A flange flatness real-time measuring system and method for a large flange on-site processing milling machine

Abstract

The application provides a flange flatness real-time measuring system and a detecting method for a large flange on-site processing milling machine. The system comprises a regular octagonal prism shell, a camera, a computer, a light source and a topography feedback unit. The regular octagonal prism shell is used for isolating external light and fixing the camera, the light source and the topography feedback unit; the computer controls the camera to take pictures; the light source comprises eight point light sources which are respectively fixed on the inner side of the vertex of the octagonal reinforcing beam of the rigid frame and are used for providing light in different directions; and the topography feedback unit reflects the topography of the flange surface in real time. When the milling machine drives the system to move on the flange surface, the universal joint and the supporting rod connected with the roller move up and down correspondingly according to the unevenness of the flange surface, so as to drive the flexible film to deform. The deformed flexible film is reconstructed in three dimensions by using photometric stereo technology, so as to realize the real-time measurement of the flatness.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical processing, in particular, especially relates to a large flange on-site machining milling machine flange flatness real-time measurement system and detection method. BACKGROUND

[0002] With the increasing demand for manufacturing and installation of large industrial equipment, large flanges, as one of the important parts connecting pipes and equipment, have a large market demand. In the assembly process of large flanges, the flatness of the flange is a key factor to determine its sealing and firmness. By improving the measurement accuracy and efficiency of the flatness of large flanges, the processing errors of the flanges can be timely checked and corrected by the workers to improve the product quality and installation accuracy of the flanges and reduce the safety hazards in the construction process. Therefore, the measurement technology of the flatness of large flanges is a research hotspot in the related field.

[0003] At present, there are two major problems to be solved in the flatness measurement method of large flanges. One is that the traditional on-site machining of large flanges usually relies on manual operation, and manual measurement of the flatness of the flange requires a lot of time and labor, and human factors will further amplify the processing error, reduce the quality of the flange and increase the cost. The second is that in the traditional machining of large flanges, the off-line method is often used to measure and adjust the flatness of the flange, which cannot obtain the morphology of the flange in real time and adjust the milling tool attitude in advance, and can only measure the flatness after the machining is completed and repeatedly process until it is qualified, which greatly reduces the machining efficiency of the flange.

[0004] In summary, under the limitation of the existing measurement technology of the flatness of large flanges, the on-site machining of large flanges not only has low efficiency and product quality, but also has high processing cost. Therefore, new technology and method need to be proposed to optimize the measurement process of the flatness of large flanges to realize efficient, real-time and accurate on-site machining of large flanges. SUMMARY

[0005] According to the above technical problems, a large flange on-site machining milling machine flange flatness real-time measurement system and method are provided. The system does not need manual measurement, the method is simple, the cost is low, the real-time measurement can be realized, and the measurement accuracy is high. In addition, the measurement speed is fast, the efficiency is high, the personal safety of workers is ensured, and the labor intensity of workers is greatly reduced.

[0006] The technical means adopted by the present application are as follows:

[0007] A large flange on-site machining milling machine flange flatness real-time measurement system, comprising: an octagonal prism shell, a camera, a computer, a light source and a morphology feedback unit, wherein:

[0008] The regular octagonal shell is used for isolating external light, fixing the camera, the light source and the topography feedback unit.

[0009] The camera is used for collecting images.

[0010] The computer is used for controlling the camera to collect images, receiving the images collected by the camera, and completing the correction and preprocessing of the images.

[0011] The light source is used for providing light in different directions.

[0012] The topography feedback unit is used for reflecting the topography of the flange surface in real time.

[0013] Further, the regular octagonal shell is composed of a regular octagonal shell top plate, an octagonal reinforcing beam, a rigid bottom plate, a light-tight shell and a regular octagonal rigid frame.

[0014] Further, the camera is arranged at the center of the regular octagonal shell top plate, and the optical axis of the camera is kept vertical.

