Wall thickness detection device and method based on dual-ray system

Abstract

The invention relates to the technical field of industrial nondestructive testing, in particular to a wall thickness detection device and method based on a dual-ray system, and the method comprises the steps: synchronously shooting vertical and horizontal projection images of a pipe through a dual-ray source; extracting first line gray data of the bidirectional projection image, and capturing an edge position through an automatic threshold method; grabbing inflection points of the inner wall and the outer wall of the pipe according to the edge position, and totally obtaining eight inflection points; calculating inner and outer diameters of the pipe by using a mathematical model based on the inflection point position Calculating the wall thickness, the ovality, the eccentricity value and the concentricity according to the inner diameter and the outer diameter; according to the invention, full detection in the pipe production process is realized, the detection efficiency is high, the influence of slight shaking of the pipe can be resisted, the detection result is accurate, and the device is suitable for detecting the wall thickness and related quality indexes of linear materials such as PVC pipes and cables.

Description

Technical Field

[0001] This invention relates to the field of industrial nondestructive testing technology, and in particular to a wall thickness detection device and method based on a dual-ray system. Background Technology

[0002] With the development of science and technology and the improvement of people's living standards, the demand for PVC pipes and cables is increasing. These products are usually manufactured using extrusion molding, but during the manufacturing process, due to factors such as uneven flow of raw materials and uneven control of equipment temperature and pressure, the wall thickness on one side may be too thin or too thick. If the manufacturing parameters are not corrected in time, it will cause serious quality problems.

[0003] X-ray flaw detection is a method that uses a light tube to emit X-rays that penetrate objects. A detector is responsible for receiving the penetrated rays and transferring them into digital images through electrons.

[0004] However, PVC pipes or cables have a cross-section that is approximately circular. If they are tested by unidirectional X-ray irradiation, the complete wall thickness information cannot be obtained because the cross-section of the pipe is approximately circular, which can easily lead to measurement errors. Summary of the Invention

[0005] The purpose of this invention is to provide a wall thickness detection device and method based on a dual-ray system, which solves the problems of low pipe detection efficiency and incomplete unidirectional detection information in the prior art.

[0006] To achieve the above objectives, the present invention provides a wall thickness detection device based on a dual-ray system, comprising a horizontal X-ray source, a vertical X-ray source, a horizontal detector, a vertical detector, and a data processing unit; The horizontal X-ray source is used to emit X-rays along the radial horizontal direction of the pipe to be inspected; The vertical X-ray source is used to emit X-rays in the radial vertical direction along the pipe to be inspected, and is perpendicular to the X-rays emitted by the horizontal X-ray source, intersecting at the pipe inspection area. The horizontal detector is located on the opposite side of the horizontal X-ray source and is used to receive horizontal X-rays after penetrating the pipe to be inspected and convert the optical signal into a digital image signal. The vertical detector is located on the opposite side of the vertical X-ray source and is used to receive vertical X-rays after penetrating the pipe to be inspected and convert the optical signal into a digital image signal. The data processing unit is electrically connected to the horizontal detector and the vertical detector, respectively, and is used to receive digital image signals and perform image processing, edge extraction and index calculation.

[0007] On the other hand, the present invention also includes a wall thickness detection method based on a dual-ray system, comprising the following: step: The vertical and horizontal projection images of the pipe are captured simultaneously using dual X-ray sources. Extract the first row of grayscale data from the bidirectional projection images and capture the edge positions using an automatic thresholding method; The inflection points of the inner and outer walls of the pipe were captured based on the edge location, and a total of 8 inflection points were obtained; The inner and outer diameters of the pipe are calculated using a mathematical model based on the inflection point location. Calculate the wall thickness, ellipticity, eccentricity, and concentricity based on the inner and outer diameters.

[0008] In the section on "Simultaneous capture of vertical and horizontal projection images of the pipe using dual X-ray sources": The pipe moves at a constant speed along the axial direction through the intersection area of ​​the two rays, and the two detectors synchronously acquire images at a frequency of ≥25 frames / second.

[0009] Specifically, in the step of "extracting the first row of grayscale data from the bidirectional projection images and capturing edge positions using an automatic thresholding method," the automatic thresholding method includes: Calculate the slope distribution of the first row of grayscale data; Edge boundaries are determined by identifying local extreme points of the slope.

