CN101566461B - Method for quickly measuring blade of large-sized water turbine - Google Patents
Method for quickly measuring blade of large-sized water turbine Download PDFInfo
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Abstract
The invention discloses a method for quickly measuring a blade of a large-sized water turbine, which is characterized by comprising the following steps: firstly, sticking a mark point to the surface of the blade, then shooting a group of photos from different angles as measured primary data, and inputting the data to a computer to carry out analytic processing; by carrying out image detection for the group of photos in a measurement software, identifying the mark point in each photo and positioning the center of the mark point, and matching the mark points with the same name; finally, reconstructing a three-dimensional coordinate of corresponding object points according to a plurality of two-dimensional coordinates of the mark points, fitting a sparse framework model of a target by the reconstructed three-dimensional mark points, then scanning the surface of the blade block by block by using a binocular grating scanning method to acquire a local dense point cloud, and aligning the dense point cloud to an overall coordinate system according to the local mark points to acquire a dense point model of the blade; and by comparing the dense point model with a CAD designed model after aligning, calculating a three-dimensional processing error of the surface of a workpiece.
Description
Technical field
The present invention relates to a kind of method that blade of large-sized water turbine is measured fast, particularly a kind ofly use the method that vision measurement technology centering blade of large-sized water turbine size and profile are measured fast.
Background technology
For the large-sized water turbine unit that involves great expense, blade is the hydraulic turbine " heart ", and quality that it is surperficial and manufacturing accuracy will directly have influence on hydraulic performance, the generating efficiency of whole unit, the stability and the serviceable life of running.But because the profile of blade of large-sized water turbine be complicated free form surface, its volume and weight is huge, therefore in the process of making and processing, is in the industry a difficult problem to the full-scale detection of blade overall dimensions and profile always.
Document " present Research and the development trend of rotary wheel of water turbine maintenance equipment " is (what Tsing-Hua University etc., big motor technology, 2003) summed up several main methods in the current blade of large-sized water turbine detection, had: three-dimensional template method, template method, broach method, three coordinate measuring machine method, mechanical arm method, laser interferometer method, photoelectricity footpath latitude instrument method, laser tracker method, light cross-section method and underwater photography method etc. by the equipment and instrument difference of using.The employed combination model of three-dimensional template method is manual the manufacturing, and poor rigidity, easy deformation progressively are eliminated.Though three coordinate measuring machine precision height, to measurement environment require high, not portable, measurement range is little; Particularly huge three coordinate machine is costliness extremely, and turbine blade is put on the three-dimensional board and adjusted difficulty, also needs foundation and the measurement programming of carrying out detection coordinates system consuming time early stage.Joint arm, laser tracker, transit can carry out high-acruracy survey at the scene, but owing to be the point-to-point measurement mode, efficiency of measurement is on the low side, can't reach full-scale anti-design and the required point of density cloud of production testing asked and gather requirement.Therefore present research focus concentrates on the non-contact optical measuring method that merges computer vision technique and photogrammetric technology, this method has rigorous theoretical foundation, range has bigger elasticity, and quite high precision and higher efficiency of measurement can be provided, be to solve a kind of feasible scheme of the three-dimensional full-scale detection difficult problem of medium-and-large-sized workpiece.
Be meant based on the detection system of computer vision methods and utilize ccd video camera as imageing sensor, technology such as integrated use Flame Image Process, precision measurement are carried out the detection system of noncontact two dimension or three-dimensional coordinate measurement.Document " vision measurement technology and application " (leaf good reputation academician, Chinese engineering science, 1999) has been summed up the different directions and the application thereof of vision measurement technical development, has proposed several vision-based detection prototype systems.But because the restriction of conditions such as the operational speed of a computer and Image Acquisition precision, the actual detection system is not employed.
In recent years, because the photoelectric technology of computer technology and aspects such as relevant optics, Digital Image Processing, theory on computer vision constantly develops, research has become possibility based on the large complicated carved three-dimensional measurement of optics, Digital Image Processing and theory on computer vision.Therefore, study new large complicated carved portable quick three-dimensional measuring method, and will detect standardization such as step, data processing, promptly have important significance for theories, have great practical value again based on optics, digital picture and visual information fusion.
