Circular hole fitting method based on data point cloud

Abstract

The invention provides a data point cloud-based circular hole fitting method, which comprises the following steps of: obtaining coordinates (a, b) of an initial circle center of a circular hole according to a data point cloud of the circular hole; for each contour point located at the edge in the circular hole data point cloud, calculating the distance between the contour point and the initial circle center (a, b); determining the radius r of the circular hole according to the calculated distances of all the contour points; removing the contour points of which the distances are greater than a first set value in all the contour points to obtain a contour point set; determining the sum of squares of differences between each contour point in the contour point set and the radius r, solving partial derivatives of the sum of squares of differences, correspondingly changing the coordinate values a and b of the initial circle center according to two partial derivative functions, obtaining the change rates of the coordinate values a and b after the change, and when the change rates of the coordinate values a and b are both smaller than a second set value, determining that the radius r is smaller than a second set value. And taking the changed coordinate values a and b as the circle center coordinates (a, b) of the circular hole. According to the invention, the circular hole fitting efficiency and precision can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of visual intelligent detection, and particularly relates to a circular hole fitting method based on data point cloud. Background Art

[0002] With the continuous advancement of China's industrialization process, higher requirements are put forward for industrial manufacturing and assembly accuracy. The assembly accuracy depends to a large extent on the size and geometric tolerance of the holes on the parts. Therefore, high-precision and high-efficiency fitting of holes has become a problem to be solved. At present, the circular hole detection methods based on visual measurement generally include the following two: The first is to use the least squares method, but this method is sensitive to discrete points and the fitting accuracy is prone to deviation. When there is noise interference or partial data loss, the fitting accuracy drops significantly; The second is to use the random sample consensus algorithm. This method can eliminate discrete outliers through iterative sampling, but it depends on a preset threshold and has low efficiency in processing large-scale data. Summary of the Invention

[0003] The present invention provides a circular hole fitting method based on data point cloud to solve the problem that the current circular hole fitting accuracy and efficiency are both low.

[0004] According to the first aspect of the embodiments of the present invention, a circular hole fitting method based on data point cloud is provided, including:

[0005] Step S100: Obtain the coordinates (a, b) of the initial center of the circular hole according to the circular hole data point cloud;

[0006] Step S200: For each contour point located at the edge in the circular hole data point cloud, calculate the distance between the contour point and the initial center (a, b); Determine the radius r of the circular hole according to the distances of all the calculated contour points;

[0007] Step S300: Remove the contour points with distances greater than a first set value from all the contour points to obtain a contour point set;

[0008] Step S400: Determine the sum of the squares of the differences between each contour point in the contour point set and the radius r, take the partial derivatives of the sum of the squares of the differences, and for the two partial derivative functions, correspondingly change the coordinate values a and b of the initial center to obtain the change rates of the coordinate values a and b after this change. If the change rates of the coordinate values a and b are both less than a second set value, then use the coordinate values a and b after this change as the final center coordinates (a, b) of the circular hole; Otherwise, update the coordinates (a, b) of the initial center after this change, and return to execute step S200.

[0009] In an optional implementation manner, step S100 specifically includes: Processing the circular hole data point cloud by using the least squares method to obtain the coordinates (a, b) of the initial center of the circular hole.

[0010] In another alternative implementation, based on the least squares principle, by monitoring whether the sum of the squares of the distances from the data points in the circular hole data point cloud to the fitted circle reaches the minimum value, the coordinates (a, b) of the initial center of the circular hole are obtained when the minimum value is reached.

[0011] In another alternative implementation, before the step S100, it further includes: removing the outlier points in the circular hole data point cloud.

[0012] In another alternative implementation, before removing the outlier points in the circular hole data point cloud, it further includes: screening out the circular hole data point cloud conforming to the plane feature from the original three-dimensional point cloud by setting sampling and verification rules.

[0013] In another alternative implementation, the RANSAC algorithm is used to determine the plane where the circular hole area is located from the original three-dimensional point cloud, obtain the circular hole data point cloud conforming to the plane feature, and remove the outlier points in the circular hole data point cloud.

