CN103438803A - Method for performing view-field-across accurate measurement on size of rectangular part through computer vision technology - Google Patents

Abstract

The invention discloses a method for performing view-field-across accurate measurement on the size of a rectangular part through a computer vision technology. The method comprises the following steps of arranging a rectangular part to be measured on a rectangular reference block, wherein a symmetry axis O and a symmetry axis O' are parallel to each other or form a certain included angle alpha, and alpha is greater than or equal to 0 degree and less than 15 degrees; adjusting to guarantee that the part does not go beyond the edge of the rectangular reference block; calculating the edge line size of the rectangular part to be measured by combination of the lengths of line segments EE', FF', GG', HH' and EF in the rectangular reference block, and the lengths of line segments EI, I'E', FJ, J'F', GK, K'G', HP and P'H' which are accurately detected by a preset computer image processing program. According to the invention, the precision of the detection result is high, the cost of a detection system is reduced, and the method can be applied to accurate measurement on the size of the rectangular part.

Description

Computer vision technique is accurately measured the method for Rectangular Parts size across visual field

Technical field

The present invention relates to the accurate fields of measurement of computer vision, refer in particular to a kind of computer vision technique and accurately measure the method for Rectangular Parts size across the visual field.

Background technology

The actual measurement size of industrial products part is the important evidence of its quality of judgement, and the size of controlling part is the important means that guarantees quality of finished in the error range of design.At present, the detection of industrial products accessory size comprises contact measurement method and the large class of contactless measurement two.Contact measurement method mainly contains vernier caliper, milscale, three-coordinates measuring machine etc., although the result of this type of measuring method is accurate, the measuring process time and effort consuming, easily damage, the surface of scratching products part, is difficult to meet the large demand of producing of industry.Contactless measurement mainly contains laser optical method and computer vision measurement method, and this type of measuring method has favorable reproducibility, and detection speed is fast, easily realizes the advantages such as online detection; Wherein the computer vision measurement method can detect a plurality of dimensional parameters on product parts surface simultaneously, has been widely used in the size detection of industrial products part.

At present, computer vision has been used to accurately detect the fine feature of object to be measured in fixing visual field.Patent " a kind of high precision microscopic fatigue tester " (application number: 200810207563.2) disclose a kind of method of utilizing Computer Vision Detection microfissure size.The method is amplified the image in sample fatigue crack zone in visual field by microscope, through camera, take the image under this visual field and send into computing machine, accurately measures the length of sample crackle in visual field by image processing techniques.When whole piece crackle to be measured does not exceed microscopical visual field, the method can be measured the length of crackle accurately; When certain part of crackle to be measured has exceeded microscopical visual field, the method is difficult to measure the length of crackle, so the method can not accurately detect and exceeds the fixedly fine feature of field of view.

When utilizing computer vision accurately to measure, in order effectively to catch the local feature of sample, camera or microscopical visual field size are limited often, the length of visual field or the wide 2mm～5mm that is generally, and characteristic parameter to be measured often exceeds camera or microscopical field of view as the length of product parts, width, thickness etc., how across visual field, accurately to detect above-mentioned characteristic parameter is the difficult point in computer vision measurement field.For this problem, patent " a kind of part vision detection device " (application number: 200910079737.6) disclose a kind of computer vision and detected the device of surface defects of parts and appearance and size across visual field.This device utilizes CCD camera and enlarging objective etc. to form imaging system, and part to be measured is fixed on displacement platform, and pick-up unit is provided with the detection system that records displacement platform displacement simultaneously.In the visual field of the sending into imaging system fringe region of part is continuous by displacement platform of this device, the displacement that the part edge image of finally taking by imaging system and displacement detection system record calculates the appearance and size of part.Because the measuring accuracy of this device is not only relevant with the visual identity precision of part edge image, and closely related to the registration accuracy of mechanical shift platform stroke with displacement detection system, therefore can not realize high-acruracy survey.Patent " a kind of digital displacement measuring instrument " (application number: 201120026446.3) disclose and a kind ofly utilized a plurality of camera couplings to carry out the method for computer vision high-acruracy survey.At first the method obtains the image information of object regional area to be measured in each viewing field of camera, then utilize the regional area Image Mosaics that the Image Mosaics technology is obtained each camera to become the panoramic picture of an object to be measured, and then utilize computer vision technique to carry out high-acruracy survey to object to be measured.Although the measuring accuracy of this pick-up unit can not be subject to the impact of mechanical shift platform, but when parameter to be measured than large tens times of viewing field of camera, hundreds of times, when even more, the coupling of needs tens, even more polyphasers up to a hundred just can complete measurement, easily causes testing cost higher.