Summary of the invention
At the profile of blade of large-sized water turbine in process and the detection problem of size, how to guarantee under the preceding topic that precision meets the demands, improve the speed that detects, reduce and measure cost, how to realize the on-the-spot interference such as vibration in the environment, temperature variation, humidity, dust that detect and avoid.The present invention proposes a kind ofly, and, can carry out on-site rapid measurement blade of large-sized water turbine size and profile through experimental verification based on photogrammetric and measuring method principle of stereoscopic vision.
For reaching above purpose, the present invention takes following technical scheme to be achieved:
A kind of method for quickly measuring blade of large-sized water turbine comprises the steps:
The first step, at surface and the placed around circular index point and the monumented point that has the annular coding of blade, monumented point comprises encoded point, non-encoded point; Monumented point is sticked on magnetic as on the rubber cushion, and be adsorbed on blade surface, put according to the requirement interval sticky cloth of back point of density cloud collecting device;
Second step, place overall scale, scale is a foundation of recovering the blade physical size, and its two ends are coding maker point or the non-coding maker points that fix, and the distance between the monumented point of two ends is through strict calibration;
The 3rd step, adopt special digital camera, comprehensive tested blade is taken pictures, obtain the one group of photo that comprises coding maker point, non-coding maker point, overall scale information;
The 4th step, the calculation flag point coordinate, operating measurement software, in computing machine, import the group of taking a picture, carry out Flame Image Process, measure the two-dimensional coordinate of monumented point in the group of photos, calculate the three-dimensional coordinate of all monumented points in the space according to two-dimensional coordinate then, non-coding maker point point cloud has promptly constituted the overall sparse point model of tested blade among the result, and this model carries out the foundation of world coordinates alignment after as next step local dense point cloud collection;
The 5th step, tested blade surface point of density cloud is gathered and alignment, adopt the binocular raster-scan method, take the strip encoding of investing body surface by projector synchronously with two cameras, Survey Software carries out obtaining behind three-dimensional coupling and the three-dimensional reconstruction monumented point and the point of density cloud of blade surface part automatically, and the world coordinates of finishing this local dense point cloud according to this local monumented point in the position of the sparse point model of the overall situation aligns; The above-mentioned binocular raster-scan method of repeated using obtains all local dense point clouds of world coordinates alignment.
The 6th step, pre-service of point of density cloud and modeling, because the blade point of density cloud model that obtains has certain data redundancy, before carrying out modeling, earlier it is handled, deletion lap point cloud, and each local dense point cloud merged, obtain the whole point of density cloud model of blade outer surface, also be the blade measurement model;
The 7th step, the coordinate system of blade measurement model with the blade cad model alignd, measurement model is carried out coordinate conversion;
The 8th step, blade measurement model and the contrast of blade cad model, two models are carried out simple vector subtract computing, can obtain each position of blade cast(ing) surface and the deviation that designs a model, realize and show by programming with the form of 3D, or, generate the deviation data of 2D by the sectional view of commercial comparison software according to each position and direction.
In the said method, described the 3rd step comprehensively takes pictures to tested blade, the shooting station location is set adopts three height that increase successively, and highly all around 360 degree, photographing request is as follows for each:
1) with maximal value in the three-dimensional chi of blade as the honest shooting of shooting distance.
2) make each monumented point captured as far as possible by the shooting station of 4 above diverse locations.
3) make the intersection angle of each monumented point at 60 °～120 ° as far as possible.
4) make the incident angle of each monumented point less than 45 ° as far as possible.
5) make each shooting station can both take as much as possible monumented point as far as possible, the overlapping and common point more than 60% is arranged between the photo that keeps adjacent shooting station to take.
Monumented point two-dimensional coordinate in the measurement group of photos in described the 4th step, concrete steps are as follows:
1) edge in the employing Canny algorithm detected image obtains the wide closure edge collection of single pixel;
2) calculate position weighted value with gradient magnitude as weights, marginal position made sub-pixel-level along gradient direction proofread and correct along gradient direction:
Wherein, d
iBe the distance of a pixel along gradient direction and detected marginal point, g
iIt is gradient magnitude;
3) adopt the circularity criterion to identify the ellipse that the edge is concentrated, and utilize following prior imformation to remove the ellipse of the condition that do not conform to, comprise that oval area is too little, elliptic contour is concavity, misclosure, too near with the adjacent ellipses distance;
4) adopt for twice least square fitting to go out oval center, get rid of the edge of distance after the match for the first time, carry out the match second time again greater than 3 times of standard deviations;
5) judge whether oval periphery has endless belt, if be not non-encoded point; If have then radially make the line of inner and outer boundary, the first-class distance samples of line 5 times, make comparisons with the intermediate value of 5 samplings and the gray scale threshold values of gauge point, greater than threshold values then this endless belt be encoded to 1, otherwise be 0; Per 36 ° (corresponding to 10 encoded points) repeat aforesaid operations, obtain the binary number of shape as " 0100100111 " after rotating a circle;
6) table look-up and obtain the ID of encoded point, if can not find out then regard non-encoded point as.
