CN115014248A - A method for identification and flatness determination of laser projection lines - Google Patents

Abstract

The invention relates to the technical field of laser detection, in particular to a method for identifying a laser projection line and judging the flatness, which vertically shoots a laser line image through a camera, firstly extracts the color, the outline and the characteristics of the laser projection line, carries out filtering treatment on the laser projection line to reserve effective pixels of the laser main line, uses the effective pixels, then carries out plane fitting on all effective pixels by using a least square method, calculates the current plane discrete degree, simultaneously simulates a three-dimensional image when the levelness deviates by 20 seconds, calculates the plane discrete degree when the levelness deviates by 20 seconds, and contrasts and judges whether the flatness of the laser projection line is qualified or not; the method can detect the brightness and the flatness of the laser projection line, and compares the brightness and the flatness with standard parameters to judge the qualification degree of the laser head.

Description

A method for identification and flatness determination of laser projection lines

technical field

The invention relates to the technical field of laser detection, in particular to a method for identifying and flatness determination of a laser projection line.

Background technique

Laser line projection instrument, also known as laser marking instrument or laser level, is actually a type of measuring instrument made by installing and fixing a laser device on the telescope barrel of an ordinary level. The instrument emits a laser beam, and makes the laser beam pass through the prism light guide system to form a laser surface to project horizontal and vertical laser lines, and finally achieve the purpose of measurement. Among them, the multi-functional floor-to-wall laser line projection instrument with twelve lines is the most popular at present, and the quality of judgment is mainly measured by the laser head. Therefore, in order to ensure that the factory can provide a qualified laser line projection instrument, it is necessary to test the pass rate of the laser head before leaving the factory, so as to exclude the unqualified laser head.

The horizontal offset angle of the laser emitted by the laser head is an important factor in judging whether the laser head is qualified or not. The horizontal offset angle within 20 seconds is qualified, and if it is greater than 20 seconds, it is unqualified. The existing laser head incoming inspection is all manual inspection. Manually adjust the laser head to a fixed position through a manual turntable, and judge whether it is qualified or not by observing the relative position of the laser line in the screen. Due to factors such as human subjective judgment, human eye fatigue and slow manual adjustment, errors in detection may occur. At the same time, if the laser is directly exposed to human eyes for a long time, it will cause burns and other hazards, and there is only one detection standard and a single detection item. .

Therefore, a technique is urgently needed to solve this problem.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the above-mentioned problems of the prior art, and to provide a method for identifying and judging the flatness of a laser projection line. The line flatness overcomes the singleness of judging the offset position of the laser line by the comparison method in the previous detection method, and formulates the inspection standard, which improves the scientificity and accuracy of the detection.

The above purpose is achieved through the following technical solutions:

A method for identifying and judging flatness of a laser projection line, comprising the following steps:

Step (1) takes the light source point of the laser head to be detected as the center origin, and arranges 4 parallel light pipes at equal distances around the laser head to be detected, and the included angle between the adjacent parallel light pipes is 90°, so Cross tick marks are respectively provided on the reticle in the collimator light pipe, and the center points of the 4 cross tick marks are located on the same horizontal plane as the light source point; the image of the reticle tick marks on each of the reticle is obtained to obtain 4 tick images;

Step (2) extracts skeletons respectively to 4 described tick marks images in step (1), and records the pixel coordinates of the center point of the cross tick marks and the pixel spacing of two minimum scales;

Step (3) lighting the to-be-detected laser head, acquiring the laser line images projected on the 4 described reticles, and obtaining 4 laser line sample images;

Step (4) extracts characteristic colors from 4 described laser line sample images in step (3) to obtain laser line images;

Step (5) segmenting the laser line image described in step (4), extracting skeleton features, and obtaining an image of the center line of the laser line;

Step (6) extracts the sub-pixel precise contour from the outer contour area of the laser line in the laser line image described in the step (4), and performs approximate calculation straight line calculation to the XLD of the line segment to obtain a complete laser contour line;

Step (7) segmenting the laser line target area image of the laser line sample image described in step (3), calculating the average gray value of the characteristic area, indicating the brightness of each laser line;

In step (8), threshold segmentation is performed on the four laser line sample images in step (3), and the effective pixel points are converted into coordinates, and the pixel coordinates of the center point of the cross tick mark in step (2) are used as the origin. , change the pixel coordinate to the position coordinate, and bring it into the three-dimensional space coordinate system, and use the fitting space plane algorithm to calculate the discrete degree of the plane, indicating the flatness σ;

Step (9) For all the pixels in the area image of the laser line in step (3), simulate the three-dimensional image when the deviation is 20 seconds, calculate the flatness σ ₂₀ when the deviation is 20 seconds, and compare the flatness in step (8) σ,

If σ<σ ₂₀ , it is qualified;

If σ≥σ ₂₀ , it is unqualified.

