CN101387501B - Ultra-large workpiece circular section shape and azimuthal measurement apparatus and method - Google Patents

Abstract

The invention relates to a device and a method for measuring the shape and the orientation of a circular section of an ultra-large workpiece. Aiming at the difficult problem that size information is difficult to evaluate accurately because of few measuring points on the circular section, the invention provides a distribution measuring network, which comprises a laser tracker, an end face geometrical measuring network and a workpiece axis correcting and measuring network. A light vision coordinate measuring sensor with a linear structure is taken as a coordinate acquisition device. The network for measuring the shapes of the end face and the circular section adopts multi-group paired vision sensors to acquire horizontal parallel chords and vertical parallel chords of a circle, solves the center of the circle through the theorem that the midpoint connecting line passes through the center of the circle, and then solves the radius by a least square method. The axis correcting and measuring network adopts the multi-group paired vision sensor to measure a plurality of circular sections of a column, and the connection line of the center of the circle is the axis of the column, so the axis correcting and measuring network can completely evaluate six-dimensional information comprising shapes and orientations, and can correct the error for measuring the shape of the end face introduced by a position. The laser tracker as an overall measuring device measures the coordinate system uniformly. The method can measure the shapes and the orientations of large-sized columnar workpieces quickly with high precision.

Description

Ultra-large workpiece circular section shape and azimuthal measurement apparatus and method

Technical field

The present invention relates to large scale geometric measurement technology, particularly a kind of ultra-large workpiece circular section shape and azimuthal measurement apparatus and method.

Background technology

The circular section shape measurement is one of basic task of commercial measurement, the measuring method of conventional round section size is more, measuring accuracy and efficient all are easy to ensure, and the measurement of the large scale round section geometric configuration more than several meters even tens meters is an industrial difficult problem always, as aircraft cabin body, hydraulic generator unit and large size bearing etc. all is similar cross-section shapes such as circle, ellipse, accurately measure significant to its size, particularly during the assembling of aircraft, steamer equal segments parts, require the end face geometric shape measuring accuracy height of built-up member.

The difficult point of restriction large-scale circular section gauge is that the measured object size is big, and each measuring equipment can only be measured the fraction point relatively, often is difficult to gather enough points and covers whole measured object.So not only cause information few, and the point set skewness, cause fitting precision not high.To cause cost too high and be difficult to safeguard the global calibration difficulty and place multisensor.Promptly allow to obtain the bulk information on the uniform whole circumference, also need to spend the plenty of time, need carry out repeatedly station transfer as laser tracker, transit needs artificial pointwise aiming efficient low.And large-size workpiece is subjected to the influence of surrounding environment bigger, especially temperature effect.Temperature ladder variation in the long-time measuring process can make the measurement data noise strengthen.Owing to each side reasons such as measurement skill levels, measure and sneak into noise inevitably in addition.These all cause the decline of measuring accuracy, and large-scale metrology is especially responsive for noise.Therefore need the more effective measuring method of research.

Summary of the invention

The object of the present invention is to provide the device and method of a kind of ultra-large workpiece circular section shape and measurement of bearing, can solve the difficult problem of ultra-large workpiece circular section geometric measurement.The present invention has that all measuring points are measured simultaneously, the complete advantage such as the sextuple information of workpiece of obtaining.

The device of a kind of ultra-large workpiece circular section shape provided by the invention and measurement of bearing comprises: net is measured in laser tracker, end face geometric shape measuring net and axis of workpiece correction, described end face geometric shape measuring net comprises horizontal survey net and vertical survey net, measure the online at least two pairs of vision sensors of arranging at each, be used for measuring simultaneously a circular section; Laser tracker is as global measuring equipment, and each vision sensor and laser tracker are used for measuring simultaneously the point in the public view field.Vision sensor is general contactless measurement of coordinates sensor, and it mainly is made up of semiconductor laser transmitter, ccd sensor and cylindrical mirror.