[0014] In another alternative implementation, in the step S200, the distance d i , y i ) between the contour point (x i :

[0015] The radius r of the circular hole is determined according to the following formula: n represents the number of contour points in the circular hole data point cloud, and i is an integer greater than 0 and less than n + 1.

[0016] In another alternative implementation, the step S400 specifically includes:

[0017] Step S410, setting the learning rate and loss function l(a, b) of the gradient descent method:

[0018] where d j represents the contour point in the contour point set, m represents the number of contour points in the contour point set, and j is an integer greater than 0 and less than m + 1;

[0019] Step S420, respectively obtaining the gradient descent directions of the coordinate values a and b according to the following formulas, and obtaining the change rates of the coordinate values a and b:

[0020]

[0021] Step S430, changing the coordinate values a and b, and obtaining the change rates and Judge the change rate respectively and whether they are both less than the second set value. If so, use the coordinate values a and b after this change as the final center coordinates (a, b) of the circular hole; otherwise, update the coordinates (a, b) of the initial center after this change, and return to execute step S200.

[0022] In another alternative implementation, after determining the final center coordinates (a, b) of the circular hole in step S400, use the radius r based on which the final center coordinates (a, b) are determined as the final radius r of the circular hole.

[0023] In another alternative implementation, for a circular hole on a plane, when the distance between the sampling point of the data point cloud sampling device and the final center coordinates (a, b) is equal to the third set value, do not adjust the final radius r; if the distance between the data sampling point and the final center coordinates (a, b) is not equal to the third set value, adjust the final radius r according to the distance between the data sampling point and the final center coordinates (a, b);

[0024] For a circular hole on a curved surface, adjust the final radius r according to the positional relationship between the sampling point of the three-dimensional point cloud sampling device and the final center coordinates (a, b) and the distribution of the sampled three-dimensional point cloud, so as to obtain the final radius of the circular hole and the specific distribution of the data points corresponding to the circular hole.

[0025] The beneficial effects of the present invention are as follows:

[0026] 1. When the present invention performs circular hole fitting, first, an initial center coordinate (a, b) of the circular hole is determined according to the circular hole data point cloud. The radius r of the circular hole is determined according to the contour points in the circular hole data point cloud. Then, based on the contour points and the radius r of the circular hole, the initial center coordinate (a, b) is adjusted. During the adjustment process, the present invention removes the contour points greater than the first set value in the contour points, so that fine adjustment of the initial center coordinate (a, b) can be achieved, and the adjustment efficiency of the initial center coordinate (a, b) can be improved. In addition, when the present invention adjusts the center coordinate, first, the sum of the squares of the differences between each contour point in the contour point set and the radius r is determined, and the partial derivative of the sum of the squares of the differences is obtained to obtain two partial derivative functions, so as to obtain the change rates of a and b. Then, for the two partial derivative functions, the coordinate values a and b are changed to determine the change rates of the coordinate values a and b. When the change rates of both are less than the second set value, the changed a and b are used as the center coordinates. Otherwise, the coordinates of the initial center after this change are updated, and step S200 is returned to execute to adjust the radius r and the contour points in the contour point set. Thus, each time a and b are changed, the radius r and the contour point set based on which the change rates of a and b are determined are different, so that continuous convergence of the center coordinate adjustment can be achieved, thereby improving the determination efficiency and accuracy of the center coordinate and the radius, and improving the machining quality of the circular hole. In addition, the circular hole fitting method of the present invention is also very simple;

[0027] 2. The present invention first removes the outlier points in the circular hole data point cloud to avoid adverse effects of the outlier points on the fitting accuracy of the least squares method, and then uses the least squares method to process the circular hole data points to obtain the coordinates (a, b) of the initial center of the circular hole, so that the fitting accuracy of the initial center coordinate can be improved;