[0010] In the section "Based on the edge position, capture the inflection points of the inner and outer walls of the pipe, and obtain a total of 8 inflection points": Capture two outer wall inflection points and two inner wall inflection points from the horizontal image; The vertical image captures two outer wall inflection points and two inner wall inflection points.

[0011] In the section "Calculating the inner and outer diameters of pipes using a mathematical model based on inflection point locations," the wall thickness calculation specifically includes: A unified coordinate system is established with the intersection point O of the virtual centerlines of the two radiation sources as the origin; Based on the detector's pixel size, the inflection point pixel coordinates are converted into physical coordinates; The position of the center of the circle can be deduced by the geometric relationship between the tangent of the ray source and the inflection point of the image in the same direction. Calculate the inner and outer diameters based on the center position.

[0012] In the section "Inferring the center position of the circle from the geometric relationship between the tangent of the ray source and the inflection point of the image in the same direction": A horizontal X-ray source connects to the outer wall inflection point of a horizontal image to form two outer wall tangents, and connects to its inner wall inflection point to form two inner wall tangents. A vertical ray source is connected to the inflection point of the outer wall of the vertical image to form two outer wall tangents, and connected to the inflection point of the inner wall to form two inner wall tangents; The coordinates of the outer wall center are determined by the unique intersection of the angle bisector of the angle between the two outer wall tangents of the same horizontal ray source and the angle bisector of the angle between the two outer wall tangents of the same vertical ray source in a unified coordinate system. The coordinates of the inner wall center are determined by the unique intersection of the angle bisector of the angle between the two inner wall tangents from the same horizontal ray source and the angle bisector of the angle between the two inner wall tangents from the same vertical ray source in a unified coordinate system.

[0013] This invention discloses a wall thickness detection device and method based on a dual-ray system. It simultaneously images the pipe using both vertical and horizontal ray systems. After acquiring the images, the positions of the inner and outer walls of the pipe within the images are located. The image pixel length is converted into the actual length, and coordinate systems for the ray source and detector in different directions are constructed. These two coordinate systems are then transformed to a coordinate system with the intersection of the two virtual centerlines as the origin. In actual detection, the distance between the ray source and detector in both directions is fixed (focal length is fixed); only the distance between the object and detector changes (object distance changes). This is reflected in the X-ray image as the object boundary always shifting left and right. However, since the X-ray system performs real-time imaging, the offset can be calculated in real-time. Finally, the radius of the inner and outer walls of the pipe is calculated through geometric positional relationships, and information such as wall thickness, ellipticity, eccentricity, and concentricity can also be obtained. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0015] Figure 1 This is a schematic diagram of the installation positions of the horizontal X-ray source and the vertical X-ray source of the present invention.

[0016] Figure 2 This is a schematic diagram of the dual-ray source irradiating radially along the pipeline and acquiring images according to the present invention.

[0017] Figure 3 This is a schematic diagram of a pipe image captured by the horizontal detector of the present invention.

[0018] Figure 4 This is a grayscale curve of the first row of grayscale data in the image according to the present invention.

[0019] Figure 5 This is a schematic diagram of the grayscale data slope (k) of the present invention.

[0020] Figure 6 This is a schematic diagram of the coordinate system of the present invention, with pixel x as the horizontal coordinate and slope k as the vertical coordinate.

[0021] Figure 7 This is a schematic diagram of the present invention, which locates the inflection points of the inner and outer walls by using the local extreme points of the slope.

[0022] Figure 8 This is a schematic diagram of the planar coordinate system and related geometric relationships of the dual-ray system of the present invention.

[0023] Figure 9 This is a schematic diagram of the pipe wall thickness measurement results (wall thickness values ​​at different angles) of the present invention.

[0024] Figure 10 This is a flowchart of the wall thickness detection method based on a dual-ray system according to the present invention.

[0025] Figure 11 This is a schematic diagram of the wall thickness detection device based on a dual-ray system according to the present invention.

[0026] In the diagram: 101-Horizontal X-ray source, 102-Vertical X-ray source, 103-Horizontal detector, 104-Vertical detector, 105-Data processing unit. Detailed Implementation

[0027] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0028] Please see Figure 1 and Figure 11 ,in Figure 1 This is a schematic diagram showing the installation positions of the horizontal and vertical X-ray sources. Figure 11 This is a schematic diagram of a wall thickness detection device based on a dual-ray system.

