Part pre-positioning method based on point cloud surface shape feature descriptor registration algorithm

Abstract

The application discloses a kind of based on point cloud surface shape feature descriptor registration algorithm's pre-positioning method of measured part, comprising the following steps: step S1, measured part is placed on workbench;Step S2, manual operation mechanical arm, scan measured part by line laser scanner carried by mechanical arm, obtain local point cloud;Step S3, measured part global point cloud is generated based on part CAD model;Step S4, measured part global point cloud is registered to scanning part local point cloud, obtains the transformation matrix T1 of both;Step S5, manual operation mechanical arm, drive line laser scanner scans mechanical arm base, establishes robot base coordinate system;Step S6, the conversion relationship of C-Track coordinate system and robot base coordinate system is solved, obtains the transformation matrix T2 of both;Step S7, based on T1, T2 carries out coordinate transformation, transforms part coordinate system to under mechanical arm base coordinate system, and then realizes pre-positioning of measured part.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement, and particularly relates to a pre-positioning method for a part under test based on a point cloud surface shape feature descriptor registration algorithm. Background Technology

[0002] With the popularization of digital technology in the manufacturing industry, more and more complex curved surfaces are being used in aerospace, automobile manufacturing, shipbuilding and other fields. In actual production applications, the machining accuracy of complex curved surface parts directly affects the various performances of the products. Therefore, higher requirements are put forward for the detection capability of machining accuracy of complex curved surface parts. Achieving high-precision and automated detection of free-form surface parts has become an important development direction of detection technology.

[0003] As a non-contact measurement method, laser scanners offer high accuracy and efficiency, enabling the acquisition of large amounts of point cloud data in a short time. To improve the detection efficiency and accuracy of freeform surfaces, a new approach is emerging: fixing a line laser scanner to the end effector of an industrial robot. This method, utilizing the robot's motion to drive the scanner and scan the target object, is becoming a new direction for automated inspection. This combination not only solves the inefficiency problem of contact scanning but also expands the scanning range. The optimal automatic scanning path is solved offline using a CAD model based on the freeform surface, making it well-suited for freeform surface parts. However, this method places high demands on determining the relative positional relationship between the part being measured and the robot during the actual scanning process—that is, the pre-positioning problem of the part being measured. Summary of the Invention

[0004] The purpose of this invention is to provide a pre-positioning method for a part under test based on a point cloud surface shape feature descriptor registration algorithm.

[0005] To achieve the objective of this invention, the technical solution provided by this invention is as follows:

[0006] A pre-location method for a test part based on a point cloud surface shape feature descriptor registration algorithm includes the following steps:

[0007] Step S1: Place the part to be tested on the worktable;

[0008] Step S2: Manually operate the robotic arm to scan the part to be tested using the line laser scanner mounted on the robotic arm to obtain a local point cloud;

[0009] Step S3: Generate a global point cloud of the part to be tested based on the part's CAD model;

[0010] Step S4: Register the global point cloud of the part to be tested to the local point cloud of the scanned part to obtain the transformation matrix T1 between the two.

[0011] Specifically, the registration of the global point cloud to the local scanned point cloud is achieved by using a point cloud registration algorithm based on surface shape feature descriptors. The local point cloud obtained by scanning is located in the coordinate system of the C-Track tracking system. The coordinate transformation matrix from the workpiece coordinate system to the tracking system coordinate system is obtained through registration.

[0012] in,

[0013] The point cloud registration algorithm based on surface shape feature descriptors is as follows:

[0014] Step S41: Perform voxel downsampling on the local point cloud and the global point cloud;

[0015] Step S410, voxelize the point cloud.

[0016] Step S411: Take the average or weighted average of the points contained in each voxel to obtain a new point, which replaces all the points in the original voxel. By downsampling voxels, the number of points is reduced, and the calculation speed is improved.

[0017] Step S42: Using the Internal Shape Descriptor (ISS) algorithm to represent the solid geometry, the point cloud feature points containing rich geometric information are solved, further reducing the number of points to be processed.