[0028] 3. The present invention only screens out the circular hole data point cloud that conforms to the plane feature. For the circular hole on the curved surface, the screened circular hole data point cloud may only include part of the data point cloud of the circular hole, which is very different from the traditional fitting method that needs to project the curved surface where the circular hole is located and continuously rotate the plane corresponding to the circular hole to obtain all the data points of the circular hole. On the one hand, although the number of data points is reduced, the determination of the initial center coordinate has little relation with the number of data points, so the determination accuracy of the initial center coordinate will not be reduced. On the other hand, the reduction of the number of data points can improve the determination efficiency of the initial center coordinate. It can be seen that the present invention is also applicable to the fitting of circular holes on the curved surface. Compared with the circular hole on the plane, the determination accuracy of the initial center coordinate of the circular hole on the curved surface is the same, and the determination efficiency is higher;

[0029] 4. The present invention removes the contour points with a distance greater than the first set value among all the contour points to obtain a contour point set, so that the center coordinate of the circular hole is adjusted based on the contour point set. In this way, not only the adjustment efficiency of the center coordinate can be improved, but also the adjustment accuracy of the center coordinate can be improved;

[0030] 5. Based on the radius r determined in step S200 and each contour point in the contour point set, the present invention adjusts the initial center coordinates (a, b) obtained in step S100 by using the gradient descent method. The adjustment method is simple, reducing the amount of calculation, and both the adjustment efficiency and accuracy are relatively high. Thus, efficient and accurate adjustment of the center coordinates can be achieved. Additionally, the present invention first uses the least squares method to determine the initial center coordinates of the circular hole. On the premise that the determined initial center coordinates themselves have relatively high accuracy, the gradient descent method is then used to finely adjust the initial center coordinates, which can further ensure the determination efficiency and accuracy of the center coordinates.

[0031] 6. The present invention uses the radius r based on which the final center coordinates (a, b) are determined as the final radius r of the circular hole, which can ensure the determination accuracy of the center radius. For a circular hole on a plane, after the final center coordinates of the circular hole are determined in step S400, if the distance between the data sampling point and the final center coordinates is not equal to the third set value, the final radius r is adjusted according to the distance between the data sampling point and the final center coordinates, which can further ensure the determination accuracy of the radius of the circular hole on the plane. For a circular hole on a curved surface, after the final center coordinates are determined in step S400, the final radius r is adjusted according to the positional relationship between the sampling points of the three-dimensional point cloud sampling device and the final center coordinates and the distribution of the sampled three-dimensional point cloud, so as to obtain the final radius of the circular hole and the specific distribution of the corresponding data points of the circular hole on the curved surface, which can further ensure the determination accuracy of the radius of the circular hole on the curved surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flowchart of an embodiment of the method for fitting a circular hole based on a point cloud data of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention and make the above-mentioned objects, features, and advantages of the embodiments of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be further described in detail below with reference to the drawings.

[0034] In the description of the present invention, unless otherwise specified and limited, it should be noted that the term "connection" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the communication inside two components. It can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific situations.

[0035] See Figure 1 , which is a flowchart of an embodiment of the method for fitting a circular hole based on a point cloud data of the present invention. The method may include the following steps:

[0036] Step S100: Obtain the coordinates (a, b) of the initial center of the circular hole based on the point cloud of the circular hole data.

[0037] In this step, the least squares method can be used to process the point cloud of the circular hole data to obtain the coordinates (a, b) of the initial center of the circular hole. Among them, based on the principle of the least squares method, the least squares method monitors whether the sum of the squares of the distances from the data points in the point cloud of the circular hole to the fitted circle reaches the minimum value, and obtains the coordinates (a, b) of the initial center of the circular hole when the minimum value is reached.

[0038] Before the step S100, the method may further include: removing the outlier points in the point cloud of the circular hole data. The present invention first removes the outlier points in the point cloud of the circular hole data to avoid the adverse effects of the outlier points on the fitting accuracy of the least squares method, and then uses the least squares method to process the point cloud of the circular hole data to obtain the coordinates (a, b) of the initial center of the circular hole, so as to improve the fitting accuracy of the coordinates of the initial center.