Compare with the three-dimensional template method of prior art, laser tracker method, joint arm method etc., the present invention is based on vision measuring method and have following advantage:
1, owing to adopt CCD, be the non-contact measurement mode, can not injure blade surface, also be not subjected to the influence of blade surface shape and roughness as sensor, can loss measurement equipment yet.
2, owing to adopting region-by-region scanning and aliging automatically by software, Measuring Time depends primarily on the blockette number of blade surface, can also adopt many scanning device concurrent workings to large-scale blade, with respect to the point-to-point measurement mode, in-site measurement efficient is higher, and the some cloud in later stage is handled and the model contrast can be left site disposal.
3, owing to adopt point of density cloud scan mode, be specially adapted to the numerous task of blade surface measurement point, measurement result is the blade complete model that the point of density cloud is represented, can carry out the measurement of any geometric sense on this basis.
4, because measurement result is complete blade triangular facet model, under the help of comparison software, can automatically carry out full-scale three-dimensional stratographic analysis, random customization deviation tolerance limit is carried out qualification determination, testing result is directly perceived, quick.
5, as the blade point cloud model of measuring intermediate result, can be used as raw data, carry out reverse engineering design.
6, owing to adopt CCD as sensor, the measuring equipment low price that adopts in this method, it is low to measure cost.
Description of drawings
Fig. 1 is that pedestal figure is laid in blade measurement of the present invention.
Fig. 2 is non-coding maker point and coding maker point reference scheme figure.
Fig. 3 is the photo of tested blade behind the stickup monumented point.
Fig. 4 is the sparse illustraton of model of three-dimensional symbol point blade that computing machine generates.
Fig. 5 is a binocular raster scanning method acquisition system schematic diagram.
Fig. 6 is the leaf model photo that block-by-block surface point of density cloud is gathered and alignd.
Fig. 7 is the leaf model photo after pre-service of point of density cloud and the modeling.
Fig. 8 is blade measurement model and the 3D contrast photo that designs a model.
Fig. 9 is the positive cotton-shaped photo of the 2D of a certain profile deviations of blade.
Figure 10 is the cotton-shaped photo in 2D side of Fig. 9 blade section deviation.
Figure 11 is the signal of coding maker point coding collar scheme.
Figure 12 is that diagrammatic sketch is arranged at the shooting station.
Embodiment
The present invention is described in further detail below in conjunction with drawings and Examples.
A kind of method for quick of blade of large-sized water turbine size and profile:
The placement of turbine blade, turbine blade is because volume is bigger, and part position wall thickness is thinner, and the placement of free state can bring certain deformation, and is influential to measurement result.And vision measurement need be taken pictures from different positions to measurand, therefore needs to consider the modes of emplacement of blade.Follow principle: the one, be convenient to photography and take pictures; The 2nd, can not produce deformation and make things convenient for execute-in-place, raise the efficiency.Can process as the blade of Fig. 1 and measure base.Pedestal can be reused.
The first step: at blade surface and arranged around monumented point.Monumented point comprises encoded point, non-encoded point; Use circular index point can obtain to compare high orientation precision.The monumented point that has the annular coding then can conveniently be discerned its numbering, selects suitable monumented point pattern and material, because blade uses cast steel material mostly, therefore monumented point can be sticked on magnetic as on the rubber cushion, conveniently arranges and removes.And it is reusable.As shown in Figure 2.