The device of a kind of ultra-large workpiece circular section shape provided by the invention and measurement of bearing comprises: net is measured in laser tracker, end face geometric shape measuring net and axis of workpiece correction, and described measurement net is to be made of some vision sensors; Vision sensor is general contactless measurement of coordinates sensor, and it mainly is made up of semiconductor laser transmitter, ccd sensor and cylindrical mirror.

Described end face geometric shape measuring net has eight vision sensors at least, one group four are used to form the horizontal survey net, comprise two pairing vision sensors, each pairing vision sensor is placed with the center symmetry by two vision sensors and is formed, another group is formed and the orthogonal vertical survey net of horizontal survey net, is used for measuring simultaneously a circular section;

Described axis correction is measured net and is had six vision sensors at least, and every group of three vision sensors are measured a circular section simultaneously.All vision sensors are all gathered the measured point three-dimensional based on the binocular vision principle, and inside comprises semiconductor laser transmitter, ccd sensor and cylindrical mirror.

Laser tracker is as global measuring equipment, and each vision sensor and laser tracker are used for measuring simultaneously the point in the public view field.

The step that the method that a kind of ultra-large workpiece provided by the invention is measured comprises:

1) vision sensor is placed in measured workpiece effective working distance scope, through the semiconductor laser incident point of survey sensor inside light source to cylindrical mirror, incident line structure finishing tool is to measured object, inner binocular ccd sensor is to the finishing tool imaging, utilize the finishing tool of sub-pix algorithm of subdivision refinement Gaussian distribution, unique point is as coordinate on the extraction finishing tool, and precision can reach 0.05 pixel.Utilize principle of triangulation, the two-dimensional coordinate calculating measured point three-dimensional coordinate from two cameras can obtain all point coordinate on the total striation.

2) end face geometric shape measuring net is divided into horizontal survey net and vertical survey net, respectively many horizontal chord of measuring workpieces end face circular section and the vertical string of a musical instrument, adopt two vision sensors to place with the center symmetry, each bar string of a musical instrument is measured in pairing, two pairing vision sensor emission coplanar structure finishing tools, and light switches on the measured circle tee section, and the light bending takes place at the circumference place, and the inflection point is two tested unique point d ₁And d ₂Thereby, obtain 2 d on the circular section ₁And d ₂Coordinate, obtain the circle a string d ₁d ₂, and can calculate the mid point M of string ₁=(d ₁+ d ₂)/2.

The horizontal survey net is made of such n parallel pairing vision sensor, and promptly the every string of a musical instrument is parallel to each other, obtains the mid point M of n bar parallel chords ₁, M ₂... M _n, at last with these mid point match straight lines l _HIn like manner, go out straight line l by vertical survey net also measurements and calculations _VMid point line according to one group of parallel chords in the circle must be through center of circle theorem, and the intersection point of two mid point lines is exactly the center of circle O=l that asks _H∩ l _V

All pairing vision sensors are measured simultaneously, have improved the sensitivity and the precision of end face geometric configuration center, have improved anti-interference.Because the pairing survey sensor of design is symmetrically distributed with the center, therefore has the variate ability.

3) obtain the center of circle after, utilize center of circle constraint, use least square fitting radius of circle r again.

$\min f(a,b,r)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(\sqrt{{(x_i-a)}^2+{(y_i-b)}^2}-r)}^2$

Wherein (a, b) as known quantity, the substitution as a result that above-mentioned parallel chord method is obtained, thus find the solution radius r.

Although most measuring task only need the geometric configuration three-dimensional measurement of cylindrical workpiece end face, the sextuple information evaluation in orientation, round section place is then more comprehensive.What is more important, during the general measure cylindrical work, when the measurement circular section was not orthogonal to axis, the actual oval cross section that records caused measuring error.Add axis of workpiece correction net, measure anastomose for two and close thoroughly evaluating workpiece geometries and azimuth information more, can revise because the inaccurate measuring uncertainty of bringing in measured workpiece installation site reduces tested ultra-large workpiece is installed accurately vertical requirement.