[0039] Before removing the outlier points in the point cloud of the circular hole data, the method may further include: screening out the point cloud of the circular hole data that conforms to the plane feature from the original three-dimensional point cloud by setting sampling and verification rules. The present invention only screens out the point cloud of the circular hole data that conforms to the plane feature. For the circular hole on the curved surface, the screened point cloud of the circular hole data may only include some of the data points of the circular hole, which is very different from the traditional fitting method that needs to project the curved surface where the circular hole is located and continuously rotate the corresponding plane of the circular hole to obtain all the data points of the circular hole. On the one hand, although the number of data points is reduced, the determination of the coordinates of the initial center has little to do with the number of data points, so the determination accuracy of the coordinates of the initial center will not be reduced; on the other hand, the reduction of the number of data points can improve the determination efficiency of the coordinates of the initial center; it can be seen that the present invention is also applicable to the fitting of circular holes on the curved surface. Compared with the circular hole on the plane, the determination accuracy of the coordinates of the initial center of the circular hole on the curved surface is the same, and the determination efficiency is higher.

[0040] Among them, the RANSAC algorithm can be used to determine the plane where the circular hole area is located from the original three-dimensional point cloud, obtain the point cloud of the circular hole data that conforms to the plane feature, and remove the outlier points in the point cloud of the circular hole data.

[0041] Step S200: For each contour point located at the edge in the point cloud of the circular hole data, calculate the distance between the contour point and the initial center (a, b); determine the radius r of the circular hole according to the distances of all the calculated contour points.

[0042] In the step S200, the distance d between the contour point (x i , y i ) and the initial center (a, b) can be calculated according to the following formula i : Determine the radius r of the circular hole according to the following formula: n represents the number of contour points in the data point cloud of the circular hole, and i is an integer greater than 0 and less than n + 1.

[0043] Among them, after determining the final center coordinates (a, b) of the circular hole, use the radius r based on when determining the final center coordinates (a, b) as the final radius r of the circular hole. For a circular hole on a plane, whether the line connecting the sampling point of the data point cloud sampling device and the center of the circular hole is perpendicular to the plane or the line forms a certain angle with the plane, as long as the distance between the sampling point and the final center coordinates (a, b) is equal to the third set value, the final radius r will not be adjusted. As the distance between the sampling point and the final center coordinates (a, b) changes, when the distance between the data sampling point and the final center coordinates (a, b) is not equal to the third set value, the final radius r can be adjusted proportionally.

[0044] For a circular hole on a curved surface, the final radius r can be adjusted according to the positional relationship between the sampling points of the three-dimensional point cloud sampling device and the final center coordinates (a, b) and the distribution of the sampled three-dimensional point cloud, so as to obtain the final radius of the circular hole and the specific distribution of the data points corresponding to the circular hole. The present invention uses the radius r based on when determining the final center coordinates (a, b) as the final radius r of the circular hole, which can ensure the accuracy of determining the center and radius. For a circular hole on a plane, after determining the final center coordinates of the circular hole in step S400, if the distance between the data sampling point and the final center coordinates is not equal to the third set value, the final radius r is adjusted according to the distance between the data sampling point and the final center coordinates, so as to further ensure the accuracy of determining the radius of the circular hole on the plane; for a circular hole on a curved surface, after determining the final center coordinates in step S400, the final radius r is adjusted according to the positional relationship between the sampling points of the three-dimensional point cloud sampling device and the final center coordinates and the distribution of the sampled three-dimensional point cloud, so as to obtain the final radius of the circular hole and the specific distribution of the data points corresponding to the circular hole on the curved surface, so as to further ensure the accuracy of determining the radius of the circular hole on the curved surface.

[0045] Step S300: Remove the contour points in all the contour points whose distance is greater than a first set value (for example, greater than 0.2 mm) to obtain a set of contour points. Since the initial center coordinates determined in Step S100 may have offsets, if the initial center coordinates are still adjusted based on all the contour points at this time, a large number of data points will affect the efficiency of center adjustment; and if the contour points less than the corresponding set value are removed, since the center moves towards the contour points farther away from it during the adjustment process, the farther contour points have a greater impact on the movement of the center, resulting in a larger distance for each movement of the center, so the accuracy of center adjustment will be affected. Therefore, in the present invention, the contour points in all the contour points whose distance is greater than the first set value are removed to obtain a set of contour points, so that the center coordinates of the circular hole are adjusted based on the set of contour points. In this way, not only can the efficiency of center coordinate adjustment be improved, but also the accuracy of center coordinate adjustment can be improved.

