CN106441200B - A kind of method for three-dimensional measurement of more measurement patterns - Google Patents
A kind of method for three-dimensional measurement of more measurement patterns Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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Abstract
The present invention relates to 3 D digital imaging fields, more particularly to a kind of method for three-dimensional measurement of more measurement patterns, include the following steps: S1, establish unified data structuring model, the measurement data that the unified data structuring model is used to obtain a variety of measurement patterns carries out unified representation；S2, under single measurement pattern, expressed using the unified data structure per a piece of cloud what measurement obtained, and calculated and pre-processed；S3, the data obtained to different measurement patterns are spliced, and the two panels point cloud of any position is snapped to unified coordinate system；S4, mixing global optimization is carried out to spliced data, obtains measurement result.The method for three-dimensional measurement of more measurement patterns of the invention can be realized real time fusion and optimization to measurement data under a variety of measurement patterns, realizes the three-dimensional measurement of high-precision, high details, is with a wide range of applications.
Description
Technical field
The present invention relates to 3 D digital imaging fields, and in particular to a kind of method for three-dimensional measurement of more measurement patterns.
Background technique
The technology of three-dimensional non-contact measurement is carried out to body surface, in many necks such as industry, medical treatment, art, education
Domain is widely used.The application of different field is all different to the technical requirements of three-dimensional measurement.For example, auto industry is wanted
The data precision of three-dimensional measurement is asked to want high, data details will be clear that；Human thermoregulation requires quickly to obtain human body three-dimensional number
According to needing measuring system that there is handhold functional, required precision is lower；The three-dimensional measurement of large-scale sculpture requires measuring system to have hand
Function is held, while data precision is higher, data have certain details.
The spatial digitizer and its measurement method being currently known will cannot all meet above-mentioned requirements well.Such as middle promulgated by the State Council
Bright patent CN1483999A discloses the method and system of measurement object dimensional surface outline, utilizes encoded light and phase shift
High accuracy three-dimensional measurement may be implemented in three-dimension measuring system.But this method and system carry out Three-dimensional Gravity using several pictures
It builds, can not achieve handhold functional.Meanwhile an equipment is able to use there are also some spatial digitizers and carries out a variety of scanning moulds
The measurement of formula.But the scanning of various modes independently carries out, the data of measurement not can be carried out processing, fusion and optimization,
It is only comparable to several scan patterns simply to focus in an equipment.In this case, using a variety of scan patterns
Optimization to measurement result and without help.
Summary of the invention
Present invention solves the technical problem that being to provide a kind of method for three-dimensional measurement of more measurement patterns, for measuring mould more
The data processing of the three-dimension measuring system of formula is merged and is optimized by the data measured to a variety of measurement patterns, realizes high
Details, high accuracy three-dimensional measurement.
Specifically, the method for three-dimensional measurement of more measurement patterns includes the following steps:
S1, unified data structuring model is established, the unified data structuring model is for obtaining a variety of measurement patterns
The measurement data obtained carries out unified representation；
S2, under single measurement pattern, expressed using the unified data structure per a piece of cloud what measurement obtained,
And it is calculated and is pre-processed；
S3, the data obtained to different measurement patterns are spliced, and the two panels point cloud of any position is snapped to unification
Coordinate system；
S4, mixing global optimization is carried out to spliced data, obtains measurement result.
Further, in step S1, a variety of measurement patterns include: sine streak measurement, digital speckle measurement, more it is parallel
Line measurement.
Further, step S1 is specifically included:
For the measurement data that a variety of measurement patterns obtain, expressed using continuous implicit function D (x), wherein x ∈
R3Indicate the position in three-dimensional space, D (x) indicate x to the shortest distance on object being measured surface, company represented by D (x)=0
Continuous curved surface measures the surface of obtained object.
Further, it in step S2, calculates and pretreatment specifically includes:
S21, use the square G of an encirclement measured zone as the scope of D (x), square G is uniformly split into
The small square g of same sizei；
Each point (P in S22, the point cloud obtained to measurementj,Nj), find PjThe small square g at placePj, wherein PjFor
The three-dimensional coordinate of point, NjFor the normal vector of point；
S23, to each gPjAnd with gPjCentered on n3A gi, calculate separately distance value D (xi) and distance value confidence weighting
Weight W (xi)；
D(xi)=Nj·(xi-Pj) (1)
Wherein, 1 < n≤10, xiIndicate the g for participating in calculatingPjAnd giCentral point, D (xi) indicate xiTo measured object body surface
The shortest distance in face is positive value in the outside of object, is negative value, W (x in the inside of objecti) indicate D (xi) confidence level, dgFor
giSide length；
S24, point cloud and grid result are obtained using Marching Cubes Algorithm (Marching Cube).