[0029] The present invention provides a wall thickness detection device based on a dual-ray system, including a horizontal X-ray source 101, a vertical X-ray source 102, a horizontal detector 103, a vertical detector 104, and a data processing unit 105; The horizontal X-ray source 101 is used to emit X-rays along the radial horizontal direction of the pipe to be inspected; The vertical X-ray source 102 is used to emit X-rays in the radial vertical direction along the pipe to be inspected, and is perpendicular to the X-rays emitted by the horizontal X-ray source 101, intersecting at the pipe inspection area. The horizontal detector 103 is located on the opposite side of the horizontal X-ray source 101, and is used to receive horizontal X-rays after penetrating the pipe to be inspected, and convert the light signal into a digital image signal. The vertical detector 104 is located on the opposite side of the vertical X-ray source 102, and is used to receive vertical X-rays after penetrating the pipe to be inspected, and convert the optical signal into a digital image signal. The data processing unit 105 is electrically connected to the horizontal detector 103 and the vertical detector 104 respectively, and is used to receive digital image signals and perform image processing, edge extraction and index calculation.

[0030] Specifically, the horizontal X-ray source 101 and the vertical X-ray source 102 are installed on both sides of the inspection station of the pipe production line. The emission directions are horizontal and vertical along the radial direction of the pipe, and the central axes of the two rays are perpendicular to each other. The intersection point is located at the center of the inspection area of ​​the pipe (i.e., the area corresponding to the axis when the pipe passes through), ensuring that the rays can penetrate the radial section of the pipe. The horizontal detector 103 and the vertical detector 104 are both linear array detectors, fixedly installed on the opposite side of the horizontal X-ray source 101 and the vertical X-ray source 102, respectively. The distance (focal length) from the X-ray source is fixed, and the receiving surface (HG plane, EF plane) of the detector is perpendicular to the emission direction of the corresponding X-ray source. The center point of the horizontal detector 103 is P, and the center point of the vertical detector 104 is Q. The line connecting the midpoint of the line connecting the two and the intersection point of the two rays is the inspection baseline (e.g., ...). Figure 1 (as shown) Figure 1 In the diagram, S1: horizontal X-ray source 101; S2: vertical X-ray source 102; EF plane: the plane where vertical detector 104 is located; HG plane: the plane where horizontal detector 103 is located; P and Q: the center points of the detectors, respectively; O: the intersection point of the centerline connection.

[0031] Please see Figures 2 to 10 ,in Figure 2 This is a schematic diagram of dual-source radial irradiation and image acquisition along a pipeline. Figure 3 This is a schematic diagram of the pipe image captured by the horizontal detector. Figure 4 It is a grayscale curve of the first row of grayscale data in the image. Figure 5 This is a schematic diagram of the slope (k) of grayscale data. Figure 6 This is a schematic diagram of a coordinate system with pixel x as the horizontal coordinate and slope k as the vertical coordinate. Figure 7 This is a schematic diagram illustrating the location of the inflection points of the inner and outer walls using local extreme points of the slope. Figure 8 This is a schematic diagram of the two-ray system's planar coordinate system and related geometric relationships. Figure 9 This is a schematic diagram showing the pipe wall thickness measurement results (wall thickness values ​​at different angles). Figure 10 This is a flowchart of a wall thickness detection method based on a dual-ray system.

[0032] The present invention also includes a wall thickness detection method based on a dual-ray system, comprising the following steps: S100: Simultaneously captures vertical and horizontal projection images of the pipe using dual X-ray sources.

[0033] Specifically, the pipe moves at a constant speed along the axial direction through the intersection area of ​​the two rays, and the two detectors synchronously acquire images at a frequency of ≥25 frames / second.

[0034] In this embodiment, the two sets of rays irradiate along the radial direction of the pipeline (e.g., Figure 2 As shown in the diagram, the two systems are perpendicular to each other, and the intersection point is the pipeline detection area. The pipeline moves along its axis at a relatively uniform speed. Both systems operate simultaneously, acquiring two sets of images separately. When the equipment is turned on, the X-ray source and detector are activated. The X-ray source continuously emits X-rays that penetrate the sample, and the detector receives the X-ray signals, converting them into digital signals to form an image. Taking the horizontal acquisition method as an example, the detector acquires images at a fixed frequency of 25 frames per second, resulting in an image as shown in the diagram. Figure 3 As shown, since the object has a circular cross-section, the images acquired in the vertical direction are basically the same as those acquired in the horizontal direction.