[0046] Step S400: Determine the sum of the squares of the differences between each contour point in the set of contour points and the radius r, take the partial derivatives of the sum of the squares of the differences, and for the two partial derivative functions, correspondingly change the coordinate values a and b of the initial center to obtain the change rates of the coordinate values a and b after this change. If the change rates of the coordinate values a and b are both less than a second set value, then take the coordinate values a and b after this change as the final center coordinates (a, b) of the circular hole; otherwise, update the coordinates (a, b) of the initial center after this change, and return to execute Step S200. The said Step S400 may specifically include:

[0047] Step S410: Take the coordinate values a and b obtained in Step S100 and the radius r determined in Step S200 as the initial values of the gradient descent method, and set the learning rate (for example, α = 0.001) and the loss function l(a, b) of the gradient descent method:

[0048] where d j represents the contour points in the set of contour points, m represents the number of contour points in the set of contour points, and j is an integer greater than 0 and less than m + 1;

[0049] Step S420: Respectively obtain the gradient descent directions (i.e., take the partial derivatives) of the coordinate values a and b according to the following formulas to obtain the change rates of the coordinate values a and b:

[0050]

[0051] Step S430: Change the coordinate values a and b to obtain the change rates and respectively judge the change rate and Is it less than the second set value (for example, less than 0.1 mm)? If both are, then use the coordinate values a and b after this change as the final center coordinates (a, b) of the round hole; otherwise, update the coordinates (a, b) of the initial center after this change, and return to execute step S200.

[0052] Based on the radius r determined in step S200 and each contour point in the contour point set, the present invention uses the gradient descent method to adjust the initial center coordinates (a, b) obtained in step S100. The adjustment method is simple, reducing the amount of calculation, and both the adjustment efficiency and accuracy are relatively high. Thus, efficient and accurate adjustment of the center coordinates can be achieved. Additionally, the present invention first uses the least squares method to determine the initial center coordinates of the round hole. On the premise that the determined initial center coordinates themselves have relatively high accuracy, the gradient descent method is then used to finely adjust the initial center coordinates. In this way, the determination efficiency and accuracy of the center coordinates can be further ensured.

[0053] As can be seen from the above embodiments, when the present invention performs round hole fitting, first, an initial center coordinate (a, b) of the round hole is determined according to the round hole data point cloud. According to the contour points in the round hole data point cloud, the radius r of the round hole is determined. Then, based on the contour points and the radius r of the round hole, the initial center coordinates (a, b) are adjusted. During the adjustment process, the present invention removes the contour points in the contour points that are greater than the first set value. In this way, fine adjustment of the initial center coordinates (a, b) can be realized, and the adjustment efficiency of the initial center coordinates (a, b) can be improved. In addition, when the present invention adjusts the center coordinates, first, the sum of the squares of the differences between each contour point in the contour point set and the radius r is determined, and the partial derivatives of the sum of the squares of the differences are obtained to obtain two partial derivative functions, thereby obtaining the change rates of a and b. Then, for the two partial derivative functions, the coordinate values a and b are changed to determine the change rates of the coordinate values a and b. When the change rates of both are less than the second set value, the changed a and b are used as the center coordinates. Otherwise, the coordinates of the initial center after this change are updated, and return to execute step S200 to adjust the radius r and the contour points in the contour point set. Thus, each time a and b are changed, the radius r and the contour point set based on which the change rates of a and b are determined are different. In this way, continuous convergence of the center coordinate adjustment can be realized, thereby improving the determination efficiency and accuracy of the center coordinates and the radius, improving the quality of round hole machining. In addition, the round hole fitting method of the present invention is also very simple. The present invention is applicable to the fitting of bathtub milling holes.

[0054] Other embodiments of the present invention will be readily apparent to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following the general principles of the invention and including known or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are pointed out by the following claims.

[0055] It should be understood that the present invention is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is governed only by the appended claims.