4) axis of workpiece correction net is made up of many groups vision sensor equally, and along the measured workpiece axis arranged, each vision sensor emission line structure finishing tool is radiated on the cylinder cylinder outline perpendicular to axis of workpiece, and light is cut the circular arc feature that obtains the circular section.Gather multiple spot coordinate on the whole piece structure light, can the match round cross section.Although a vision sensor can be gathered the enough matches of multiple spot coordinate circular section on the structure striation, fitting precision was not relatively poor when measuring point was uniform.Therefore general each cross section several vision sensors that all evenly distribute come even collection point coordinate, improve the circular section fitting precision.The line-structured light of a plurality of vision sensor projections constitutes a unified optical plane, and can cut out many camber lines at the profile glazing, by gathering the three-dimensional of multiple spot on the whole piece camber line, can calculate the center position coordinates O in cross section, camber line place _iGather the line of a plurality of kernel of section successively, just can match axis of workpiece l.Measure in the time of by axis of workpiece orientation and tested end surface shape, can draw the sextuple installation site of round section in measuring net,, make measurement more accurate with this measurement result of revising cross-sectional geometry.

More than analyze to be supposition all measurement data all under the same coordinate system, but each vision sensor is all based on separately coordinate system O _i-X _iY _iZ _iMeasure three-dimensional, therefore need all measurement data unified to global coordinate system O _W-X _WY _WZ _W, with laser tracker as global measuring equipment.Each vision sensor and tracker are measured 3 points in the public view field simultaneously, can be in the hope of derotation matrix R and translation vector T, and utilize formula F=RM+T can be in global coordinate system again with the local coordinate system data-switching.Common point obtained frequent employing standard ball measurement in the past.The present invention adopts the tracker cooperative target as common point, i.e. (spherically mountedretroreflector, SMR), tracker records prism apex coordinate F to prism of corner cube spheric reflection target.And prism of corner cube is by three orthogonal being spliced of level crossing, and CCD can be to three intersection edges direct imagings, and measures the intersection point M of 3 straight lines, obtains common point thus.Utilize the hypercomplex number method to find the solution conversion parameter:

Barycentric coordinates are respectively $\stackrel{\‾}{F}=\frac{\mathrm{\ΣF}}{3},\stackrel{\‾}{M}=\frac{\mathrm{\ΣM}}{3}$

Coordinate after the center of gravityization is respectively F _C=F-F, M _C=M-M

$S_{\mathrm{ab}}=\mathrm{\Σ}{M}_C{F}_C^T,$ A wherein, b=x, y, z

$P=\left[\begin{array}{cccc}{S}_{\mathrm{xx}}+S_{\mathrm{yy}}+S_{\mathrm{zz}}& S_{\mathrm{yz}}-S_{\mathrm{xy}}& S_{\mathrm{zx}}-S_{\mathrm{xz}}& S_{\mathrm{xy}}-S_{\mathrm{yz}}\\ S_{\mathrm{yz}}-S_{\mathrm{zy}}& S_{\mathrm{xx}}-S_{\mathrm{yy}}-S_{\mathrm{zz}}& S_{\mathrm{xy}}+S_{\mathrm{yx}}& S_{\mathrm{zx}}+S_{\mathrm{xz}}\\ S_{\mathrm{zx}}-S_{\mathrm{xz}}& S_{\mathrm{xy}}+S_{\mathrm{yx}}& S_{\mathrm{yy}}-S_{\mathrm{xx}}-S_{\mathrm{zz}}& S_{\mathrm{yz}}+S_{\mathrm{zy}}\\ S_{\mathrm{xy}}-S_{\mathrm{yx}}& S_{\mathrm{zx}}+S_{\mathrm{xz}}& S_{\mathrm{yz}}+S_{\mathrm{zy}}& S_{\mathrm{zz}}-S_{\mathrm{xx}}-S_{\mathrm{yy}}\end{array}\right]$

Find the solution eigenwert and the proper vector of P, wherein eigenvalue of maximum characteristic of correspondence vector is best hypercomplex number q, can be calculated as follows R.