[0035] S200: Extract the first row of grayscale data from the bidirectional projection images and capture the edge positions using an automatic thresholding method.

[0036] S201: Calculate the slope distribution of the first row of grayscale data; S202: Determine edge boundaries by identifying local extreme points of slope.

[0037] In this embodiment, the software reads the first horizontal row of data from the image, and its grayscale curve is shown below. Figure 4 As shown, the horizontal axis represents the pixel value (x), and the vertical axis represents the grayscale value (y). The data is differentiated (i.e., the slope k at each point is calculated, e.g.) Figure 5 As shown, k can be positive or negative, as calculated using Formula 1.

[0038] (Formula 1) After calculating all points, the x and k values ​​are used to regenerate the coordinate system, where the horizontal axis represents the pixel (x) and the vertical axis represents the slope (k), as shown below. Figure 6 As shown.

[0039] Find the local extreme points respectively. The inflection points of the outer wall correspond to the positions min1 and max1 in the figure, and the inflection points of the inner wall correspond to the positions min2 and max2 in the figure, such as... Figure 7 As shown, the same method is used to find the corresponding position in the image taken from the other direction.

[0040] S300: Capture the inflection points of the inner and outer walls of the pipe based on the edge position, and obtain a total of 8 inflection points.

[0041] Specifically, the horizontal image captures two outer wall inflection points and two inner wall inflection points; The vertical image captures two outer wall inflection points and two inner wall inflection points.

[0042] In this embodiment, in step S200, the two images are processed to obtain a total of 8 points (4 outer wall inflection points and 4 inner wall inflection points), which are then sorted from smallest to largest.

[0043] S400: Calculates the inner and outer diameters of the pipe using a mathematical model based on the inflection point location.

[0044] Specifically, S401: Establish a unified coordinate system with the intersection point O of the virtual centerlines of the two ray sources as the origin; S402: Based on the detector's pixel size, convert the inflection point pixel coordinates into physical coordinates; S403: The position of the center of the circle is deduced by the geometric relationship between the tangent of the ray source and the inflection point of the image in the same direction; S404: Calculate the inner and outer diameters based on the center position.

[0045] S4031: The horizontal ray source connects to the outer wall inflection point of the horizontal image to form two outer wall tangents, and connects to its inner wall inflection point to form two inner wall tangents. S4032: The vertical ray source connects to the outer wall inflection point of the vertical image to form two outer wall tangents, and connects to its inner wall inflection point to form two inner wall tangents; S4033: The coordinates of the outer wall center are determined by the unique intersection of the angle bisector of the angle between the two outer wall tangents of the same horizontal ray source and the angle bisector of the angle between the two outer wall tangents of the same vertical ray source in a unified coordinate system. S4034: The coordinates of the inner wall center are determined by the unique intersection of the angle bisector of the angle between the two inner wall tangents of the same horizontal ray source and the angle bisector of the angle between the two inner wall tangents of the same vertical ray source in a unified coordinate system.

[0046] In this embodiment, the planar coordinate systems of the two ray systems are as follows: Figure 8 As shown, the four outer inflection points of the outer wall correspond to points J, K, L, and M in the figure, respectively. P and Q are the detector centers. Given the pixel size of the detector, the pixel lengths of line segments PJ, PK, QL, and QM are converted into actual lengths. The lengths of line segments S1O, OP, S2O, and OQ can be obtained by measuring the distance. Therefore, the coordinates of J, K, L, and M can be obtained in the coordinate system with O as the origin.

[0047] In the coordinate system, the positions of the ray source S1 and S2 are connected to the corresponding positions of the inflection point to obtain four line segments (S1J, S1K, S2L, S2M), each of which is tangent to the pipe.

[0048] In this invention, it is assumed that there exists a standard circular object that, within a specified range of motion, can project points J, K, L, and M onto the plane containing P and Q regardless of its position, satisfying the basic principle of light projection in physics. Since the positions of points J, K, L, and M are known in practice, the radius and position information of the object's circle can be deduced. Therefore, slight vibrations in the pipe do not significantly affect the detection results.