[0018] Step S43: For the feature points in the point cloud, obtain the corresponding surface shape feature descriptor SSFD = {d1,d2,a1,a2,a3,c,o,p} respectively;

[0019] Where d1 represents the distance from the feature point to the centroid of the point cloud. Assume the coordinates of the feature point are (x1, y1, z1) and the coordinates of the centroid of the point cloud are (x2, y2, z2), as shown in formula (1):

[0020]

[0021] d2 represents the average distance between the feature point and the centroids of its neighborhood with different radii, as shown in formula (2):

[0022]

[0023] Where D1 represents the distance from the feature point to the centroid of the small-radius neighborhood point cloud, and D2 represents the distance from the feature point to the centroid of the large-radius neighborhood.

[0024] a1 represents the angle between the feature point normal and the line connecting the feature point and the centroid of the point cloud, as shown in formula (3):

[0025]

[0026] Where v1 represents the feature point normal vector, and v2 represents the line vector connecting the feature point and the centroid of the point cloud.

[0027] a2 represents the average of the sum of the angles between the feature point normal and the neighboring point cloud normal. Each angle is solved according to formula (3), and the average value is calculated according to formula (4).

[0028]

[0029] a3 represents the average of the sum of the angles between the feature point normal and the line connecting the neighboring point cloud, which is solved according to formulas (3) and (4);

[0030] c represents the curvature change at the feature point, as shown in formula (5):

[0031]

[0032] o represents the total variance of the point cloud, which has a strong ability to describe the surface undulation of the point cloud, as shown in formula (6):

[0033]

[0034] p represents the flatness of the point cloud, which can effectively represent the flatness of the fitted surface in the neighborhood of that point, as shown in formula (7):

[0035]

[0036] Where λ1, λ2, and λ3 are eigenvalues ​​based on the covariance matrix;

[0037] Step S44: After obtaining the surface shape feature descriptors corresponding to the feature points respectively, perform feature matching between the obtained local point cloud feature point surface shape feature descriptors and the global point cloud feature point surface shape feature descriptors to obtain the initial matching relationship.

[0038] Step S45: Eliminate incorrect matching point pairs using distance constraints;

[0039] Step S46: After obtaining the correct matching relationship, the coordinate transformation is performed by least squares method to obtain the optimal transformation matrix, thus completing the coarse registration of the point cloud.

[0040] Step S47: Based on this, the iterative nearest point algorithm is used to complete the fine registration of the point cloud;

[0041] Step S5: Manually operate the robotic arm to drive the line laser scanner to scan the base of the robotic arm and establish the robot's base coordinate system;

[0042] Step S6: Solve the transformation relationship between the C-Track coordinate system and the robot base coordinate system to obtain the transformation matrix T2.

[0043] Step S7: Based on T1 and T2, perform coordinate transformation to transform the coordinate system of the part to the base coordinate system of the robotic arm, thereby achieving the pre-positioning of the part to be measured.

[0044] A further preferred technical solution provided by the present invention is,

[0045] In step S2, two viewpoints to be tested are selected, requiring the viewpoints to be located at both ends of the part to be tested and to contain as much geometric information as possible; the scanner mounted on the robotic arm is manually operated to rotate 180° around the scanning direction at the viewpoints to be tested to obtain two local point clouds.

[0046] Another preferred technical solution provided by the present invention is,

[0047] Specifically, step S3 involves importing the CAD model of the part to be tested into the simulation software, and generating a global point cloud of the part based on the CAD model in the software.

[0048] A further preferred technical solution provided by the present invention is,

[0049] Specifically, step S5 involves manually operating the robotic arm to drive the line laser scanner to scan the robotic arm base. At this time, the scanned point cloud of the robotic arm base is located in the tracking system coordinate system. The robotic arm base coordinate system is constructed in the tracking system coordinate system by creating relevant entity constraints through the point cloud obtained by scanning.

[0050] Another preferred technical solution provided by the present invention is,

[0051] Specifically, step S6 involves obtaining the transformation matrix T2 of the C-Track coordinate system and the robot base coordinate system, given the origin coordinates and directions of each axis, using formulas (8), (9), and (10).