Further, the step (2) is specifically:

Let S(X) represent the skeleton of X, then the skeleton expression of the tick mark image is:

运算将X腐蚀成空集前的最后一次迭代次数，

表示连续n次用B对X进行腐蚀，即where Sn(X) is the _nth skeleton subset of X, and N is

The last number of iterations before the operation erodes X into an empty set,

Indicates that X is eroded with B for n consecutive times, that is,

Distinguish the horizontal scale line and the vertical scale line from S _n (X), after judging its angle, let deg _n be the angle of the nth skeleton, if deg _n >5°, it is the vertical scale line, It is represented by SV _n (X), if deg _n < 5°, it is a horizontal scale line, represented by SH _n (X); traverse all the scale lines, take the longest vertical scale line SH _max (X) and the longest The horizontal scale line SV _max (X), record their intersection coordinates (u _0i , v _0i ), where (u ₀ , v ₀ ) is the pixel coordinate of the center point of the cross scale line, and i is the camera number.

Further, the characteristic color of the laser line sample image extraction described in step (4) is specifically: in the RGB color model, the R, G, B color components do not affect each other, and because the laser main line color is green, the G component is separated and converted. A grayscale image is useful for color feature extraction.

Further, in the step (7), set Ni as the number of pixel points in the area, then the formula for calculating the laser brightness Li is:

where i is the camera number and j is the number of each pixel.

Further, the step (8) specifically includes the following steps:

Step (8-1) establishes a space coordinate system, takes (0, 0, 0) as the symmetrical midpoint, and assumes that the distance between the camera and the light source point arranged at the rear end of the collimated light pipe for taking pictures is D, then each The distance from the laser plane in the direction to the symmetrical midpoint is D; take the center intersection (u _0i , v _0i ) of each reticle as the coordinate origin, and perform coordinate transformation on the pixel points (u _j , v _j ) in the area , introduce the position coordinates (x _ij , y _ij , z _ij ) relative to the origin, where (u ₀ , v ₀ ) are the pixel coordinates of the center point of the cross tick mark;

Step (8-2) Establish the front view coordinates corresponding to the No. 1 camera, as follows:

x _1j =D

Establish the coordinates of the left image corresponding to the No. 2 camera, as follows:

y _2j = -D

Establish the coordinates of the rear image corresponding to camera 3, as follows:

x _3j = -D

Establish the coordinates of the right image corresponding to camera No. 4, as follows:

y _4j = -D

Step (8-3) Through the three-dimensional point cloud, the effective pixels (x _ij , y _ij , z _ij ) obtained by all cameras are placed in the three-dimensional coordinate system, and the least squares method is used to perform plane fitting to calculate the degree of plane dispersion. , the flatness σ is obtained.

Further, described step (8-3) is specifically:

Through the three-dimensional point cloud, the pixel points (x _ij , y _ij , z _ij ) within the threshold obtained by all cameras are placed in the three-dimensional coordinate system, and the plane equation in the defined space is Ax+By+Cz=0, here The standard space plane equation is defined as the following formula:

p(x, y, z)=ax-by+cz+1=0

In the formula, x, y, z are the three coordinate axes, a, b, c are the three coefficients of the space plane equation;

Let the point set M{(x ₁ , y ₁ , z ₁ ), (x ₂ , y ₂ , z ₂ ), ..., (x _n , y _n , z _n )}, its best fitting plane satisfy The following formula:

In the formula: p(x, y, z)=0, then:

成立，整理后得下式：Find 0 partial derivatives with respect to a, b, and c respectively, and satisfy

is established, the following formula is obtained after sorting:

Assume

but:

QX=K

The coefficients of the solved plane equation are:

X=Q ^-1 K

Bring the solved a, b, c into the plane equation, and draw the plane Ax+By+Cz=0 in the three-dimensional space coordinate system.