$R=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right]$

Find the solution translation vector T=F then _C-RM _C

The invention has the advantages that: propose to cooperate parallel chords match center of circle method, can improve center of circle bearing accuracy with less measuring point, thereby improve nose circle radius surface fitting precision based on the end surface measurement net of vision.The error that the out of plumb of utilizing axis correction net can revise the relative axis of end face causes.Measuring net can be with the variation flexible configuration vision sensor quantity of workpiece size.

Description of drawings

Fig. 1 is a FB(flow block) of the present invention.

Fig. 2 is a measurement mechanism synoptic diagram of the present invention.

Fig. 3 is a laser tracker global calibration synoptic diagram of the present invention.

Fig. 4 is that least square of the present invention and parallel chord method compare simulation result.

Embodiment

Be described in further detail technical solution of the present invention below in conjunction with drawings and Examples:

As shown in Figure 1, end surface shape measurement net of the present invention comprises vision sensor 1, vision sensor 2, vision sensor 3, vision sensor 4, vision sensor 5, vision sensor 6, vision sensor 7 and vision sensor 8; The axis correction is measured net and is comprised vision sensor 9, vision sensor 10 and vision sensor 11, vision sensor 12, vision sensor 13 and vision sensor 14; As shown in Figure 3, the 15th, semiconductor laser transmitter, the 16th, ccd sensor, the 17th, cylindrical mirror, the 18th, laser tracker.

The device of a kind of ultra-large workpiece circular section shape provided by the invention and measurement of bearing comprises: net is measured in laser tracker, end face geometric shape measuring net and axis of workpiece correction, and described measurement net is to be made of some vision sensors; Vision sensor is general contactless measurement of coordinates sensor, and it is made up of semiconductor laser transmitter, ccd sensor and cylindrical mirror.

Described end face geometric shape measuring net has eight vision sensors at least, one group four are used to form the horizontal survey net, comprise two pairing vision sensors, each pairing vision sensor is placed with the center symmetry by two vision sensors and is formed, another group is formed and the orthogonal vertical survey net of horizontal survey net, is used for measuring simultaneously a circular section;

Netting gear is measured in described axis correction six vision sensors, and every group of three vision sensors are measured a circular section simultaneously.All vision sensors are all gathered the measured point three-dimensional based on the binocular vision principle, and inside comprises semiconductor laser transmitter, ccd sensor and cylindrical mirror.

Laser tracker is as global measuring equipment, and each vision sensor and laser tracker are used for measuring simultaneously the point in the public view field.

The step that the method for a kind of ultra-large workpiece circular section shape provided by the invention and measurement of bearing comprises:

Vision sensor is placed in measured workpiece effective working distance scope, inner semiconductor laser 15 incident point light sources are to cylindrical mirror, form the line structure finishing tool to measured object, inner 16 pairs of finishing tool imagings of binocular CCD vision sensor obtain all point coordinate on the total striation;

Cross-sectional geometry is measured net and is divided into level and vertical survey net, respectively many horizontal chord of measuring workpieces end face circular section and the vertical string of a musical instrument, adopt two vision sensor symmetries to place, each bar string of a musical instrument is measured in pairing, two pairing vision sensor emission coplanar structure finishing tools, and light switches on the measured circle tee section, and the light bending takes place at the circumference place, obtains two unique point d on the circular section ₁And d ₂Coordinate, obtain the circle a string d ₁d ₂, and calculate the mid point M of string ₁=(d ₁+ d ₂)/2, the horizontal survey net is made of such n parallel pairing vision sensor 1 and vision sensor 2, vision sensor 3 and vision sensor 4, and promptly the every string of a musical instrument is parallel to each other, obtains the mid point M of n bar parallel chords ₁, M ₂... M _n, at last with these mid point match straight lines l _HIn like manner, but go out straight line l by the vision sensor 5 of vertical survey net and vision sensor 6, vision sensor 7 and vision sensor 8 also measurements and calculations _V, must be according to the mid point line of one group of parallel chords in the circle through center of circle theorem, the intersection point of two mid point lines is exactly the center of circle O=l that asks _H∩ l _V, utilize center of circle constraint then, least square fitting radius of circle r, all pairing vision sensors are measured simultaneously, improve anti-interference;