[0052] R = [X2,Y2,Z2] × [X1,Y1,Z1] T (8)

[0053] t = O2 - R × O1 (9)

[0054]

[0055] In formula (8), R is the rotation matrix between the two coordinate systems, X1, Y1, Z1 are the direction vectors of the three coordinate axes of the C-Track coordinate system, X2, Y2, Z2 are the direction vectors of the three coordinate axes of the robot base coordinate system, and the superscript T indicates the transpose of the vector or matrix. In formula (9), t is the translation matrix between the two coordinate systems, O1 is the origin coordinate of the C-Track coordinate system, O2 is the origin coordinate of the robot base coordinate system, and in formula (10), T2 represents the homogeneous transformation matrix composed of the rotation matrix R and the translation matrix t.

[0056] A further preferred technical solution provided by the present invention is,

[0057] Specifically, step S7 is as follows:

[0058] Transformation matrix T1 from the workpiece coordinate system to the C-Track tracking system coordinate system, and transformation matrix T2 from the C-Track tracking system coordinate system to the robot arm base coordinate system, assuming A is the workpiece coordinate system, A * Using the robot arm's base coordinate system, coordinate transformation is performed using formula (11).

[0059] A * =T2T1A (11)

[0060] It can successfully transform the coordinate system of the part to the coordinate system of the robot, thereby realizing the pre-positioning of the part to be tested.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] (1) Existing pre-positioning technologies for parts under test mostly rely on designing specific tooling fixtures or using markers for auxiliary pre-positioning, which is not only costly and cumbersome to operate, but may also cause irreversible damage to the surface of the parts under test. This invention proposes a novel non-contact pre-positioning method for parts under test, which is low-cost, simple to operate, and will not cause scratches, compression, etc. on the surface of the parts under test.

[0063] (2) By obtaining local and global point clouds through a scanner and performing point cloud registration, the pose transformation relationship between the workpiece coordinate system and the C-Track coordinate system is obtained. Then, by scanning the robot base with a scanner, the pose transformation relationship between the robot coordinate system and the C-Track coordinate system is established, thereby obtaining the pose transformation relationship between the workpiece coordinate system and the robot coordinate system. This invention makes full use of experimental equipment and provides a pre-positioning approach for the part under test within the overall structure of a scanner-tracking system-robot system.

[0064] (3) Existing point cloud registration algorithms based on point cloud features have high point cloud feature dimensions, resulting in high algorithm complexity. This invention proposes a point cloud registration algorithm based on surface shape feature descriptors for the pre-positioning of the part to be tested. By solving the low-dimensional surface shape feature descriptors, the complexity of subsequent calculations is effectively reduced. It can accurately characterize the point cloud characteristics and surface shape at the feature points. The method is simple and its registration accuracy can well meet the requirements of the pre-positioning of the part to be tested. Attached Figure Description

[0065] Figure 1 This is a structural diagram of the overall pre-positioning system for the part under test according to the present invention;

[0066] Figure 2 This is a flowchart of the overall scheme of a pre-positioning method for a part under test based on a point cloud surface shape feature descriptor registration algorithm according to the present invention;

[0067] Figure 3 This is a flowchart of the point cloud registration algorithm based on surface shape feature descriptors in step S4 of the present invention;

[0068] Figure 4 This is a diagram showing the effect of point cloud downsampling in step S4 of the present invention;

[0069] Figure 5 This is a diagram showing the result of obtaining ISS feature points in step S4 of this invention.

[0070] Figure 6 This is a diagram showing the initial matching point pairs in step S4 of this invention.

[0071] Figure 7 This is a diagram showing the result after proposing incorrect matching relationships in step S4 of this invention.

[0072] Figure 8 This is a diagram showing the effect of coarse registration in step S4 of this invention.

[0073] Figure 9 This is a diagram showing the effect of fine registration in step S4 of the present invention;

[0074] Figure 10 This is a schematic diagram showing the positional relationship between the C-Track coordinate system and the robot's base coordinate system;

[0075] Figure 11 Schematic diagram of coordinate transformation. Detailed Implementation

[0076] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings, and the present invention will be further described in detail with reference to the schematic diagram of the measurement method flow.