[0015] Further, the light source comprises eight point light sources, wherein:

[0016] The eight point light sources are respectively fixed inside the vertices of the octagonal reinforcing beam of the regular octagonal rigid frame; the colors of the eight point light sources are arranged in the order of red, green, blue, red, green, red, blue and green; the included angle between every two point light sources is 45°, the included angle between each point light source and the optical axis of the camera is 45°, and each point light source is fixed and adjusted in direction by a knob.

[0017] Further, the topography feedback unit is provided with a flexible film, a rigid support rod, a linear bearing, a universal joint, a cylindrical rigid spacer and a roller from top to bottom, wherein:

[0018] The roller and the rigid support rod are connected by the universal joint; the rigid support rod is fixed in a guide hole on the rigid bottom plate of the regular octagonal shell through the linear bearing, and the part of the rigid support rod below the rigid bottom plate has a shoulder for controlling the stroke of the rigid support rod;

[0019] The cylindrical rigid spacer is fixed on the upper part of the rigid support rod and is fixedly connected with the flexible film, so that the rigid support rod drives the flexible film to deform when moving up and down.

[0020] Further, in the topography feedback unit, when the roller passes through the convex or concave part on the flange plane, the rigid support rod fixed on the rigid bottom plate of the regular octagonal shell moves upward or downward correspondingly under the action of the linear bearing, and since the cylindrical rigid spacer fixed on the rigid support rod is fixed with the flexible film, the rigid support rod drives the flexible film to deform when moving up and down.

[0021] Further, the number of the flexible film is 1, and the size of the flexible film is determined according to the flange plane to be processed; and the size of the flexible film determines the number of the remaining parts.

[0022] Further, in actual processing, the milling cutter is connected to the flange flatness real-time measurement system of the large flange processing through a connecting rod, so as to ensure that the rotating speeds of the milling cutter and the flange flatness real-time measurement system of the large flange processing around the rotating shaft are the same, and the position of the flange flatness real-time measurement system of the large flange processing is ahead of the milling cutter.

[0023] The application also provides a detection method of the flange flatness real-time measurement system of the large flange field processing milling machine.

[0024] S1, calibrating the camera before processing the large flange:

[0025] At least 20 complete calibration plate photos in different postures are collected, the internal parameter, external parameter and distortion coefficient of the camera are calculated, and the camera calibration is completed;

[0026] S2, calibrating the light source direction before processing the large flange:

[0027] A black highlight ball is placed above the central rigid bottom plate of the regular octagonal prism shell, the light source direction is adjusted, the eight-direction light sources are sequentially and individually lighted, one photo is collected every time a light source is lighted, a total of eight photos of the light sources in different directions are collected, and the light source direction is calculated;

[0028] S3, collecting images during processing the large flange:

[0029] During processing the large flange, the eight point light sources are lighted at the same time, and one image of the flexible film is collected every second;

[0030] S4, correcting and preprocessing the images collected in step S3:

[0031] The camera internal parameter and distortion coefficient obtained by the camera calibration in step S2 are used to correct the images;

[0032] The collected images are preprocessed, including noise removal, image alignment and image matching, so as to ensure the accuracy and consistency of the photo data;

[0033] S5, three-dimensional reconstruction of the flexible film morphology is performed to obtain three-dimensional point cloud:

[0034] According to the light source direction calculated in step S3 and the images preprocessed in step S4, the three-dimensional reconstruction of the flexible film morphology is completed by photometric stereo technology, and three-dimensional point cloud is obtained;

[0035] S6, curvature calculation is performed on the three-dimensional point cloud obtained in step S5:

[0036] The normal vector of each point on the point cloud is calculated by using the nearest neighbor method, and the local surface shape at the point is estimated by fitting a plane;

[0037] The curvature of each point is calculated based on the normal vector, and the surface shape of the point is evaluated;

[0038] For each point, the average value of all curvatures within the selected range of adjacent points is calculated, i.e. the flatness of the point.