The flatness representation method is expressed in distance standard deviation as follows:

Among them, d _i is the distance from the effective pixel point to the fitting plane; _davg is the average distance from the effective pixel point to the fitting plane.

beneficial effect

The method for identifying and judging the flatness of a laser projection line provided by the present invention extracts the color, shape and texture features of the laser projection line, uses the method of plane fitting for processing, and adds laser brightness and laser stray light stripes at the same time. Detection, based on this multi-feature fusion method, makes the detection of the laser head more accurate. This method saves the time of manual adjustment, and obtains scientific standard parameters by collecting a large amount of data for different laser heads, and uses an algorithm to accurately distinguish qualified and unqualified laser heads, in order to improve the detection of incoming materials for laser heads. make some contribution.

Description of drawings

1 is a flowchart of a method for identifying and flatness determination of a laser projection line according to the present invention;

2 is a schematic diagram of an image of a cross scale line on a reticle in a method for identifying and flatness determination of a laser projection line according to the present invention;

3 is a schematic diagram of an image of a cross tick mark on a reticle extracted after preprocessing in a method for identifying and flatness judging of a laser projection line according to the present invention;

4 is a schematic diagram of contour extraction of a laser projection line in a method for identifying and flatness determination of a laser projection line according to the present invention;

5 is a fitting plan view of four laser projection line images in a method for identifying and flatness determination of a laser projection line according to the present invention;

FIG. 6 is a schematic diagram of final segmented display brightness results in a method for identifying and flatness determination of a laser projection line according to the present invention.

Detailed ways

The present invention will be described in further detail below according to the accompanying drawings and embodiments. The described embodiments are only some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in Figures 1 and 2, a method for identifying and judging flatness of a laser projection line includes the following steps:

Step (1) takes the light source point of the laser head to be detected as the center origin, and arranges 4 parallel light pipes at equal distances around the laser head to be detected, and the included angle between the adjacent parallel light pipes is 90°, so Cross tick marks are respectively provided on the reticle in the collimator light pipe, and the center points of the 4 cross tick marks are located on the same horizontal plane as the light source point; the image of the reticle tick marks on each of the reticle is obtained to obtain 4 scale line images; specifically, the collimating light pipe described in this embodiment is provided with a reticle, a light source and an eyepiece, and a camera for taking pictures is provided at the rear end of the eyepiece, and the four collimating light pipes correspond to No. 1 respectively. Camera, Camera 2, Camera 3, and Camera 4; when processing reticle images, you need to turn on the light source and obtain reticle images (ie tick images) in a bright environment; combine the Halcon18 library to process reticle and reticle images in real time. Laser projection line image, obtain the brightness information of the laser projection line and calculate the flatness, the laser projection line image sample is from a camera that is photographed in parallel in a dark environment;

In this embodiment, the angle of the laser head to be detected is adjusted through a three-dimensional angular turntable, so that the laser line emitted by it can be well projected onto the reticle; the three-dimensional angular turntable is controlled by three servo motors, including The first servo motor that controls the X-direction rotation angle, the second servo motor that controls the Y-direction rotation angle, and the third servo motor that controls the fixture (used to clamp or fix the laser to be detected) for rotation, and the three servo motors are connected to the servo control.

In step (2), the skeletons are respectively extracted from the four tick marks in step (1), and the pixel coordinates of the center point of the tick marks and the pixel spacing of the two minimum scales are recorded; the tick marks in this embodiment are The pixel coordinates of the center point are marked as (u ₀ , v ₀ ), and the pixel spacing between the two smallest scales is recorded as D _min , and the actual reticle scale size is 0.1 mm, that is, the pixel distance corresponding to 0.1 mm is D _min ;

Specifically, let S(X) represent the skeleton of X, then the skeleton expression of the tick mark image is:

运算将X腐蚀成空集前的最后一次迭代次数，

表示连续n次用B对X进行腐蚀，即where Sn(X) is the _nth skeleton subset of X, and N is

The last number of iterations before the operation erodes X into an empty set,

Indicates that X is eroded with B for n consecutive times, that is,

Distinguish the horizontal scale line and the vertical scale line from S _n (X), after judging its angle, let deg _n be the angle of the nth skeleton, if deg _n >5°, it is the vertical scale line, It is represented by SV _n (X), if deg _n < 5°, it is a horizontal scale line, represented by SH _n (X); traverse all the scale lines, take the longest vertical scale line SH _max (X) and the longest The horizontal scale line SV _max (X), record their intersection coordinates (u _0i , v _0i ), where (u ₀ , v ₀ ) is the pixel coordinate of the center point of the cross scale line, and i is the camera number;

Step (3) lighting the laser head to be detected, acquiring the laser line images projected on the 4 reticles, and obtaining 4 laser line sample images; the laser line sample images are from parallel shooting in a dark environment camera;

Step (4) extracts characteristic colors from 4 described laser line sample images in step (3) to obtain laser line images;

Specifically, the R, G, and B color components in the RGB color model do not affect each other, which is beneficial for processing the color and brightness of the image. Since the color of the main line of the laser is green, the G component is separated and converted into a grayscale image, which is more conducive to the extraction of color features.

Step (5) segmenting the laser line image described in step (4), extracting skeleton features, and obtaining an image of the center line of the laser line;

Step (6) extracts the sub-pixel precise contour from the outer contour area of the laser line in the laser line image described in the step (4), and performs approximate calculation straight line calculation to the XLD of the line segment to obtain a complete laser contour line;

Step (7) segmenting the laser line target area image of the laser line sample image described in step (3), calculating the average gray value of the characteristic area, indicating the brightness of each laser line;

In this step, set Ni as the number of pixels in the area, then the _formula for calculating the laser brightness _Li is:

where i is the camera number and j is the number of each pixel.

In step (8), threshold segmentation is performed on the four laser line sample images in step (3), and the effective pixel points are converted into coordinates, and the pixel coordinates of the center point of the cross tick mark in step (2) are used as the origin. , change the pixel coordinate to the position coordinate, and bring it into the three-dimensional space coordinate system, and use the fitting space plane algorithm to calculate the discrete degree of the plane, indicating the flatness σ;

Specifically, this step specifically includes the following steps:

Step (8-1) establishes a space coordinate system, takes (0, 0, 0) as the symmetrical midpoint, and assumes that the distance between the camera and the light source point arranged at the rear end of the collimated light pipe for taking pictures is D, then each The distance from the laser plane in the direction to the symmetrical midpoint is D; take the center intersection (u _0i , v _0i ) of each reticle as the coordinate origin, and perform coordinate transformation on the pixel points (u _j , v _j ) in the area , introduce the position coordinates (x _ij , y _ij , z _ij ) relative to the origin, where (u ₀ , v ₀ ) are the pixel coordinates of the center point of the cross tick mark;

Step (8-2) Establish the front view coordinates corresponding to the No. 1 camera, as follows:

x _1j =D

Establish the coordinates of the left image corresponding to the No. 2 camera, as follows:

y _2j = -D

Establish the coordinates of the rear image corresponding to camera 3, as follows:

x _3j = -D

Establish the coordinates of the right image corresponding to camera No. 4, as follows:

y _4j = -D

Step (8-3) Through the three-dimensional point cloud, the effective pixels (x _ij , y _ij , z _ij ) obtained by all cameras are placed in the three-dimensional coordinate system, and the least squares method is used to perform plane fitting to calculate the degree of plane dispersion. , the flatness σ is obtained.

Further, described step (8-3) is specifically:

Through the three-dimensional point cloud, the pixel points (x _ij , y _ij , z _ij ) within the threshold obtained by all cameras are placed in the three-dimensional coordinate system, and the plane equation in the defined space is Ax+By+Cz=0, here The standard space plane equation is defined as the following formula:

p(x, y, z)=ax-by+cz+1=0

In the formula, x, y, z are the three coordinate axes, a, b, c are the three coefficients of the space plane equation;

Let the point set M{(x ₁ , y ₁ , z ₁ ), (x ₂ , y ₂ , z ₂ ), ..., (x _n , y _n , z _n )}, its best fitting plane satisfy The following formula:

In the formula: p(x, y, z)=0, then:

成立，整理后得下式：Find 0 partial derivatives with respect to a, b, and c respectively, and satisfy

is established, the following formula is obtained after sorting:

Assume

but:

QX=K

The coefficients of the solved plane equation are:

X=Q ^-1 K

Bring the solved a, b, c into the plane equation, and draw the plane Ax+By+Cz=0 in the three-dimensional space coordinate system.