[0049] Based on the location of the pipe, draw two dashed lines S1G and S2G passing through the center of the circle, intersecting at detector points I and N. Since the preceding line segments are all tangents, S1G and S2G bisect ∠KS1J and ∠LS2Q respectively, i.e., α=β. The angle information of α, β, and Ω in the diagram can be calculated using trigonometric functions, as shown in formulas 2 and 3.

[0050] (Formula 2) (Formula 3) Then, the coordinate information of points I and N is obtained according to different position angles, as shown in Formula 4.

[0051] (Formula 4) Connecting S1I and S2N yields the coordinates G of the unique intersection point of the outer wall of the tested pipe within the two X-ray systems at the current position (similarly, the inner wall of the pipe is connected in the same way, yielding the intersection point G2). Since the two X-ray systems are perpendicular to each other, regardless of the position of the tested pipe within the test hole, there exists a unique central intersection point G in the unified coordinate system. Since S1O and S2O can be measured, the coordinate information of S1 (S1x, S1y) and S2 (S2x, S2y) in the coordinate system is known. Let the slope of line S1I be k1 and the intercept be b1, and the slope of line S2N be k2 and the intercept be b2. These can be calculated using formulas 5, 6, 7, and 8 respectively. (Formula 5) (Formula 6) (Formula 7) (Formula 8) The coordinates of point G(Gx, Gy) can be obtained from the equations of the two lines, as shown in formulas 9 and 10. (Formula 9) (Formula 10) After obtaining the coordinates of point G, the lengths of line segments S1G and S2G can be obtained, as shown in formulas 11 and 12. (Formula 11) (Formula 12) like Figure 8 As shown, R1 and R2 are the radii to be calculated in two directions and are perpendicular to the tangents S1J and S2L respectively. Given the lengths of S1G and S2G, as well as angles α, β, and Ω, R1 and R2 can be calculated using trigonometric functions (in the same way as R1), as shown in Formula 13. (Formula 13) After calculating R1 and R2, the actual radius R is taken as the average of R1 and R2.

[0052] S500: Calculate wall thickness, ellipticity, eccentricity, and concentricity based on inner and outer diameters.

[0053] Specifically, S501: The wall thickness is calculated by taking points at equal intervals along the simulated circular ring to calculate the distance between the inner and outer walls, and outputting the maximum, minimum and average values; S502: Ellipticity is calculated based on the difference between the horizontal and vertical outer diameters; S503: The eccentricity value is calculated based on the coordinate offset between the outer wall center and the inner wall center; S504: Concentricity is calculated by dividing the difference between the maximum and minimum wall thickness by the mean.

[0054] In this embodiment, the inner and outer walls of the pipe are simulated based on the radius. Points on the simulated circles of the inner and outer walls are taken at 45° intervals, and the difference between the inner and outer walls, i.e., the wall thickness, is calculated. Figure 9 As shown, the maximum wall thickness wmin, the minimum wall thickness wmax, and the mean wall thickness wmean are obtained.

[0055] The pipes are not perfectly round during the production process and there is a certain error. The ellipticity Ee is calculated as shown in Formula 8.

[0056] (Formula 14) During the pipe manufacturing process, the centers of the inner and outer diameters may not coincide. Therefore, the eccentricity value Ec of the pipe is the difference between the centers of the inner and outer diameters, as shown in Formula 9.

[0057] (Formula 15) The uniformity of pipe wall thickness is represented by concentricity Co, as shown in Formula 10.

[0058] (Formula 16) The present invention has the following beneficial effects: 1. An X-ray-based wall thickness measurement method was developed. It is universally applicable and can measure the wall thickness and eccentricity of linear materials such as pipelines and cables with both inner and outer walls.

[0059] 2. It can achieve full inspection with extremely high testing efficiency. Conventional methods such as ultrasound and eddy current testing are used for random inspection, which has too low testing efficiency.

[0060] 3. During pipeline inspection, slight vibrations do not affect the test results, which remain accurate. Based on the inspection images from the dual X-ray system, the center position can be located in both the horizontal and vertical directions, allowing for the calculation of magnification in each direction and ultimately yielding more precise measurement data.

[0061] The above-disclosed embodiments are merely one or more preferred embodiments of this application and should not be construed as limiting the scope of this application. Those skilled in the art can understand that all or part of the processes for implementing the above embodiments and equivalent changes made in accordance with the claims of this application still fall within the scope of this application.