Further, further includes:
If the point in the multi-disc point cloud that S25, measurement obtain repeats to fall in the same giIn, then gradually calculate the distance value
D(xi) and distance value confidence weight W (xi):
W*(xi)=W (xi)+w(xi) (4)
Wherein, D (xi) indicate the distance value before updating, W (xi) confidence weight before update, d (xi) indicate the last meter
Obtained distance value, w (xi) indicate the last confidence weight being calculated, D*(xi) indicate updated distance value, W*
(xi) indicate updated confidence weight；
Later, point cloud and grid result are obtained using Marching Cubes Algorithm (Marching Cube).
Further, further includes:
If the point in the multi-disc point cloud that S26, measurement obtain repeats to fall in the same giIn, then gradually calculate the distance value
D(xi) and distance value confidence weight W (xi), after measurement, for each gi, obtained finally using average weighted method
Df(xi) and Wf(xi):
Wf(xi)=∑ Wj(xi) (6)
Wherein, Dj(xi) and Wj(xi) it is that point jth time repetition in multi-disc point cloud falls in the same giIt is calculated when middle
Value；Later, point cloud and grid result are obtained using Marching Cubes Algorithm (Marching Cube).
Further, when measurement pattern is the measurement of more parallel lines, measurement data obtained in measurement process not into
Row calculates in real time to be updated, and is only shown by way of sampling, user is instructed to measure；
After measurement, all the points cloud that measurement obtains is placed under unified global coordinate system, then, is calculated all
The normal vector of point cloud is unified to carry out distance value D (x lateri) and distance value confidence weight W (xi) calculating.
Further, when calculating the normal vector of all the points cloud, the normal vector of each point is calculated using principal component analysis, specifically
Use following formula:
M (p)=∑ (qi-C(p))·(qi-C(p))T (8)
Wherein, p is the point of normal vector to be calculated, qiFor the point in p particular neighborhood, M (p) is covariance matrix, minimum
The corresponding feature vector of characteristic value is the normal vector of p；The direction of normal vector towards camera is set to the direction of normal vector.
Further, in step S3, splicing is carried out to the data that different measurement patterns obtain and includes thick splicing and accurate spelling
It connects, the method slightly spliced includes manually selecting splicing, index point splicing, merging features, the method packet accurately spliced
Iteration is included with regard to proximal method.
Further, step S4 is specifically included:
S41, the corresponding points that point cloud and index point is found between two frames of measurement data；
S42, error formula is minimized, obtains the rigid body transformation matrices of every frame point cloud；
S43, rigid body translation matrix is taken on every frame point cloud, the iteration process is until convergence.
Further, in step S42, the error formula that uses are as follows:
Wherein, (pk,qk) be (i, j) corresponding points, (Pk,Qk) be (i, j) respective flag point, nkFor qkNormal vector,
RTiFor the rigid body translation matrix of i-th point cloud, RT is the rigid body translation matrix of all the points cloud,WithRespectively put cloud pair
The weight with index point corresponding points should be put.
Further, work as i, when to have a frame in j be more parallel lines measurement data, then set
The method for three-dimensional measurement of more measurement patterns of the invention has used continuously the data of a variety of measurement patterns measurement
Implicit function D (x) makees unified data structure managing and expression, to achieve the purpose that different measurement pattern switchings.Meanwhile making
User's measured zone is surrounded with square, and the square is subjected to uniform subdivision, to realize the discrete expression of D (x), as rear
The basis of continuous data processing.The method for three-dimensional measurement of more measurement patterns of the invention, realizes and measures under a variety of measurement patterns
The real time fusion of data realizes high details, high accuracy three-dimensional measurement.