[0077] Figure 2 This is a flowchart illustrating the overall scheme of a pre-positioning method for a test part based on a point cloud surface shape feature descriptor registration algorithm, as described in this invention. Figure 2 The present invention is described as follows:

[0078] A pre-location method for a test part based on a point cloud surface shape feature descriptor registration algorithm includes the following steps:

[0079] Step S1: Place the part to be tested on the worktable; the overall structure of the pre-positioning system for the part to be tested is as follows: Figure 1 As shown,

[0080] Step S2: Manually operate the robotic arm to scan the part to be tested using the line laser scanner mounted on the robotic arm to obtain a local point cloud;

[0081] Specifically,

[0082] Two viewpoints to be tested are selected, requiring the viewpoints to be located at both ends of the part to be tested and to contain as much geometric information as possible; the scanner mounted on the robotic arm is manually operated to rotate 180° around the scanning direction at the viewpoints to be tested to obtain two local point clouds.

[0083] Step S3: Generate a global point cloud of the part to be tested based on the part's CAD model;

[0084] Specifically,

[0085] Specifically, step S3 involves importing the CAD model of the part to be tested into the simulation software, and generating a global point cloud of the part based on the CAD model in the software.

[0086] Step S4: Register the global point cloud of the part to be tested to the local point cloud of the scanned part to obtain the transformation matrix T1 between the two.

[0087] Figure 3 This is a flowchart of the point cloud registration algorithm based on surface shape feature descriptors in step S4, combined with... Figure 3 As shown, step S4 is explained as follows:

[0088] Specifically, the registration of the global point cloud to the local scanned point cloud is achieved by using a point cloud registration algorithm based on surface shape feature descriptors. The local point cloud obtained by scanning is located in the coordinate system of the C-Track tracking system. The coordinate transformation matrix from the workpiece coordinate system to the tracking system coordinate system is obtained through registration.

[0089] in,

[0090] The point cloud registration algorithm based on surface shape feature descriptors is as follows:

[0091] Step S41: Perform voxel downsampling on the local point cloud and the global point cloud;

[0092] Step S410, voxelize the point cloud.

[0093] Step S411: Take the average or weighted average of the points contained in each voxel to obtain a new point, which replaces all the points in the original voxel. By downsampling voxels, the number of points is reduced, and the calculation speed is improved.

[0094] Step S42: Using the Internal Shape Descriptor (ISS) algorithm to represent the solid geometry, the point cloud feature points containing rich geometric information are solved, further reducing the number of points to be processed.

[0095] Step S43: For the feature points in the point cloud, obtain the corresponding surface shape feature descriptor SSFD = {d1,d2,a1,a2,a3,c,o,p} respectively;

[0096] Where d1 represents the distance from the feature point to the centroid of the point cloud. Assume the coordinates of the feature point are (x1, y1, z1) and the coordinates of the centroid of the point cloud are (x2, y2, z2), as shown in formula (1):

[0097]

[0098] d2 represents the average distance between the feature point and the centroids of its neighborhood with different radii, as shown in formula (2):

[0099]

[0100] Where D1 represents the distance from the feature point to the centroid of the small-radius neighborhood point cloud, and D2 represents the distance from the feature point to the centroid of the large-radius neighborhood.

[0101] a1 represents the angle between the feature point normal and the line connecting the feature point and the centroid of the point cloud, as shown in formula (3):

[0102]

[0103] Where v1 represents the feature point normal vector, and v2 represents the line vector connecting the feature point and the centroid of the point cloud.

[0104] a2 represents the average of the sum of the angles between the feature point normal and the neighboring point cloud normal. Each angle is solved according to formula (3), and the average value is calculated according to formula (4).

[0105]

[0106] a3 represents the average of the sum of the angles between the feature point normal and the line connecting the neighboring point cloud, which is solved according to formulas (3) and (4);

[0107] c represents the curvature change at the feature point, as shown in formula (5):

[0108]

[0109] o represents the total variance of the point cloud, which has a strong ability to describe the surface undulation of the point cloud, as shown in formula (6):

[0110]

[0111] p represents the flatness of the point cloud, which can effectively represent the flatness of the fitted surface in the neighborhood of that point, as shown in formula (7):

[0112]

[0113] Where λ1, λ2, and λ3 are eigenvalues ​​based on the covariance matrix;

[0114] Step S44: After obtaining the surface shape feature descriptors corresponding to the feature points respectively, perform feature matching between the obtained local point cloud feature point surface shape feature descriptors and the global point cloud feature point surface shape feature descriptors to obtain the initial matching relationship.