Claims

1. A circular hole fitting method based on data point cloud, characterized in that: include: Step S100, obtaining the coordinates (a, b) of the initial center of the circular hole according to the circular hole data point cloud; Step S200, for each contour point located at the edge of the circular hole data point cloud, calculate the distance between the contour point and the initial circle center (a, b); determine the radius r of the circular hole according to the calculated distances of all contour points; Step S300, removing contour points whose distances are greater than a first set value from all contour points to obtain a contour point set; Step S400, determine the sum of the squares of the differences between each contour point in the contour point set and the radius r, calculate the partial derivative of the sum of the squares of the differences, and for the two partial derivative functions, change the coordinate values ​​a and b of the initial center of the circle accordingly, and obtain the rate of change of the coordinate values ​​a and b after the change. If the rate of change of the coordinate values ​​a and b are both less than the second set value, use the coordinate values ​​a and b after the change as the final center coordinates (a, b) of the circular hole; otherwise, update the coordinates (a, b) of the initial center of the circle after the change, and return to execute step S200.

2. The circular hole fitting method based on data point cloud according to claim 1, characterized in that: The step S100 specifically includes: using the least square method to process the circular hole data point cloud to obtain the coordinates (a, b) of the initial center of the circular hole.

3. The circular hole fitting method based on data point cloud according to claim 2, characterized in that: Based on the principle of least squares method, by monitoring whether the sum of squares of the distances from the data points in the circular hole data point cloud to the fitting circle reaches a minimum value, the coordinates (a, b) of the initial center of the circular hole are obtained when the minimum value is reached.

4. The circular hole fitting method based on data point cloud according to claim 2, characterized in that: Before step S100, the method further includes: removing outliers in the circular hole data point cloud.

5. The circular hole fitting method based on data point cloud according to claim 4, characterized in that: Before removing outliers in the circular hole data point cloud, the method further includes: screening the circular hole data point cloud that meets the plane features from the original three-dimensional point cloud by setting sampling and verification rules.

6. The circular hole fitting method based on data point cloud according to claim 5, characterized in that: The RANSAC algorithm is used to determine the plane where the circular hole area is located from the original three-dimensional point cloud, obtain the circular hole data point cloud that conforms to the plane characteristics, and remove the outliers in the circular hole data point cloud.

7. The circular hole fitting method based on data point cloud according to claim 1, characterized in that: In step S200, the contour point (x i ,y i ) and the initial center (a, b) i : The radius r of the circular hole is determined according to the following formula: n represents the number of contour points in the circular hole data point cloud, and i is an integer greater than 0 and less than n+1.

8. The circular hole fitting method based on data point cloud according to any one of claims 1 to 7, characterized in that: The step S400 specifically includes: Step S410: Set the learning rate and loss function l(a,b) of the gradient descent method: where d j represents a contour point in the contour point set, m represents the number of contour points in the contour point set, and j is an integer greater than 0 and less than m+1; Step S420: For the coordinate values ​​a and b, the gradient descent directions are calculated according to the following formulas to obtain the change rates of the coordinate values ​​a and b: Step S430: Change the coordinate values ​​a and b to obtain the change rate of the coordinate values ​​a and b and Determine the change rate and Is it less than the second set value? If so, the coordinate values ​​a and b after the change are used as the final center coordinates (a, b) of the circular hole; otherwise, the coordinates (a, b) of the initial center after the change are updated, and the process returns to step S200.

9. The circular hole fitting method based on data point cloud according to claim 7, characterized in that: After the final center coordinates (a, b) of the circular hole are determined in step S400, the radius r based on which the final center coordinates (a, b) are determined is used as the final radius r of the circular hole.

10. The circular hole fitting method based on data point cloud according to claim 9, characterized in that: For a circular hole on a plane, when the distance between the sampling point of the data point cloud sampling device and the final circle center coordinate (a, b) is equal to the third set value, the final radius r is not adjusted; if the distance between the data sampling point and the final circle center coordinate (a, b) is not equal to the third set value, the final radius r is adjusted according to the distance between the data sampling point and the final circle center coordinate (a, b); For a circular hole on a curved surface, the final radius r is adjusted according to the positional relationship between the sampling point of the three-dimensional point cloud sampling device and the final center coordinates (a, b) and the sampled three-dimensional point cloud distribution, so as to obtain the final radius of the circular hole and the specific distribution of the data points corresponding to the circular hole.

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