In practical applications, user can be convenient in conjunction with a variety of measurement patterns and quickly complete measurement task.For example,
It, can be with quick obtaining data for face part digital speckle measurement pattern when the high sculpture of measurement et al.；For text
The more high-precision data of parallel lines measurement pattern quick obtaining can be used in the part such as word, fold dress ornament abundant, ornaments,
The acquisition of sine streak measurement pattern can be used in the isolated sculpture component of (< 15cm) smaller for size, such as teapot, teacup
High-precision three-dimensional data.
Detailed description of the invention
The discretization that Fig. 1 is D (x) in the method for three-dimensional measurement of more measurement patterns of the invention indicates schematic diagram.
Specific embodiment
For a further understanding of the present invention, the preferred embodiment of the invention is described below with reference to embodiment, still
It should be appreciated that these descriptions are only further explanation the features and advantages of the present invention, rather than to the claims in the present invention
Limitation.
The present invention provides a kind of for handling the method for three-dimensional measurement of more measurement patterns of body surface three-dimensional data, energy
Enough measurement data to a variety of measurement patterns carry out real time fusion, to realize high details, high accuracy three-dimensional measurement.
This method is described in detail below by preferred embodiment:
Firstly, this method carries out data structure managing and expression to measurement data using unified data structure.
Specifically, sine streak measurement, digital speckle measurement, more parallel lines are measured these three measurement patterns and are obtained
The measurement data obtained, using a kind of unified data structure managing and expression, to achieve the purpose that different measurement measurement switchings.?
In measurement process, a continuous implicit function D (x) is safeguarded, wherein x ∈ R3Indicate the position in three-dimensional space, D (x) indicates that x is arrived
The shortest distance on object being measured surface.When using any measurement pattern, newly after measurement piece of data, changed using this sheet data
The value for becoming D (x), achievees the purpose that data fusion.After measurement, continuous curve surface represented by D (x)=0 is measured and is obtained
Object surface.
Due to the continuous data that are beyond expression in computer, so needing to D (x) discrete expression.In the present embodiment, use
One square G surrounds the region of user's measurement, using square as the scope of D (x).G is uniformly split into same size
Small square giIf (side length of G is 512, giSide length be 1, then will obtain 5123A small square).Each giIn
Heart point xiRecord two value D (xi) and W (xi)。D(xi) indicate xiTo the shortest distance of body surface, it is positive outside object
Value is negative value (as shown in Figure 1) in the inside of object.W(xi) it is accumulative weight, indicate D (xi) confidence level.W(xi) value
It is bigger to illustrate D (xi) it is more credible.
When initialization, D (xi) and W (xi) it is all 0.Under a kind of measurement pattern, after newly measurement piece of data, in data
Each point (Pj,Nj) merged in G respectively, wherein PjFor the three-dimensional coordinate of point, NjFor the normal vector of point.
Firstly, finding PjThe small square g at placePj.Preferably, in the present embodiment, only change with gPjCentered on 53
A giValue, will greatly save memory space and operation time in this way.
The g for needing to change for eachi, the distance value D (x for having symbol is calculated according to the following formulai) and distance value set
Believe weight W (xi):
D(xi)=Nj·(xi-Pj)
Wherein, dgFor giSide length.One point P of body surfacejNeighbouring curved surface, the normal plane that the point can be used are approximate
It indicates, so PjA point x in neighbouring spaceiTo the shortest distance of body surface, x can be usediTo PjThe distance of normal plane is approximate
It indicates.Work as xiTo PjDistance it is remoter, D (xi) approximation it is more inaccurate, so W (xi) same to xiTo PjDistance be inversely proportional.This
In embodiment, W (xi)∈[10,0.08]。
After measurement, for each gi, average weighted method can be used, obtain final Df(xi) and Wf
(xi):
Wf(xi)=∑ Wj(xi)
Wherein, Dj(xi) and Wj(xi) it is that point jth time repetition in multi-disc point cloud falls in the same giIt is calculated when middle
Value.
In order to guarantee the real-time update of D (x), above-mentioned formula is rewritten into cumulative mode:
W*(xi)=W (xi)+w(xi)
Wherein, D (xi) indicate the distance value before updating, W (xi) confidence weight before update, d (xi) indicate the last meter
Obtained distance value, w (xi) indicate the last confidence weight being calculated, D*(xi) indicate updated distance value, W*
(xi) indicate updated confidence weight.