The artificial target will have obvious characteristics, and sign dot center is a filled circles among the present invention, is oval through projective transformation, is used for monumented point is positioned; Its inside of coding maker is a non-coding maker, there is the concentric fan ring of circle at and center the outside, as shown in figure 11, difference according to coding rule, coding maker is divided into several codings such as 8,10,12,14,15 again, and the coded representation of n position is divided into n part with the annulus of outside, on each if the circle at color and center is homochromy, then be encoded to 1, otherwise be 0.In addition, according to the difference of color, can be divided into white background stain sign and white with black dot mark to coding maker and non-coding maker again.Scale is a foundation of recovering the blade physical size, and its two ends are coding maker point or the non-coding maker points that fix, and the distance between the monumented point of two ends is through strict calibration, and the consideration Temperature Influence.The reply blade surface is cleared up around reaching before layout monumented point and the scale, and removal iron filings, greasy dirt etc. guarantee that monumented point and scale can not drop and be shifted.
As shown in Figure 3, evenly paste non-encoded point at blade surface, the density of point should match with the single acquisition breadth of binocular raster scanning equipment, guarantees to have 3～5 non-encoded points in each scanning area at least; Evenly paste encoded point at blade surface, density is 1/5～1/3 of non-encoded point density; At the some encoded points of blade placed around, make all monumented points constitute space distribution.
Second step: at the blade placed around scale suitable with blade dimensions, make on 3 dimensions all has scale as far as possible.
The 3rd step: take global flag point photo sequence.Take pictures from each level angle around blade, the shooting station location is provided with can be with reference to Figure 12.Be distributed in three level heights according to the blade dimensions to be measured station of will making a video recording, as highly being the blade of 2m, can select 1m, 2m, three level heights of 3m; Each highly revolves three-sixth turn the shooting station is set; Be to guarantee the precision that the monumented point three-dimensional coordinate resolves, except selecting the little mm professional camera special of high resolving power, lens distortion, it is as follows that group of photos is taken principle:
3.1 with maximal value in the three-dimensional chi of blade as the honest shooting of shooting distance.
3.2 make each monumented point captured as far as possible by the shooting station of 4 above diverse locations.
3.3 the intersection angle that makes each monumented point as far as possible is at 60 °～120 °.
3.4 the incident angle that makes each monumented point as far as possible is less than 45 °.
Can both take as much as possible monumented point 3.5 make each take the photograph the station as far as possible, the overlapping and common point more than 60% is arranged between the photo that keeps adjacent shooting station to take.
The 4th step: indicate point coordinate in the measurement group of photos.The group of photos that obtains is carried out two-dimentional Flame Image Process earlier, identify monumented point and coding in every photo, measure the centre coordinate of each monumented point, specific algorithm is as follows:
4.1 adopt the edge in the Canny algorithm detected image, obtain the wide closure edge collection of single pixel;
4.2 calculate position weighted value with gradient magnitude as weights, marginal position made sub-pixel-level along gradient direction proofread and correct along gradient direction:
Wherein, d
iBe the distance of a pixel along gradient direction and detected marginal point, g
iIt is gradient magnitude.
4.3 adopt the circularity criterion to identify the ellipse that the edge is concentrated, and utilize following prior imformation to remove the ellipse of the condition that do not conform to, comprise that oval area is too little, elliptic contour is concavity, misclosure, too near with the adjacent ellipses distance.
4.4 adopt for twice least square fitting to go out oval center, get rid of the edge of distance after the match for the first time greater than 3 times of standard deviations, carry out the match second time again.
4.5 judge oval periphery whether endless belt is arranged, if be not non-encoded point; If have then radially make the line of inner and outer boundary, the first-class distance samples of line 5 times, do to make comparisons with the gray scale threshold values of gauge point with the intermediate value of 5 times samplings, greater than threshold values then this endless belt be encoded to 1, otherwise be 0; Per 36 ° (corresponding to 10 encoded points) repeat aforesaid operations, obtain the binary number of shape as " 0100100111 " after rotating a circle.
Obtain the ID of encoded point 4.6 table look-up.If can not find out then regard non-encoded point as.
The 5th step: the three-dimensional coordinate of calculation flag point and modeling.Specific algorithm is as follows:
5.1 coding maker point is realized coupling according to unique ID number.
5.2 realize relative orientation between each photo according to coplanarity equation.
5.3 utilize the DLT method to realize the absolute orientation of each photo.
5.4 utilize the light beam method of adjustment to realize the high-precision calibrating of camera.
5.5 utilize the three-dimensional coordinate of forward intersection calculation code monumented point.
5.6 utilize the outer polar curve constraint of multiple pictures to realize the coupling of non-coding maker point.