[0039] Compared with the prior art, the present application has the following advantages:

[0040] 1. The flange flatness real-time measurement system for large flange on-site machining milling machine provided by the present application realizes real-time monitoring of large flanges, and can obtain the flatness information of the flanges in a timely manner. Based on the real-time monitoring results, the appearance of the flanges can be adjusted in advance to realize accurate machining control. Therefore, machining errors can be discovered and corrected in a timely manner during the machining process, improving the quality and sealing performance of the flanges, while reducing the workload and cost of subsequent machining adjustment.

[0041] 2. The flange flatness real-time measurement system for large flange on-site machining milling machine provided by the present application no longer relies on manual operation, and introduces automatic equipment and algorithms to improve production efficiency and machining accuracy. The method is simple, the cost is low, the real-time measurement can be realized, and the measurement accuracy is high. In addition, the measurement speed is fast and the efficiency is high, which greatly reduces the labor intensity of workers while ensuring their personal safety.

[0042] Based on the above reasons, the present application can be widely popularized in the field of mechanical machining. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0044] Figure 1 It is a schematic diagram of the flange flatness real-time measurement system for large flange on-site machining milling machine of the present application.

[0045] Figure 2 It is a schematic diagram of a single light source of the illumination unit of the present application.

[0046] Figure 3 It is a schematic diagram of the appearance feedback unit of the present application.

[0047] Figure 4 Schematic diagram for application of the present application.

[0048] In the figure: 1, top plate of regular octagonal prism shell; 2, octagonal reinforcing beam; 3, camera; 4, rigid bottom plate; 5, light-tight shell; 6, point light source; 7, knob; 8, flexible film; 9, rigid support rod; 10, linear bearing; 11, universal joint; 12, cylindrical rigid spacer; 13, guide hole; 14, roller; 15, connecting rod; 16, milling cutter; 17, flange flatness real-time measurement system; 18, rotating shaft; 19, large flange; 20, regular octagonal prism rigid frame; 21, computer. DETAILED DESCRIPTION

[0049] It should be noted that the embodiments and features of the embodiments in the present application can be combined with each other without conflict. The technical solutions in the embodiments of the present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0050] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. The description of the at least one exemplary embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0051] It should be noted that the terms used herein are only for describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0052] The foregoing is considered as illustrative only of the principles of the application. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the application to the exact construction and practice described. Accordingly, all suitable modifications and equivalents can be resorted to falling within the scope of the application. Unless otherwise indicated herein, the contents of all patents, patent applications, publications, and test methods cited herein are hereby incorporated by reference in their entirety for all purposes.

[0053] In the description of the present application, it is to be understood that the orientation or positional relationships indicated by terms such as "front", "back", "up", "down", "left", "right", "lateral", "vertical", "horizontal", "top", "bottom", and the like are generally based on the orientation or positional relationships shown in the drawings, and are merely intended to facilitate the description and simplify the description, and do not indicate or imply that the device or element referred to must have a particular orientation or be constructed and operated in a particular orientation, and therefore cannot be construed as limiting the scope of protection of the present application. The orientation terms "inner", "outer" refer to the inner and outer relative to the contour of the parts themselves.

[0054] For the convenience of description, spatial relative terms such as "over", "above", "upper surface", "upper", and the like can be used herein to describe the spatial positional relationship of one device or feature with respect to other devices or features as shown in the drawings. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation of the device as described in the drawings. For example, if the device in the drawings is inverted, the device described as "above" or "over" other devices or structures will be positioned "below" or "under" the other devices or structures. Thus, the exemplary term "above" can include both "above" and "below" orientations. The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein are interpreted accordingly.

[0055] In addition, it should be noted that the use of the terms "first", "second", and the like, to describe various components, do not necessarily indicate any special significance, and are merely intended to distinguish the corresponding components, and therefore cannot be construed as limiting the scope of protection of the present application.

[0056] As Figure 1As shown in the drawings, the present application provides a flange flatness real-time measurement system for large flange field machining milling machine, comprising: a regular octagonal shell, a camera, a computer, a light source and a topography feedback unit, wherein:

[0057] The regular octagonal shell is used to isolate external light, fix the camera, the light source and the topography feedback unit;

[0058] The camera is used to collect images;

[0059] The computer is used to control the camera to take pictures and collect images, correct and pretreat the images;

[0060] The light source is used to provide light in different directions;

[0061] The topography feedback unit is used to reflect the topography of the flange surface in real time.