In measurement process or after measurement, marching cube (MarchingCube) method can be used to obtain
Point cloud and grid result.
In data fusion, need to know the normal vector of each point in monolithic data.Sine streak measurement and digital speckle
What measurement pattern obtained is ordered into a cloud, and normal vector is easy to calculate.But what more parallel lines measurement patterns obtained is straight line
The point cloud of distribution can not calculate normal vector just with single frames point cloud data.Therefore, in measurement method of the invention, Duo Genping
Without fusion during row line measurement, is shown only by the mode of sampling, user is instructed to measure.When measurement terminates
Afterwards, all the points cloud that measurement obtains is placed under unified global coordinate system, then, calculates the normal vector of all the points cloud, finally,
It merges together.In method of the invention, the normal vector of each point is calculated using principal component analysis.Specific formula is:
M (p)=∑ (qi-C(p))·(qi-C(p))T
Wherein p is with the point for calculating normal vector, qiFor the point in p particular neighborhood, M (p) is covariance matrix, minimum special
The corresponding feature vector of value indicative is the normal vector of p.Then, the direction of normal vector towards camera is set to the direction of normal vector.
The point found in neighborhood is to have used the data structure of above-mentioned uniform subdivision in the present embodiment than relatively time-consuming, accelerated neighbour
The searching put in domain.
Later, the splicing between different measurement data is carried out.
Point cloud is the process that the two panels point cloud of any position is snapped to unified coordinate system.Complete splicing
It is generally divided into two steps: thick splicing and accurate splicing.Thick splicing refers to the process of the two panels point cloud gross alignment of any position.Working as
The method slightly spliced being able to use under preceding scene manually selects splicing, index point splicing, merging features.Manually select splicing
Refer to and gross alignment is completed by man-machine interactively, this method is highly stable, but than relatively time-consuming, needs extra workload.
For measuring scene in real time, can not slightly be spliced in this way.Index point splicing refers to by object being measured
Surface mount label, to instruct a method for cloud alignment.This method is highly stable, and speed is fast, but for can not label adhering
Note measured body (such as human body, antique etc.), this method will be unable to using.Accurate splicing refers to the two panels point of gross alignment
The process of cloud Accurate align.The most general method of accurate splicing is ICP (Iterative closest point).ICP's is basic
Principle is the corresponding points in iteration optimization two panels point cloud, makes the distance and minimum of corresponding points.
If the data of measurement will be unable to merge without splicing, what measuring instrument user can not also observe and measure at any time
Situation, such as be not measured by there are also which place.First frame after measurement pattern switching, it is necessary to complete splicing.?
That is the main body of splicing is the point cloud and a frame point cloud data extracted in D (x).If being switched to sine streak measurement pattern,
Index point splicing, merging features manually select splicing and can use.If digital speckle measurement pattern is switched to, due to this
Mode is real-time measurement, so manually selecting splicing cannot use.If being switched to more parallel lines measurement patterns, equally
Due to being real-time measurement, manually selecting splicing cannot be used.Since a frame data amount is very small, merging features are not available yet.
So can only be spliced using index point.
Finally, measuring the mixing global optimization of data.
Above-mentioned splicing is two-by-two optimization process of the present frame with data after fusion.If object being measured is excessive, or
Frame number is too many, easily generation cumulative errors.Cumulative errors influence whole precision.If there is circuit, intersect in circuit
Place, may generate big deformation or staggered floor.So needing the process of global optimization.
In more parallel lines measurement patterns, the data volume of single frames is considerably less, so can not be carried out using point cloud information complete
Office's optimization.Index point global optimization can get up the data organization of three kinds of models, but there is also problems.1) due to not having
Have using point cloud information, since the local detail after optimization is bad；2) when carrying out the measurement of no marks point, this method cannot make
With.
Based on above-mentioned consideration, the joint global optimization method of index point and point cloud is used.Firstly, being found a little between frame two-by-two
The corresponding points of cloud and index point.Then, error formula is minimized, the rigid body variation of every frame point cloud is obtained.Finally, by rigid body translation
It is applied on every frame point cloud, the iteration process is until convergence.The error formula used is:
Wherein, (pk,qk) be (i, j) corresponding points, (Pk,Qk) be (i, j) respective flag point, nkFor qkNormal vector,
RTiFor the rigid body translation matrix of i-th point cloud.RT is the rigid body translation matrix of all the points cloud.WithRespectively put cloud pair
The weight with index point corresponding points should be put.Work as i, having a frame in j is more parallel lines measurements, then setsWhenAll
When equal to 0, which has reformed into pure index point global optimization.WhenWhen being equal to 0, which has reformed into pure point Yun Quan
Office's optimization.