[0115] Step S45: Eliminate incorrect matching point pairs using distance constraints;

[0116] Step S46: After obtaining the correct matching relationship, the coordinate transformation is performed by least squares method to obtain the optimal transformation matrix, thus completing the coarse registration of the point cloud.

[0117] Step S47: Based on this, the iterative nearest point algorithm is used to complete the fine registration of the point cloud;

[0118] The registration process effect diagram is as follows Figures 4-9 As shown.

[0119] Step S5: Manually operate the robotic arm to drive the line laser scanner to scan the base of the robotic arm and establish the robot's base coordinate system;

[0120] Specifically,

[0121] The robotic arm is manually operated to drive the line laser scanner to scan the base of the robotic arm. At this time, the point cloud of the scanned robotic arm base is located in the coordinate system of the tracking system. The base coordinate system of the robotic arm in the coordinate system of the tracking system is constructed by creating relevant entity constraints through the point cloud obtained by scanning.

[0122] Step S6: Solve the transformation relationship between the C-Track coordinate system and the robot base coordinate system to obtain the transformation matrix T2.

[0123] Figure 10 A schematic diagram illustrating the positional relationship between the C-Track coordinate system and the robot's base coordinate system, as shown below. Figure 10 As shown,

[0124] Specifically,

[0125] Given the origin coordinates of the C-Track coordinate system and the robot base coordinate system, and the directions of each axis, using formula (8),

[0126] (9) and (10) yield the transformation matrix T2 of both;

[0127] R = [X2,Y2,Z2] × [X1,Y1,Z1] T (8)

[0128] t = O2 - R × O1 (9)

[0129]

[0130] Step S7: Based on T1 and T2, perform coordinate transformation to transform the coordinate system of the part to the base coordinate system of the robotic arm, thereby achieving the pre-positioning of the part to be measured.

[0131] Figure 11 A diagram illustrating coordinate transformation is shown below. Figure 11 As shown,

[0132] Specifically,

[0133] Transformation matrix T1 from the workpiece coordinate system to the C-Track tracking system coordinate system, and transformation matrix T2 from the C-Track tracking system coordinate system to the robot arm base coordinate system, assuming A is the workpiece coordinate system, A * Using the robot arm's base coordinate system, coordinate transformation is performed using formula (11).

[0134] A * =T2T1A (11)

[0135] It can successfully transform the coordinate system of the part to the coordinate system of the robot, thereby realizing the pre-positioning of the part to be tested.