[0062] In specific implementation, as a preferred embodiment of the present application, continuing to refer to Figure 1 The regular octagonal shell is composed of a regular octagonal shell top plate 1, an octagonal reinforcing beam 2, a rigid bottom plate 4, a light-tight shell 5 and a regular octagonal rigid frame 20.

[0063] In specific implementation, as a preferred embodiment of the present application, continuing to refer to Figure 1 The camera 3 is arranged at the center of the regular octagonal shell top plate 1, and the optical axis of the camera 3 is kept vertical.

[0064] In specific implementation, as a preferred embodiment of the present application, as shown in Figure 2 The light source comprises eight point light sources 6, wherein: the eight point light sources 6 are respectively fixed inside the vertices of the octagonal reinforcing beam 2 of the regular octagonal rigid frame 22; the colors of the eight point light sources 6 are arranged in the order of red, green, blue, red, green, red, blue and green; the included angle between every two point light sources 6 is 45°, and the included angle between each point light source 6 and the optical axis of the camera 3 is 45°, and the direction is fixed and adjusted by a knob 7. In this embodiment, the included angle is about 45°, and the included angle should not be too large or too small, otherwise the flexible film cannot be illuminated in full view, which will affect the measurement result. At the same time, the distance between the camera 3, the point light source 6 and the flexible film 8 should be adjusted according to the actual situation.

[0065] In specific implementation, as a preferred embodiment of the present application, as shown in Figure 3As shown, the top-down, the topography feedback unit is respectively provided with flexible film 8, rigid support rod 9, linear bearing 10, universal joint 11, cylindrical rigid gasket 12 and roller 14, wherein: the roller 14 and the rigid support rod 9 are connected by the universal joint 11; the rigid support rod 9 is fixed in the guide hole 13 on the rigid bottom plate 4 of the regular octagonal housing through the linear bearing 10, the part of the rigid support rod 9 below the rigid bottom plate 4 has a shaft shoulder for controlling the stroke of the rigid support rod 9; the rigid support rod 9 is fixedly provided with a cylindrical rigid gasket 12 on the upper part, and is fixedly connected with the flexible film 8, so that the rigid support rod 9 drives the flexible film 8 to deform when moving up and down.

[0066] In the topography feedback unit, when the roller 14 passes through the convex or concave part on the flange plane 19, the rigid support rod 9 fixed on the rigid bottom plate 4 of the regular octagonal housing moves upward or downward under the action of the linear bearing 10, and since the cylindrical rigid gasket 12 fixed on the rigid support rod 9 is fixed with the flexible film 8, the rigid support rod 9 drives the flexible film 8 to deform when moving up and down.

[0067] In specific implementation, as a preferred embodiment of the present application, the number of the flexible film 8 is 1, and the size of the flexible film 8 is determined according to the processed flange plane; the size of the flexible film 8 determines the number of the remaining parts. In this embodiment, the flexible film is set to be a square of 500mm, and the number of the remaining parts is 9.

[0068] In specific implementation, as a preferred embodiment of the present application, as shown in the figure, Figure 4 In actual processing, the milling cutter 16 and the large flange 19 processing flange flatness real-time measurement system 17 are connected by the connecting rod 15 to ensure that the rotating speeds of the two around the rotating shaft 18 are the same, and the position of the large flange processing flange flatness real-time measurement system 17 is ahead of the milling cutter 16.