The above description of the embodiment is only used to help understand the method for the present invention and its core ideas.It should be pointed out that pair
For those skilled in the art, without departing from the principle of the present invention, the present invention can also be carried out
Some improvements and modifications, these improvements and modifications also fall within the scope of protection of the claims of the present invention.
Claims (12)
1. a kind of method for three-dimensional measurement of more measurement patterns, which comprises the steps of:
S1, unified data structuring model is established based on implicit function, the unified data structuring model is used for a variety of measurements
The measurement data that mode obtains carries out unified representation；
S2, under single measurement pattern, expressed using the unified data structuring model per a piece of cloud what measurement obtained,
And it is calculated and is pre-processed；
S3, the data obtained to different measurement patterns are spliced, and the two panels point cloud of any position is snapped to unified coordinate
System；
S4, mixing global optimization is carried out to spliced data, obtains measurement result.
2. the method for three-dimensional measurement of more measurement patterns as described in claim 1, which is characterized in that in step S1, a variety of measurements
Mode includes: sine streak measurement, digital speckle measurement, more parallel lines measurements.
3. the method for three-dimensional measurement of more measurement patterns as described in claim 1, which is characterized in that step S1 is specifically included:
For the measurement data that a variety of measurement patterns obtain, expressed using continuous implicit function D (x), wherein x ∈ R3It indicates
Position in three-dimensional space, D (x) indicate x to the shortest distance on object being measured surface, continuous curve surface represented by D (x)=0
The surface of the object measured.
4. the method for three-dimensional measurement of more measurement patterns as claimed in claim 3, which is characterized in that in step S2, calculate and pre-
Processing specifically includes:
S21, use the square G of an encirclement measured zone as the scope of D (x), square G is uniformly split on an equal basis
The small square g of sizei；
Each point (P in S22, the point cloud obtained to measurementj, Nj), find PjThe small square g at placePj, wherein PjFor point
Three-dimensional coordinate, NjFor the normal vector of point；
S23, to each gPjAnd with gPjCentered on n3A gi, calculate separately distance value D (xi) and distance value confidence weight W
(xi)；
D(xi)=Nj·(xi-Pj) (1)
Wherein, 1 < n≤10, xiIndicate the g for participating in calculatingPjAnd giCentral point three-dimensional coordinate, D (xi) indicate xiTo be measured
The shortest distance of body surface is positive value in the outside of object, is negative value, W (x in the inside of objecti) indicate D (xi) it is credible
Degree, dgFor giSide length；
S24, point cloud and grid result are obtained using Marching Cubes Algorithm.
5. the method for three-dimensional measurement of more measurement patterns as claimed in claim 4, which is characterized in that further include:
If the point in the multi-disc point cloud that S25, measurement obtain repeats to fall in the same giIn, then gradually calculate the distance value D (xi)
With the confidence weight W (x of distance valuei):
W*(xi)=W (xi)+w(xi) (4)
Wherein, D (xi) indicate the distance value before updating, W (xi) confidence weight before update, d (xi) indicate that the last time calculates
The distance value arrived, w (xi) indicate the last confidence weight being calculated, D*(xi) indicate updated distance value, W*(xi)
Indicate updated confidence weight；
Later, point cloud and grid result are obtained using Marching Cubes Algorithm.
6. the method for three-dimensional measurement of more measurement patterns as claimed in claim 4, which is characterized in that further include:
If the point in the multi-disc point cloud that S26, measurement obtain repeats to fall in the same giIn, then gradually calculate the distance value D (xi)
With the confidence weight W (x of distance valuei), after measurement, for each gi, final D is obtained using average weighted methodf
(xi) and Wf(xi):
Wf(xi)=∑ Wj(xi) (6)
Wherein, Dj(xi) and Wj(xi) it is that point jth time repetition in multi-disc point cloud falls in the same giThe value being calculated when middle；It
Afterwards, point cloud and grid result are obtained using Marching Cubes Algorithm.