Claims

1. A wall thickness detection device based on a dual-ray system, characterized in that, It includes a horizontal X-ray source, a vertical X-ray source, a horizontal detector, a vertical detector, and a data processing unit; The horizontal X-ray source is used to emit X-rays along the radial horizontal direction of the pipe to be inspected; The vertical X-ray source is used to emit X-rays in the radial vertical direction along the pipe to be inspected, and is perpendicular to the X-rays emitted by the horizontal X-ray source, intersecting at the pipe inspection area. The horizontal detector is located on the opposite side of the horizontal X-ray source and is used to receive horizontal X-rays after penetrating the pipe to be inspected and convert the optical signal into a digital image signal. The vertical detector is located on the opposite side of the vertical X-ray source and is used to receive vertical X-rays after penetrating the pipe to be inspected and convert the optical signal into a digital image signal. The data processing unit is electrically connected to the horizontal detector and the vertical detector, respectively, and is used to receive digital image signals and perform image processing, edge extraction and index calculation.

2. A wall thickness detection method based on a dual-ray system, applied to the wall thickness detection device based on a dual-ray system as described in claim 1, characterized in that, The vertical and horizontal projection images of the pipe are captured simultaneously using dual X-ray sources. Extract the first row of grayscale data from the bidirectional projection images and capture the edge positions using an automatic thresholding method; The inflection points of the inner and outer walls of the pipe were captured based on the edge location, and a total of 8 inflection points were obtained; The inner and outer diameters of the pipe are calculated using a mathematical model based on the inflection point location. Calculate the wall thickness, ellipticity, eccentricity, and concentricity based on the inner and outer diameters.

3. The wall thickness detection method based on a dual-ray system as described in claim 2, characterized in that, In "Simultaneous imaging of vertical and horizontal projection images of pipes using dual X-ray sources": The pipe moves at a constant speed along the axial direction through the intersection area of ​​the two rays, and the two detectors synchronously acquire images at a frequency of ≥25 frames / second.

4. The wall thickness detection method based on a dual-ray system as described in claim 2, characterized in that, In the step of "extracting the first row of grayscale data from the bidirectional projection image and capturing edge positions using an automatic thresholding method," the automatic thresholding method specifically includes: Calculate the slope distribution of the first row of grayscale data; Edge boundaries are determined by identifying local extreme points of the slope.

5. The wall thickness detection method based on a dual-ray system as described in claim 2, characterized in that, In the task of "capturing the inflection points of the inner and outer walls of the pipe based on its edge location, obtaining a total of 8 inflection points": Capture two outer wall inflection points and two inner wall inflection points from the horizontal image; The vertical image captures two outer wall inflection points and two inner wall inflection points.

6. The wall thickness detection method based on a dual-ray system as described in claim 2, characterized in that, In the section "Calculating the inner and outer diameter of pipes using a mathematical model based on the inflection point location," the wall thickness calculation specifically includes: A unified coordinate system is established with the intersection point O of the virtual centerlines of the two radiation sources as the origin; Based on the detector's pixel size, the inflection point pixel coordinates are converted into physical coordinates; The position of the center of the circle can be deduced by the geometric relationship between the tangent of the ray source and the inflection point of the image in the same direction. Calculate the inner and outer diameters based on the center position.

7. The wall thickness detection method based on a dual-ray system as described in claim 6, characterized in that, In "Inferring the center position of the circle by using the geometric relationship between the tangent of the ray source and the inflection point of the image in the same direction": A horizontal X-ray source connects to the outer wall inflection point of a horizontal image to form two outer wall tangents, and connects to its inner wall inflection point to form two inner wall tangents. A vertical ray source is connected to the inflection point of the outer wall of the vertical image to form two outer wall tangents, and connected to the inflection point of the inner wall to form two inner wall tangents; The coordinates of the outer wall center are determined by the unique intersection of the angle bisector of the angle between the two outer wall tangents of the same horizontal ray source and the angle bisector of the angle between the two outer wall tangents of the same vertical ray source in a unified coordinate system. The coordinates of the inner wall center are determined by the unique intersection of the angle bisector of the angle between the two inner wall tangents of the same horizontal ray source and the angle bisector of the angle between the two inner wall tangents of the same vertical ray source in a unified coordinate system.

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