5.7 utilize forward intersection to calculate the three-dimensional coordinate of non-coding maker point.
5.8 utilize the optimization of light beam adjustment whole resolve the result.
5.9 derive whole three-dimensional non-coding maker points, obtain the sparse model of blade thus.
The 6th step: cloud collection of blade local dense point and alignment.
Adopt the binocular raster-scan method, its system principle as shown in Figure 5, about two cameras take synchronously the strip encoding of investing body surface by projector, Survey Software is carried out the monumented point and the point of density cloud of acquisition blade surface part behind three-dimensional coupling and the three-dimensional reconstruction automatically.Finish the world coordinates alignment of this local dense point cloud in the position of the sparse point model of the overall situation according to this local monumented point.
Concrete steps are as follows:
6.1 the leaf model data that non-encoded point cloud is represented derive from photogrammetric software, import in the close packing point cloud acquisition software reference when aliging as local dense point cloud.
6.2 remove the coding maker point that blade surface is pasted, keep non-coding maker point.
6.3 with binocular raster scanning equipment over against the blade surface zone, about two cameras take two local pictures, because two camera relative positions and direction calibrate in advance, are given data, therefore can calculate the relative space position relation of local monumented point according to the space intersection method.
6.4 adjust the relative position of binocular raster scanning equipment and target, the number of the feasible non-coding maker point that calculates is more than 3.At three dimensions, utilize subgraph isomorphism algorithm matching area monumented point and overall key point cloud: local monumented point is expressed as " subgraph ", and global flag point cloud to be matched is expressed as " big figure ", search isomorphism subgraph in " big figure ".
6.5 after the match is successful, calculate the zone to whole rotation matrix R and translation matrix t.
6.6 to the local projection of blade coded structured light, left and right sides camera synchronization is taken the sequence photo, handles through on the image by projection arrangement, three-dimensional coupling generates local intensive cloud data behind the three-dimensional reconstruction.If the blade reflecting properties is too poor, then need before scanning, spray developer.
6.7 the local dense cloud data is transformed under the global coordinate system according to rotation matrix in the previous step and translation matrix [R|t].
6.8 region-by-region scanning obtains whole point of density cloud model.
6.9 mobile raster scanning equipment does not stay under the situation in slit in assurance, region-by-region scanning blade surface also aligns automatically, obtains the blade integral point of density cloud model of certain data redundancy.See Fig. 6.
The 7th step: some cloud pre-service and trigonometric ratio modeling.Adopt the average clustering procedure of K to carry out the deletion and the Data Fusion of multi-viewpoint cloud faying surface.Utilize general reverse engineering software (as Geomagic) that the blade point cloud model is carried out noise reduction, goes the orphan, behind level and smooth, the vacuate, carries out trigonometric ratio and generate the triangular network model, carry out filling-up hole and handle cover the cavity that produces by monumented point at last.Obtain the whole triangular network model of blade thus, seen Fig. 7.
The 8th step: measurement model aligns with the coordinate that CAD designs a model.If blade has processing datum in process, so can be according to orthogonal definite blade design coordinate system more than three, with the monumented point cloud model that measures according to " face---line---point " promptly " 3-2-1 " mode carry out coordinate conversion design under the coordinate system so that snap to.Should be after obtaining by the monumented point point cloud model, finish this coordinate conversion before the collection of point of density cloud.
If blade to be measured does not have processing datum, can utilize commercial comparison software (as GeomagicQualify) to read in measurement model and design a model, carry out " best global registration " order, to finish the Optimum Matching of two models.
The 9th step: blade measurement model and the deviation contrast that designs a model.
After the measurement model and the alignment that designs a model, able to programme or use commercial comparison software (as GeomagicQualify), operation " relatively three-dimensional " order obtains the three-dimensional chromatogram deviation of measurement data and blade design digital-to-analogue, sees Fig. 8.
Require to pay close attention to dissecing of position arbitrarily according to technology, detection, can obtain the every position of blade 2D color chips easily and clap the cotton-shaped figure of unfavourable balance, see Fig. 9, Figure 10.