[0069] The working principle of the flange flatness real-time measurement system for large flange on-site processing milling machine of the present application is as follows:

[0070] When the measuring tool is used for processing, when the roller 14 of the topography feedback unit passes the convex or concave part on the flange plane 19, the rigid support rod 9 fixed on the rigid bottom plate 4 of the regular octagonal housing will move up or down under the action of the linear bearing 10: when the flange plane 19 is concave, the wheel and the support rod move downward together under the action of gravity; when the flange plane 19 is convex, the convex part will make the wheel and the support rod move upward. Since the cylindrical rigid pad 12 fixed on the rigid support rod 9 is fixed with the flexible film 8, when the rigid support rod 9 moves up and down, it can drive the flexible film 8 to deform. The images of the flexible film 8 at different positions are collected, the topography of the flexible film is reconstructed with high precision by using photometric stereo technology to obtain a three-dimensional point cloud, and the curvature of the point cloud is calculated, so that the flatness information of the flexible film 8 can be accurately and clearly obtained. According to the above principle, combined with image processing and photometric stereo technology, the real-time measurement problem of the flatness of the large flange plane in the above-mentioned large flange plane processing is solved.

[0071] The application also provides a detection method of the flange flatness real-time measurement system for a large flange on-site processing milling machine.

[0072] S1, before processing the large flange, calibrate the camera:

[0073] At least 20 complete calibration plate photos under different postures are collected, the internal parameter, external parameter and distortion coefficient of the camera are calculated, and the camera calibration is completed;

[0074] S2, before processing the large flange, calibrate the light source direction:

[0075] A black highlight ball is placed above the central part of the rigid bottom plate 4 of the regular octagonal housing, the light source direction is adjusted, the eight-direction light sources are sequentially and individually lighted, one photo is collected for each lighted light source, a total of eight photos of the light sources in different directions are collected, and the light source direction is calculated;

[0076] S3, during processing the large flange, image collection is performed:

[0077] During processing the large flange, the eight point light sources 6 are lighted at the same time, and one image of the flexible film 8 is collected per second;

[0078] S4, the image collected in step S3 is corrected and preprocessed:

[0079] The camera internal parameter and distortion coefficient obtained by the camera calibration in step S2 are used to correct the image;

[0080] The collected image is preprocessed, including noise removal, image alignment and image matching, to ensure the accuracy and consistency of the photo data;

[0081] S5, three-dimensional reconstruction of the flexible film shape is performed to obtain a three-dimensional point cloud;

[0082] Based on the light source direction calculated in the step S3 and the image preprocessed in the step S4, three-dimensional reconstruction of the flexible film 8 shape is performed by photometric stereo to obtain a three-dimensional point cloud;

[0083] S6, curvature calculation is performed on the three-dimensional point cloud obtained in the step S5:

[0084] A normal vector of each point on the point cloud is calculated by using the nearest neighbor method, and a local surface shape at the point is estimated by fitting a plane;

[0085] Curvatures of each point are calculated based on the normal vector, and for each point, an average value of all curvatures within a selected range of adjacent points is calculated to obtain a flatness of the point.

[0086] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A real-time flange flatness measurement system for a large flange on-site milling machine, characterized in that, include: The enclosure consists of a regular octagonal prism, a camera, a computer, a light source, and a shape feedback unit, among which: The regular octagonal prism shell is used to isolate external light and fix the camera, light source and shape feedback unit; the regular octagonal prism shell is composed of a regular octagonal prism shell top plate (1), an octagonal reinforcing beam (2), a rigid bottom plate (4), an opaque shell (5) and a regular octagonal prism rigid frame (20); The camera is used to acquire images; the camera (3) is set in the center of the top plate (1) of the octagonal prism shell, and the optical axis of the camera (3) remains vertical; The computer is used to control the camera to take pictures and receive the images captured by the camera, and to perform image correction and preprocessing. The light source is used to provide illumination from different directions; The topography feedback unit is used to reflect the topography of the flange surface in real time; the topography feedback unit is provided with a flexible film (8), a rigid support rod (9), a linear bearing (10), a universal joint (11), a cylindrical rigid gasket (12), and a roller (14) from top to bottom, wherein: The roller (14) and the rigid support rod (9) are connected by a universal joint (11); the rigid support rod (9) is fixed in the guide hole (13) on the rigid base plate (4) of the regular octagonal prism shell by a linear bearing (10); the part of the rigid support rod (9) below the rigid base plate (4) has a shoulder for controlling the stroke of the rigid support rod (9); A cylindrical rigid pad (12) is fixedly installed on the upper part of the rigid support rod (9) and is fixedly connected to the flexible film (8), so that the rigid support rod (9) causes the flexible film (8) to deform when it moves up and down.