[0136] The above description of the disclosed embodiments enables those skilled in the art to implement or use this application. The described embodiments are merely some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for pre-positioning of a part to be measured based on a point cloud surface shape feature descriptor registration algorithm, characterized in that, The method comprises the following steps: Step S1, placing the part to be measured on a workbench; Step S2, manually operating a mechanical arm to scan the part to be measured by a line laser scanner carried by the mechanical arm to obtain a local point cloud; Step S3, generating a global point cloud of the part to be measured based on a CAD model of the part; Step S4, registering the global point cloud of the part to be measured to the local point cloud of the scanned part to obtain a transformation matrix T1 therebetween; Specifically, the registration of the global point cloud to the local scanned point cloud is achieved by a point cloud registration algorithm based on a surface shape feature descriptor, and the local point cloud obtained by scanning is located in a coordinate system of a C-Track tracking system, and the coordinate conversion matrix of the workpiece coordinate system to the tracking system coordinate system is obtained through registration; Wherein, The point cloud registration algorithm based on the surface shape feature descriptor specifically comprises: Step S41, voxel down-sampling the local point cloud and the global point cloud; Step S410, voxelizing the point cloud, Step S411, taking an average or a weighted average of the points contained in each voxel to obtain a new point to replace all the points in the original voxel, thereby reducing the number of points through voxel down-sampling and improving the operation speed; Step S42, solving the point cloud feature points containing rich geometric information by an internal shape descriptor algorithm representing a three-dimensional geometric shape, and further reducing the number of processing points; Step S43, respectively calculating the corresponding surface shape feature descriptors SSFD={d1,d2,a1,a2,a3,c,o,p} for the point cloud feature points; Wherein, d1 represents the distance from the feature point to the point cloud centroid, assuming that the feature point coordinate is (x1, y1, z1) and the point cloud centroid coordinate is (x2, y2, z2), as shown in formula (1): d2 represents the average distance from the feature point to the centroid of the different radius neighborhood, as shown in formula (2): Wherein, D1 represents the distance from the feature point to the small radius neighborhood point cloud centroid, and D2 represents the distance from the feature point to the large radius neighborhood centroid; a1 represents the angle between the feature point normal and the connecting line between the feature point and the point cloud centroid, as shown in formula (3): Wherein, v1 represents the feature point normal vector, and v2 represents the connecting line vector between the feature point and the point cloud centroid; a2 represents the average of the sum of the angles between the feature point normal and the neighborhood point cloud normal, which is solved according to formula (3) and averaged according to formula (4); a3 represents the average of the sum of the angles between the feature point normal and the neighborhood point cloud connecting line, which is solved according to formula (3) and formula (4); c represents the curvature change at the feature point, as shown in formula (5): o represents the point cloud total variance, which has the ability to describe the degree of surface fluctuation of the point cloud, as shown in formula (6): p represents the point cloud flatness, which can effectively represent the flatness of the fitting surface in the neighborhood of the point, as shown in formula (7): Wherein, λ1, λ2, λ3 are eigenvalues based on the covariance matrix; Step S44, after the surface shape feature descriptors of the feature points are respectively calculated, the feature matching is performed between the surface shape feature descriptors of the local point cloud feature points and the surface shape feature descriptors of the global point cloud feature points to obtain an initial matching relationship; Step S45, eliminating the wrong matching point pairs through distance constraint; Step S46, after obtaining the correct matching relationship, the optimal transformation matrix is obtained by coordinate transformation through the least square method, and the point cloud coarse registration is completed; Step S47, on this basis, the point cloud fine registration is completed using the iterative closest point algorithm; Step S5, the mechanical arm is manually operated to drive the line laser scanner to scan the mechanical arm base, and the robot base coordinate system is established; Step S6, the conversion relationship between the C-Track coordinate system and the robot base coordinate system is solved, and the transformation matrix T2 of the two is obtained; Step S7, based on T1 and T2, the coordinate transformation is carried out, the part coordinate system is transformed into the mechanical arm base coordinate system, and then the pre-positioning of the measured part is realized.

2. The method of claim 1, wherein, In step S2, two measured viewpoints are selected, the viewpoints are required to be located at both ends of the measured part, and more geometric information is required to be contained as much as possible; the scanner carried by the mechanical arm is manually operated to rotate 180° around the scanning direction at the measured viewpoint, and two local point clouds are obtained.

3. The method of claim 1, wherein, Step S3 is specifically that the CAD model of the measured part is imported into the simulation software, and the global point cloud of the part is generated based on the CAD model of the measured part in the software.

4. The method of claim 1, wherein, Step S5 is specifically that the mechanical arm is manually operated to drive the line laser scanner to scan the mechanical arm base, and the point cloud of the scanned mechanical arm base is located in the tracking system coordinate system, and the point cloud obtained by scanning is used to create related entity constraints to build the mechanical arm base coordinate system in the tracking system coordinate system.

5. The method of claim 1, wherein, Step S6 is specifically that the origin coordinates and the directions of the axes of the C-Track coordinate system and the robot base coordinate system are known, and the transformation matrix T2 of the two is obtained through formulas (8), (9) and (10); R = [X2, Y2, Z2] x [X1, Y1, Z1] T (8) t=O2-R×O1 (9) In formula (8), R is the rotation matrix between the two coordinate systems, X1, Y1 and Z1 are the direction vectors of the three coordinate axes of the C-Track coordinate system, X2, Y2 and Z2 are the direction vectors of the three coordinate axes of the robot base coordinate system, the upper right subscript T represents the transpose of the vector or matrix, t is the translation matrix between the two coordinate systems in formula (9), O1 is the origin coordinate of the C-Track coordinate system, O2 is the origin coordinate of the robot base coordinate system, and T2 in formula (10) represents the homogeneous transformation matrix composed of the rotation matrix R and the translation matrix t.

6. The method of claim 1, wherein, Step S7 is specifically that A * A * = T2T1A (11) The part coordinate system can be successfully transformed into the robot coordinate system, and then the pre-positioning of the measured part is realized.

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