Claims (3)
1. a method for quickly measuring blade of large-sized water turbine is characterized in that, comprises the steps:
The first step, at surface and the placed around circular index point and the monumented point that has the annular coding of blade, monumented point comprises encoded point, non-encoded point; Monumented point is sticked on the magnetic rubber pad, and be adsorbed on blade surface, paste layout at interval according to the requirement of back point of density cloud collecting device;
Second step, place overall scale, scale is a foundation of recovering the blade physical size, and its two ends are coding maker point or the non-coding maker points that fix, and the distance between the monumented point of two ends is through strict calibration;
The 3rd step, adopt special digital camera, comprehensive tested blade is taken pictures, obtain the one group of photo that comprises coding maker point, non-coding maker point, overall scale information;
The 4th step, the calculation flag point coordinate, operating measurement software, in computing machine, import the group of taking a picture, carry out Flame Image Process, measure the two-dimensional coordinate of monumented point in the group of photos, calculate the three-dimensional coordinate of all monumented points in the space according to two-dimensional coordinate then, non-coding maker point point cloud has promptly constituted the overall sparse point model of tested blade among the result, and this model carries out the foundation of world coordinates alignment after as next step local dense point cloud collection;
The 5th step, tested blade surface point of density cloud is gathered and alignment, adopt the binocular raster-scan method, take the strip encoding of investing body surface by projector synchronously with two cameras, Survey Software carries out obtaining behind three-dimensional coupling and the three-dimensional reconstruction monumented point and the point of density cloud of blade surface part automatically, and the world coordinates of finishing this local dense point cloud according to this local monumented point in the position of the sparse point model of the overall situation aligns; The above-mentioned binocular raster-scan method of repeated using obtains all local dense point clouds of world coordinates alignment;
The 6th step, pre-service of point of density cloud and modeling, because the blade point of density cloud model that obtains has certain data redundancy, before carrying out modeling, earlier it is handled, deletion lap point cloud, and each local dense point cloud merged, obtain the whole point of density cloud model of blade outer surface, also be the blade measurement model;
The 7th step, the coordinate system of blade measurement model with the blade cad model alignd, measurement model is carried out coordinate conversion;
The 8th step, blade measurement model and the contrast of blade cad model, two models are carried out simple vector subtract computing, can obtain each position of blade cast(ing) surface and the deviation that designs a model, realize and show by programming with the form of 3D, or, generate the deviation data of 2D by the sectional view of commercial comparison software according to each position and direction.
2. method for quickly measuring blade of large-sized water turbine as claimed in claim 1, it is characterized in that described the 3rd step comprehensively takes pictures to tested blade, the shooting station location is set adopts three level heights that increase successively, highly all around 360 degree, photographing request is as follows for each:
1) with maximal value in the three-dimensional chi of blade as the honest shooting of shooting distance;
2) make each monumented point captured by the shooting station of 4 above diverse locations;
3) make the intersection angle of each monumented point at 60 °～120 °;
4) make the incident angle of each monumented point less than 45 °;
5) make each shooting station can both take as much as possible monumented point, the overlapping and common point more than 60% is arranged between the photo that keeps adjacent shooting station to take.
3. method for quickly measuring blade of large-sized water turbine as claimed in claim 1 is characterized in that, monumented point two-dimensional coordinate in the measurement group of photos in described the 4th step, and concrete grammar is as follows:
1) edge in the employing Canny algorithm detected image obtains the wide closure edge collection of single pixel;
2) calculate position weighted value with gradient magnitude as weights, marginal position made sub-pixel-level along gradient direction proofread and correct along gradient direction:
Wherein, d
iBe the distance of a pixel along gradient direction and detected marginal point, g
iIt is gradient magnitude;
3) adopt the circularity criterion to identify the ellipse that the edge is concentrated, and utilize following prior imformation to remove the ellipse of the condition that do not conform to, comprise that oval area is too little, elliptic contour is concavity, misclosure, and is too near with the adjacent ellipses distance;
4) adopt for twice least square fitting to go out oval center, get rid of the edge of distance after the match for the first time, carry out the match second time again greater than 3 times of standard deviations;
5) judge whether oval periphery has endless belt, if be not non-encoded point; If have then radially make the line of inner and outer boundary, the first-class distance samples of line 5 times, make comparisons with the intermediate value of 5 samplings and the gray scale threshold values of gauge point, greater than threshold values then this endless belt be encoded to 1, otherwise be 0; Per 36 °, corresponding to 10 encoded points, repeat aforesaid operations, obtain the binary number of shape after rotating a circle as " 0100100111 ";
6) table look-up and obtain the ID of encoded point, if can not find out then regard non-encoded point as.
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