The flatness representation method is expressed in distance standard deviation as follows:

Among them, d _i is the distance from the effective pixel point to the fitting plane; _davg is the average distance from the effective pixel point to the fitting plane.

Step (9) For all the pixels in the area image of the laser line in step (3), simulate the three-dimensional image when the deviation is 20 seconds, calculate the flatness σ ₂₀ when the deviation is 20 seconds, and compare the flatness in step (8) σ,

If σ<σ ₂₀ , it is qualified;

If σ≥σ ₂₀ , it is unqualified.

Since the laser line projected by the laser head should be a horizontal plane, the main error lies in the angle error projected by the laser. The factory process standard is that the deviation is less than 20 seconds. Therefore, the effective pixel points obtained by the current camera are used to simulate the laser line. A position image with a deviation of 20 seconds on the reticle, and the pixels of this image are placed in the three-dimensional space coordinate system, and the least square method is used to perform plane fitting to calculate the plane dispersion degree σ ₂ . Bring the image in one of the directions into the coordinates with an error of 20 seconds. Here we change the coordinates in camera 1, corresponding to (u ₀₁ , v ₀₁ ) in step F to (u ₀₁ +D _min , v ₀₁ ) ), and then calculate σ ₂ :

In contrast, if σ<σ ₂ , it means that the levelness is qualified; if σ>σ ₂ , it means that the levelness is unqualified.

The above description is only to illustrate the embodiments of the present invention, and is not intended to limit the present invention. For those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention, All should be included within the protection scope of the present invention.

Claims (6)

1. A method for identifying a laser projection line and judging flatness is characterized by comprising the following steps:

the method comprises the following steps that (1) a light source point of a laser head to be detected is taken as a central original point, 4 parallel light tubes are arranged on the periphery of the laser head to be detected at equal intervals, an included angle between every two adjacent parallel light tubes is 90 degrees, cross scale marks are respectively arranged on a dividing plate in each parallel light tube, and the central points of the 4 cross scale marks and the light source point are located on the same horizontal plane; acquiring a cross scale line image on each reticle to obtain 4 scale line images;

respectively extracting skeletons from the 4 scale mark images in the step (1), and recording the pixel coordinate of the central point of the cross scale mark and the pixel distance of two minimum scales;

step (3) lightening the laser head to be detected, and acquiring laser line images projected on 4 reticles to obtain 4 laser line sample images;

step (4) extracting characteristic colors of the 4 laser line sample images in the step (3) to obtain laser line images;

step (5) segmenting the laser line image in the step (4), extracting skeleton characteristics and obtaining an image of a laser line central line;

step (6) extracting sub-pixel precise contours from the outer contour region of the laser line in the laser line image in the step (4), and performing approximate calculation linear calculation on XLD of the line segment to obtain a complete laser contour line;

step (7) dividing the laser line target area image of the laser line sample image in the step (3), calculating the average gray value of the characteristic area, and expressing the brightness of each section of laser line;

step (8) performing threshold segmentation on the 4 laser line sample images in the step (3), performing coordinate conversion on effective pixel points, changing pixel coordinates into position coordinates by taking the pixel coordinates of the central point of the cross scale line in the step (2) as an original point, and bringing the position coordinates into a three-dimensional space coordinate system, and calculating the dispersion degree of a plane by using a fitting space plane algorithm to express the flatness sigma;

step (9) simulating a three-dimensional image when the deviation is 20 seconds for all pixel points in the area image of the laser line in the step (3), and calculating the planeness sigma when the deviation is 20 seconds ₂₀ Comparing the flatness sigma in the step (8),

if σ < σ ₂₀ If so, the product is qualified;

if sigma is larger than or equal to sigma ₂₀ And then the test is not qualified.

2. The method as claimed in claim 1, wherein the step (2) is specifically as follows:

assuming that S (X) represents the skeleton of X, the skeleton expression of the scale line image is as follows:

wherein S is _n (X) is the nth backbone subset of X, N is

The operation erodes X the number of last iterations before empty set,

denotes etching X with B n successive times, i.e.

