The fitting grid is started from the first grid close to the origin and moves towards x Axis direction and y Get every other grid in the axis direction; described x The mesh is connected along the axis x Axis direction, the grid between the two fitted grids; described y The mesh is connected along the axis y Axis direction, the grid between the two fitted grids; The circumferentially connected grid is the grid of the four fitting grid centers; Step 4: Determine the fitting range of the grid polynomial; Step 5: Calculate the fitted grid polynomial: according to the fitting range of the fitted grid polynomial, use the least square method to solve each fitted grid polynomial; Step 6: x Calculation of mesh polynomials in the axial direction: x The axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. x It is determined based on the principle that the distance in the axial direction is inversely proportional to the distance; Step 7 y Calculation of mesh polynomials in the axial direction: y The axial direction connection grid polynomial is generated by the dynamic weighting of two adjacent fitting grid polynomials, and the weight is based on the distance between the two fitting grids. y It is determined based on the principle that the distance in the axial direction is inversely proportional to the distance; Step 8. Calculation of circumferential mesh polynomial: The circumferential mesh polynomial is generated by dynamically weighting the four adjacent fitting mesh polynomials. The weights are calculated based on the distance from the four fitting meshes. x axis, y It is determined based on the principle that the distance in the axial direction is inversely proportional.

2. A polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: The number of independent variables is 2, and the number of dependent variables is 1.

3. The polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: In step 4, when the number of three-dimensional point cloud data falling into the fitting grid is less than the number of fitting polynomial variables, the fitting range needs to be extended based on the fitting grid; when the number of three-dimensional point cloud data falling into the fitting grid is greater than the number of fitting polynomial variables, the fitting grid range is directly selected as the fitting range.

4. The polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: In step 5, the least squares method is used to solve the calculation expression of each fitting grid polynomial: ； in, The coordinates are ( m , n )’s fitting grid polynomial corresponding to the fitting grid; B is the basis function vector; C is the coefficient vector; m for x Axis direction index; n for y Axis direction index.

5. The polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: In the step six, x The calculation formula of the axial connection grid polynomial is: ； Split the above formula and combine similar terms to get: ； Substituting the corresponding fitting grid polynomial into the above formula, we can obtain x The mesh polynomial in the axial direction is: ； in, The coordinates are ( m , n )of x Axis direction connection grid polynomial; x is the horizontal axis variable; and Respectively indicate the numbers and The grid horizontal coordinate of For coordinates The fitting mesh polynomial corresponding to the fitting mesh of .

6. The polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: In the step seven, y The calculation formula of the axial connection grid polynomial is: ； Split the above formula and combine similar terms to get: Substitute the corresponding fitting grid polynomial into the above formula to obtain y The mesh polynomial in the axial direction is: in, for y The mesh polynomial in the axial direction; y is the vertical axis variable; and Respectively indicate the numbers and The grid vertical coordinate of The coordinates are The fitting mesh polynomial corresponding to the fitting mesh of .

7. The polynomial fitting method for three-dimensional point cloud data according to claim 1, characterized in that: In step eight, the calculation formula of the circumferential connection grid polynomial is: ； Split the above formula and combine similar terms to get: ； Will y Substitute the axial direction fitting grid polynomial into the above formula to obtain: ； Substituting the fitted grid polynomial into the above formula, the circumferential connection grid polynomial is obtained as follows: ； in, is the circumferential mesh polynomial.

8. A three-dimensional point cloud data polynomial fitting system, used to execute the three-dimensional point cloud data polynomial fitting method according to any one of claims 1 to 7, characterized in that: include: 3D point cloud data variable determination module: used to respectively determine the independent variables and dependent variables of the 3D point cloud data polynomial to be fitted; Independent variable range determination module: used to project the three-dimensional point cloud data to be fitted onto the two-dimensional plane formed by the independent variable, and connect the projection boundary points to obtain the independent variable range; Data grid division module: used to divide the two-dimensional plane formed by the independent variable into grids according to the range and polynomial fitting accuracy, and obtain the fitting grid, x Axis direction connection grid, y Axial connection grid and circumferential connection grid; Grid polynomial fitting range determination module: used for determining the grid polynomial fitting range; Polynomial calculation module: used to fit grid polynomials, x Axis direction connection grid polynomial, y Calculation of axial mesh polynomials and circumferential mesh polynomials.

9. A polynomial fitting device for three-dimensional point cloud data, characterized in that: It comprises a memory and a processor; the memory is used to store a computer program; the processor is used to implement the three-dimensional point cloud data polynomial fitting method according to any one of claims 1 to 7 when executing the computer program.

10. A storage medium, characterized in that: The storage medium can store a three-dimensional point cloud data polynomial fitting program, and when the program is read and executed by a computer, the three-dimensional point cloud data polynomial fitting method according to any one of claims 1 to 7 can be implemented.

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