2. The real-time flange flatness measurement system for large flange on-site milling machines according to claim 1, characterized in that, The light source includes eight point light sources (6), wherein: Eight point light sources (6) are fixed to the inner side of the apex of the octagonal reinforcing beam (2) of the rigid octagonal prism frame (20); the colors of the eight point light sources (6) are arranged in the order of red, green, blue, red, green, red, blue, green; the included angle between each pair of point light sources (6) is 45°, each point light source (6) is at a 45° angle with the optical axis of the camera (3), and the direction is fixed and adjusted by the knob (7).

3. The real-time flange flatness measurement system for large flange on-site milling machines according to claim 1, characterized in that, In the shape feedback unit, when the roller (14) passes through the protrusion or depression on the flange plane, under the action of the linear bearing (10), the rigid support rod (9) fixed on the rigid base plate (4) of the regular octagonal prism shell moves upward or downward accordingly. Since the cylindrical rigid gasket (12) fixed on the rigid support rod (9) is fixed together with the flexible film (8), the rigid support rod (9) causes the flexible film (8) to deform when it moves up and down.

4. The real-time flange flatness measurement system for large flange on-site milling machines according to claim 1, characterized in that, The number of the flexible film (8) is 1, and the size of the flexible film (8) is determined according to the flange plane being processed; the size of the flexible film (8) determines the number of the remaining parts.

5. The real-time flange flatness measurement system for large flange on-site milling machines according to claim 1, characterized in that, In actual processing, the milling cutter (16) and the flange flatness real-time measurement system (17) for processing the large flange (19) are connected by a connecting rod (15) to ensure that the two rotate around the rotation axis (18) at the same speed, and the position of the flange flatness real-time measurement system (17) for processing the large flange is ahead of the milling cutter (16).

6. A detection method for a real-time flange flatness measurement system for a large flange on-site milling machine as described in any one of claims 1-5, characterized in that, include: S1. Calibrate the camera before machining the large flange: Collect at least 20 complete calibration plate photos under different postures, calculate the camera's intrinsic parameters, extrinsic parameters, and distortion coefficients, and complete the camera calibration; S2. Before machining large flanges, the direction of the light source is calibrated: Place a black highlight sphere above the rigid base plate (4) of the outer shell of the regular octagonal prism, adjust the direction of the light source, and light up the eight light sources in turn. Take a picture for each light source that is lit up, and take a total of eight pictures of light sources in different directions. Calculate the direction of the light source. S3. Image acquisition during large flange processing: During the processing of large flanges, eight point light sources (6) are lit simultaneously, and an image of a flexible film (8) is captured every second; S4. Correct and preprocess the image acquired in step S3: The image is corrected using the camera intrinsic parameters and distortion coefficients obtained from the camera calibration in step S2. The acquired images are preprocessed, including noise removal, image alignment, and image matching, to ensure the accuracy and consistency of the photo data; S5. Perform three-dimensional reconstruction of the flexible thin film morphology to obtain a three-dimensional point cloud: Based on the light source direction calculated in step S3 and the image after preprocessing in step S4, the three-dimensional reconstruction of the morphology of the flexible film (8) is completed by photometric stereo technology and a three-dimensional point cloud is obtained. S6. Calculate the curvature of the three-dimensional point cloud obtained in step S5: The nearest neighbor method is used to calculate the normal vector of each point in the point cloud, and the local surface shape at that point is estimated by fitting a plane. The curvature of each point is calculated based on the normal vector, and the surface shape at that point is evaluated. For each point, the flatness of that point can be obtained by calculating the average of all curvatures within the range of selected adjacent points.

Images