7. the method for three-dimensional measurement of more measurement patterns as claimed in claim 4, which is characterized in that when measurement pattern is more flat
When row line measurement, measurement data obtained in measurement process is only carried out by way of sampling without calculating update in real time
It has been shown that, instructs user to measure；
After measurement, all the points cloud that measurement obtains is placed under unified global coordinate system, then, calculates all the points cloud
Normal vector, later unify carry out distance value D (xi) and distance value confidence weight W (xi) calculating.
8. the method for three-dimensional measurement of more measurement patterns as claimed in claim 7, which is characterized in that calculate the normal direction of all the points cloud
When amount, the normal vector of each point is calculated using principal component analysis, specifically used following formula:
M (p)=∑ (qi-C(p))·(qi-C(p))T (8)
Wherein, p is the point of normal vector to be calculated, qiFor the point in p particular neighborhood, M (p) is covariance matrix, minimal eigenvalue
Corresponding feature vector is the normal vector of p；The direction of normal vector towards camera is set to the direction of normal vector.
9. the method for three-dimensional measurement of more measurement patterns as described in claim 1, which is characterized in that in step S3, to different surveys
It includes thick splicing and accurate splicing that the data that amount mode obtains, which carry out splicing, and the method slightly spliced includes manually selecting spelling
It connects, index point splicing, merging features, the method accurately spliced includes iteration with regard to proximal method.
10. such as the method for three-dimensional measurement of the described in any item more measurement patterns of claim 1-9, which is characterized in that step S4 tool
Body includes:
S41, the corresponding points that point cloud and index point is found between two frames of measurement data；
S42, error formula is minimized, obtains the rigid body translation matrix of every frame point cloud；
S43, rigid body translation matrix is taken on every frame point cloud, the iteration process is until convergence.
11. the method for three-dimensional measurement of more measurement patterns as claimed in claim 10, which is characterized in that in step S42, use
Error formula are as follows:
Wherein, (pk, qk) be (i, j) corresponding points, (Pk, Qk) be (i, j) respective flag point, nkFor qkNormal vector, RTiFor
The rigid body translation matrix of i-th point cloud, RTjFor the rigid body translation matrix of jth piece point cloud, RT is the rigid body translation square of all the points cloud
Battle array,WithRespectively put the weight of cloud corresponding points and index point corresponding points.
12. the method for three-dimensional measurement of more measurement patterns as claimed in claim 11, which is characterized in that work as i, there is a frame to be in j
When more parallel lines measurement data, then set
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| CA3018886A CA3018886C (en) | 2016-04-08 | 2016-07-27 | Three-dimensional measuring system and measuring method with multiple measuring modes |
| JP2018542770A JP6579639B2 (en) | 2016-04-08 | 2016-07-27 | Multi-measurement mode three-dimensional measurement system and measurement method |
| KR1020187026659A KR102207725B1 (en) | 2016-04-08 | 2016-07-27 | 3D survey system and survey method in multiple survey mode |
| PCT/CN2016/091913 WO2017173744A1 (en) | 2016-04-08 | 2016-07-27 | Multi-measurement-mode three-dimensional measurement system and measurement method |
| AU2016401548A AU2016401548B2 (en) | 2016-04-08 | 2016-07-27 | Multi-measurement-mode three-dimensional measurement system and measurement method |
| EP16897677.7A EP3293481B1 (en) | 2016-04-08 | 2016-07-27 | Multi-measurement-mode three-dimensional measurement system and measurement method |
| US15/833,950 US10317199B2 (en) | 2016-04-08 | 2017-12-06 | Three-dimensional measuring system and measuring method with multiple measuring modes |
| US16/432,466 US11280605B2 (en) | 2016-04-08 | 2019-06-05 | Three-dimensional measuring system and measuring method with multiple measuring modes |
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| CN106846406A (en) * | 2017-02-24 | 2017-06-13 | 上海坤辕检测科技有限公司 | A kind of point cloud coordinate system construction method for object dimensional measurement of coordinates |
| CN107101606A (en) * | 2017-05-27 | 2017-08-29 | 江苏密斯欧智能科技有限公司 | A kind of revolving dial attitude error measuring method |
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