Add axis of workpiece correction net, thoroughly evaluating workpiece cross-sectional geometry and orientation 6D information more, revise because the inaccurate measuring uncertainty of bringing in measured workpiece installation site, axis of workpiece correction net is made up of many groups vision sensor, along the measured workpiece axis arranged, each vision sensor emission line structured light is perpendicular to axis of workpiece, beat the circular arc feature that on profile, promptly obtains the circular section, can measure the profile of workpiece, gather multiple spot coordinate on the whole piece structure light, get final product the match round cross section, each cross section several vision sensors that all evenly distribute come even collection point coordinate, improve the circular section fitting precision, the line-structured light of a plurality of vision sensor projections constitutes a unified optical plane, and can cut out many camber lines at the profile glazing, by gathering the three-dimensional of multiple spot on the whole piece camber line, can calculate the center position coordinates O in cross section, camber line place _i, gather the line of a plurality of kernel of section successively, just can obtain axis of workpiece l, measure in the time of by axis of workpiece orientation and tested end surface shape, can draw the 6D installation site of round section in measuring net,, make measurement more accurate with this measurement result of revising cross-sectional geometry;

Each vision sensor is all based on separately coordinate system O _i-X _iY _iZ _iMeasure three-dimensional, need all measurement data unified to global coordinate system O _W-X _WY _WZ _WWith laser tracker 18 as global measuring equipment, each vision sensor and tracker are measured 3 points in the public view field simultaneously, can be in the hope of derotation matrix R and translation vector T, utilize formula F=RM+T can be in global coordinate system again with the local coordinate system data-switching, adopt the tracker cooperative target as common point, be prism of corner cube spheric reflection target (spherically mounted retroreflector, SMR), tracker records prism apex coordinate F, and CCD is to three level crossing intersection edges direct imaging in the prism of corner cube, and measures the intersection point M of 3 straight lines, obtain common point thus, utilize the hypercomplex number method to find the solution conversion parameter.

Application Example:

As shown in Figure 2, arrange end surface shape measurement net, vision sensor apart from end face in best effort apart from 350mm, wherein vision sensor 1 and vision sensor 2, vision sensor 3 and vision sensor 4 are formed pairing three-dimensional coordinates measurement sensor, mutual group becomes the level net, vision sensor 5 and vision sensor 6, vision sensor 7 and vision sensor 8 are formed pairing three-dimensional coordinates measurement sensor, the common vertical web of forming, open the semiconductor line structure finishing tool transmitter of pairing vision sensor, it is parallel with vertical web to adjust level net laser respectively, light switches to the place, circular section, form unique point, two WAT-902H black-white CCDs obtain the 768*576 pixel image to the finishing tool imaging in the vision sensor, utilize principle of triangulation calculated characteristics point coordinate.Thereby obtain string of a musical instrument d ₁d ₂, d ₃d ₄, its mid point is M ₁, M ₂, both fitting a straight line l _H, with reason d ₅d ₆And d ₇d ₈Obtain l _VBoth intersection points are center of circle O.Fixedly behind the O of the center of circle, find the solution radius r with the principle of least square again.The XI model laser tracker of producing with FARO 18 is a global measuring equipment, measures three common point C1 simultaneously with each vision sensor, and C2 and C3 are as Fig. 3.Utilize the hypercomplex number decomposition method that the measured value of each survey sensor is transformed under the tracker coordinate system.