From S _n (X) distinguishing the horizontal scale mark and the vertical scale mark, judging the angle of the horizontal scale mark and the vertical scale mark, and setting deg _n Angle of the nth skeleton, if deg _n More than 5 degrees, the vertical scale mark is formed, and SV is used _n (X) represents, if deg _n Less than 5 deg. is horizontal scale mark, using SH _n (X) represents; traversing all the scale marks, and taking the longest vertical scale mark SH _max (X) and the longest horizontal scale line SV _max (X) recording their intersection coordinates (u) _0i ，v _0i ) Wherein (u) ₀ ，v ₀ ) And i is the pixel coordinate of the center point of the cross scale line, and i is the camera number.

3. The method as claimed in claim 1, wherein the step (4) of extracting the characteristic color from the laser line sample image comprises: r, G, B color components in the RGB color model are not affected each other, and because the laser main line color is green, the G component is separated and converted into a gray scale map, which is beneficial to extracting color features.

4. The method as claimed in claim 1, wherein in the step (7), N is set _i Calculating the laser brightness L for the number of pixel points in the region _i The formula of (1) is:

where i is the camera number and j is the number of each pixel.

5. The method as claimed in claim 1, wherein the step (8) comprises the following steps:

step (8-1) establishing a space coordinate system, taking (0, 0, 0) as a symmetrical midpoint, setting the distance from a camera for taking pictures, which is arranged at the rear end of the collimator tube, to a light source point to be D, and setting the distance from the laser plane distance in each direction to the symmetrical midpoint to be D; with each reticle center intersection (u) _0i ，v _0i ) As the origin of coordinates, to pixel points (u) in the region _j ，v _j ) Performing coordinate conversion, introducing the position coordinate (x) converted to relative to the origin _ij ，y _ij ，z _ij ) Wherein (u) ₀ ，v ₀ ) Is the pixel coordinate of the central point of the cross scale mark;

and (8-2) establishing a front view coordinate corresponding to the camera No. 1, wherein the front view coordinate is as follows:

x _1j ＝D

establishing the coordinates of the left image corresponding to the camera No. 2 as follows:

y _2j ＝-D

establishing the coordinates of the rear graph corresponding to the camera No. 3 as follows:

x _3j ＝-D

establishing the coordinates of a right image corresponding to the camera No. 4 as follows:

y _4j ＝-D

step (8-3) obtaining effective pixel points (x) obtained by all cameras through three-dimensional point cloud _ij ，y _ij ，z _ij ) And placing the three-dimensional coordinate system in a three-dimensional coordinate system, performing plane fitting by using a least square method, and calculating the plane dispersion degree to obtain the flatness sigma.

6. The method as claimed in claim 4, wherein the step (8-3) is specifically as follows:

obtaining pixel points (x) within a threshold value acquired by all cameras through three-dimensional point cloud _ij ，y _ij ，z _ij ) Put into a three-dimensional coordinate system, the plane equation in the defined space is Ax + By + Cz ═ 0, and here, the standard spatial plane equation is defined as follows:

p(x，y，z)＝ax-by+cz+1＝0

in the formula, x, y and z are respectively 3 coordinate axes, and a, b and c are respectively 3 coefficients of a space plane equation;

set point set M { (x) ₁ ，y ₁ ，z ₁ )，(x ₂ ，y ₂ ，z ₂ )，...，(x _n ，y _n ，z _n ) The best fit plane of which satisfies the following equation:

in the formula: when p (x, y, z) is 0, then:

respectively calculating 0 partial derivative for a, b and c, and satisfying

If true, the following formula is obtained after finishing:

is provided with

X＝[a，b，c] ^T ，

Then:

QX＝K

the coefficients of the plane equation are solved as follows:

X＝Q ^-1 K

and substituting the solved a, b and c into a plane equation, and drawing a plane Ax + By + Cz as 0 in a three-dimensional space coordinate system.

The flatness representation is expressed in terms of distance standard deviation, as follows:

wherein d is _i The distance from the effective pixel point to the fitting plane is obtained; d _avg And the average distance from the effective pixel point to the fitting plane.

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