Lay axis correction net as Fig. 2, comprise that two groups of circular sections measure, in the circular section 1, vision sensor 9, vision sensor 10 and vision sensor 11 are opened laser, adjust the laser coplane, gather the camber line coordinate, match center of circle O ₁In like manner vision sensor 12, vision sensor 13 and vision sensor 14 are measured the center of circle O of circular section 2 ₂, line O ₁O ₂Be the cylinder axle center.By axle center l and end face center of circle O and radius r, can judge the orientation of cylindrical work in the space, realized the sextuple measuring system that shape and position are estimated simultaneously.This example is example with the minimal configuration, and diameter and length increase with workpiece can increase survey sensor arbitrarily.

By emulation, the precision of the relative least square of parallel chord method improves.As Fig. 4.

Claims (2)

1. the device of ultra-large workpiece circular section shape and measurement of bearing, it is characterized in that it comprises: net is measured in laser tracker, end face geometric shape measuring net and axis of workpiece correction, and it is respectively to be made of some vision sensors that net is measured in described end face geometric shape measuring net and axis of workpiece correction; Vision sensor is general contactless measurement of coordinates sensor, and it is made up of semiconductor laser transmitter, ccd sensor and cylindrical mirror;

Described end face geometric shape measuring net has eight vision sensors at least, one group four are used to form the horizontal survey net, comprise two pairing vision sensors, each pairing vision sensor is placed with the center symmetry by two vision sensors and is formed, another group is formed and the orthogonal vertical survey net of horizontal survey net, is used for measuring simultaneously a circular section;

Netting gear is measured in described axis correction six vision sensors, and every group of three vision sensors are measured a circular section simultaneously

All vision sensors are all gathered the measured point three-dimensional based on the binocular vision principle, and inside comprises semiconductor laser transmitter, ccd sensor and cylindrical mirror;

Laser tracker is as global measuring equipment, and each vision sensor and laser tracker are used for measuring simultaneously the point in the public view field.

2. method of utilizing described ultra-large workpiece circular section shape of claim 1 and azimuthal measurement apparatus to measure is characterized in that the step that it comprises:

1) vision sensor is placed in measured workpiece effective working distance scope, through the semiconductor laser incident point of vision sensor inside light source to cylindrical mirror, form the line structure finishing tool to measured object, inner binocular ccd sensor is to the finishing tool imaging, utilize the finishing tool of sub-pix algorithm of subdivision refinement Gaussian distribution, unique point is utilized principle of triangulation as coordinate on the extraction finishing tool, calculate the measured point three-dimensional coordinate from the two-dimensional coordinate of two cameras, can obtain all point coordinate on the total striation;

2) the horizontal survey net in the end face geometric shape measuring net and vertical survey net many horizontal chord and the vertical string of a musical instrument of measuring workpieces end face circular section respectively, adopt two vision sensors to place with the center symmetry, each bar string of a musical instrument is measured in pairing, two vision sensor emission coplanar structure finishing tools, and light switches on the measured circle tee section, the light bending takes place at the circumference place, and the inflection point is two tested unique point d ₁And d ₂Thereby, obtain 2 d on the circular section ₁And d ₂Coordinate, obtain the circle a string d ₁d ₂, and can calculate the mid point M of string ₁=(d ₁+ d ₂)/2;

The horizontal survey net is made of n parallel pairing vision sensor, and promptly the every string of a musical instrument is parallel to each other, obtains the mid point M of n bar parallel chords ₁, M ₂... M _n, at last with these mid point match straight lines l _HIn like manner, go out straight line l by vertical survey net also measurements and calculations _V, must be according to the mid point line of one group of parallel chords in the circle through center of circle theorem, the intersection point of two mid point lines is exactly the center of circle O=l that asks _H∩ l _V

3) obtain the center of circle after, utilize center of circle constraint, use the least square fitting radius of circle again:

$\min f(a,b,r)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(\sqrt{{(x_i-a)}^2+{(y_i-b)}^2}-r)}^2$

A wherein, b be as known quantity, the substitution as a result that above-mentioned parallel chord method is obtained, thus find the solution radius r;

4) start the axis of workpiece correction simultaneously and measure net mensuration, vision sensor is along the measured workpiece axis arranged, each vision sensor emission line structure finishing tool is perpendicular to axis of workpiece, be radiated on the cylinder cylinder outline, light is cut the circular arc feature that obtains the circular section, gather multiple spot coordinate on the whole piece structure light, get final product the match round cross section; The line-structured light of a plurality of vision sensor projections constitutes a unified optical plane, and can cut out many camber lines at the profile glazing, by gathering the three-dimensional of multiple spot on the whole piece camber line, can calculate the center position coordinates O in cross section, camber line place _iGather the line of a plurality of kernel of section successively, just can match axis of workpiece l, measure in the time of by axis of workpiece orientation and tested end surface shape, can draw the sextuple installation site of cylindrical work in measuring net, revise the measurement result of cross-sectional geometry with this;

5) each vision sensor is all based on separately coordinate system O _i-X _iY _iZ _iMeasure three-dimensional, need all measurement data unified to global coordinate system O _W-X _WY _WZ _WWith laser tracker as global measuring equipment, adopt the tracker cooperative target as common point, it is prism of corner cube spheric reflection target, tracker records prism apex coordinate F, each vision sensor and tracker are measured 3 points in the public view field simultaneously, find the solution rotation matrix R and translation vector T, utilize formula F=RM+T can be with the local coordinate system data-switching in global coordinate system again; Prism of corner cube is by three orthogonal being spliced of level crossing, and CCD is to three intersection edges direct imagings, and measures the intersection point M of 3 straight lines, obtains common point thus, utilizes the hypercomplex number method to find the solution conversion parameter:

Barycentric coordinates are respectively $\stackrel{\‾}{F}=\frac{\mathrm{\ΣF}}{3},$ $\stackrel{\‾}{M}=\frac{\mathrm{\ΣM}}{3}$

Coordinate after the center of gravityization is respectively

F _C＝F-F，M _C＝M-M

$S_{\mathrm{ab}}=\mathrm{\Σ}{M}_C{F}_C^T$

A wherein, b=x, y, z

$P=\left[\begin{array}{cccc}{S}_{\mathrm{xx}}+S_{\mathrm{yy}}+S_{\mathrm{zz}}& S_{\mathrm{yz}}-S_{\mathrm{zy}}& S_{\mathrm{zx}}-S_{\mathrm{xz}}& S_{\mathrm{xy}}-S_{\mathrm{yx}}\\ S_{\mathrm{yz}}-S_{\mathrm{zy}}& S_{\mathrm{xx}}-S_{\mathrm{yy}}-S_{\mathrm{zz}}& S_{\mathrm{xy}}+S_{\mathrm{yx}}& S_{\mathrm{zx}}+S_{\mathrm{xz}}\\ S_{\mathrm{zx}}-S_{\mathrm{xz}}& S_{\mathrm{xy}}+S_{\mathrm{yx}}& S_{\mathrm{yy}}-S_{\mathrm{xx}}-S_{\mathrm{zz}}& S_{\mathrm{yz}}+S_{\mathrm{zy}}\\ S_{\mathrm{xy}}-S_{\mathrm{yx}}& S_{\mathrm{zx}}+S_{\mathrm{xz}}& S_{\mathrm{yz}}+S_{\mathrm{zy}}& S_{\mathrm{zz}}-S_{\mathrm{xx}}-S_{\mathrm{yy}}\end{array}\right]$

Find the solution eigenwert and the proper vector of P, wherein eigenvalue of maximum characteristic of correspondence vector is best hypercomplex number q, can be calculated as follows R:

$R=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right]$

Find the solution translation vector T=F then _C-RM _C