Summary of the invention

The object of the present invention is to provide computer vision technique accurately to measure the method for Rectangular Parts size across visual field, with realization, the size of Rectangular Parts is accurately measured.

In order to eliminate the mechanical shift platform to the impact of measuring accuracy and the cost of effectively controlling detection system, the technical solution used in the present invention is as follows:

The present invention is based on computer vision technique and accurately measures the device of Rectangular Parts size across the visual field, comprises that rectangle reference block ABCD, Rectangular Parts A ' B ' C ' D ' to be measured, Vision imaging system, computing machine, mechanical shift platform form;

The length breadth ratio of described rectangle reference block ABCD is identical with the length breadth ratio of Rectangular Parts A ' B ' C ' D ' standard component to be measured, and the area large 5%～20% of the Area Ratio Rectangular Parts A ' B ' to be measured C ' D ' standard component of rectangle reference block ABCD; Be provided with the reference line EE ' of two horizontal directions and reference line GG ' and the HH ' of FF ' and two vertical direction on rectangle reference block ABCD, and the length L of reference line EE ' _{eE '}, reference line FF ' length L _{fF '}, reference line GG ' length L _{gG '}, reference line HH ' length L _{hH '}, the length L between reference point E and reference point F _eF, the length L between reference point G and reference point H _gH, four edges edge line AB, BC, the CD of rectangle reference block ABCD, the length L of DA _aB, L _bC, L _cD, L _dAbe known; Dotted line O is rectangle reference block ABCD axis of symmetry in the vertical direction;

Described Rectangular Parts A ' B ' C ' D ' to be measured axis of symmetry in the vertical direction is dotted line O '; Described Vision imaging system is comprised of camera, camera lens, light source, image pick-up card and data line, and Vision imaging system is fixedly installed on the mechanical shift platform; The image processing program that described built-in computer is developed in advance, can obtain, store, process the image that Vision imaging system obtains; Described mechanical shift platform can carry Vision imaging system and do tangential movement along the path of setting above rectangle reference block ABCD.

Accurately measure the method for Rectangular Parts size based on computer vision technique across visual field, it is characterized in that comprising the following steps:

Step 1, be positioned over rectangle reference block ABCD by Rectangular Parts A ' B ' C ' D ' to be measured upper, makes axis of symmetry O and axis of symmetry O ' be parallel to each other or mutual α at a certain angle, and 0 °≤α<15 °;

Step 2, check whether any part of Rectangular Parts A ' B ' C ' D ' to be measured exceeds the edge of rectangle reference block ABCD, concrete minute following three processes:

Process one, the mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A in the surface level of distance rectangle reference block ABCD upper surface 2mm～200mm, in mobile process, Vision imaging system is taken four edges edge line AB, BC, the CD of rectangle reference block ABCD, the image of DA continuously, and is stored in computing machine;

Process two, computing machine is processed by the image of the four edges edge line AB to rectangle reference block ABCD, BC, CD, DA, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process three, if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, return to step 1; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, enter step 3;

Step 3, the mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface 2mm～200mm, obtain respectively reference line EE ', FF ', GG ', HH ' not by the image of Rectangular Parts A ' B ' C ' D ' to be measured cover part, take altogether 8 width images, shooting process makes in the complete visual field that appears at Vision imaging system of line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H '.Wherein I, I ' are respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' are respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' are respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', and P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4, utilize the line segment length in the accurate detecting step 38 width images of Computer Image Processing program that set in advance, and obtains respectively the length L of line segment EI _eI, line segment I ' E ' length L _{i ' E '}, line segment FJ length L _fJ, line segment J ' F ' length L _{j ' F '}, line segment GK length L _gK, line segment K ' G ' length L _{k ' G '}, line segment HP length L _hP, line segment P ' H ' length L _{p ' H '};

Step 5, utilize the length of rectangle reference block ABCD middle conductor EE ', FF ', GG ', HH ', EF, the length of the line segment EI obtained in integrating step four, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H ', calculate the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '};

The edge line size L of described Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '}below minute, two kinds of modes are calculated:

Mode one: when satisfying condition

the time (0.0001<x<0.05), can think that the axis of symmetry O of rectangle reference block ABCD and the axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured are parallel to each other, L _{a ' B '}and L _{a ' D '}computing formula be respectively:

L _A’B’=L _II’=L _EE’-L _EI-L _I’E’

L _A’D’=L _KK’=L _GG’-L _GK-L _K’G’

Mode two: when satisfying condition

when (0.0001<x<0.05), can think the axis of symmetry O of rectangle reference block ABCD and the mutual α at a certain angle of axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured; In order to determine the size of angle α, the J of take makes vertical line and intersects at the Q point with EI as starting point to line segment EI, and α=∠ IJQ, can obtain thus $\cos \mathrm{\&alpha;}=\frac{L_{\mathrm{JQ}}}{L_{\mathrm{JI}}}=\frac{L_{\mathrm{JQ}}}{\sqrt{L_{\mathrm{JQ}}^2+L_{\mathrm{QI}}^2}}=\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}};$ Due to the existence of angle α, make LA ' B ' ≠ LII ', the I of therefore take makes vertical line also as starting point to B ' C ' and B ' C ' intersects at Q ' point, and ∠ Q ' II '=∠ IJQ=α; L _{a ' B '}computing formula be:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{\mathrm{EI}}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

In like manner can obtain L _{a ' D '}computing formula be:

$L_{A^{,}{D}^{,}}=L_{K{K}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{\mathrm{GK}}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

The present invention has beneficial effect.The present invention, by corresponding reference point and reference line are set on the rectangle reference block, has carried out accurate measurement in conjunction with computer vision technique to the Rectangular Parts size much larger than the single visual field of Vision imaging system size.Although in the process detected, need the Mechanical Moving platform to carry the zones of different that Vision imaging system moves to the rectangle reference block and carry out image taking, but do not need to input the travel parameters of mechanical mobile platform in the computing formula of rectangular dimension to be measured, so the precision of testing result no longer is subject to the impact of mobile platform kinematic accuracy.In testing process, do not need the collaborative of a plurality of cameras can complete accurately measuring across visual field of large scale parameter simultaneously, effectively controlled the cost of detection system.

The accompanying drawing explanation

Fig. 1 is rectangle reference block schematic diagram;

Fig. 2 is Rectangular Parts schematic diagram to be measured;

Fig. 3 is that computer vision is accurately measured the schematic diagram of Rectangular Parts size across visual field.

Embodiment

Below by each embodiment, describe the present invention.But these embodiments do not limit the present invention, the conversion on the structure that those of ordinary skill in the art makes according to these embodiments, method or function all is included in protection scope of the present invention.

A kind of computer vision technique is accurately measured the method for Rectangular Parts size across the visual field, comprise that rectangle reference block ABCD, Rectangular Parts A ' B ' C ' D ' to be measured, Vision imaging system, computing machine, mechanical shift platform form.

As shown in Figure 1, the length breadth ratio of rectangle reference block ABCD and Rectangular Parts A ' B ' C ' D ' standard component to be measured is 1:2, and the area large 14.79% of the Area Ratio Rectangular Parts A ' B ' to be measured C ' D ' standard component of rectangle reference block ABCD; The length L of reference line EE ' _{eE '}the length L of=60mm, reference line FF ' _{fF '}the length L of=60mm, reference line GG ' _{gG '}the length L of=120mm, reference line HH ' _{hH '}length L between=120mm, reference point E and reference point F _eFlength L between=80mm, reference point G and reference point H _gHthe length L of the four edges edge line AB of=35mm, rectangle reference block ABCD, BC, CD, DA _aB=L _cD=60mm, L _bC=L _dA=120mm; Dotted line O is rectangle reference block ABCD axis of symmetry in the vertical direction;

As shown in Figure 2, Rectangular Parts A ' B ' C ' D ' to be measured axis of symmetry in the vertical direction is dotted line O ';

The model that the model that the model that in Vision imaging system, the model of camera is BasleracA1600-20gm, camera lens is OPTOTC2312, light source is CSTCOL-040-R, image pick-up card is ADLinkGIE64+;

The model of mechanical shift platform is HY10DY (50-500) C, Vision imaging system be fixedly installed on the mechanical shift platform and camera lens apart from the distance of rectangle reference block ABCD for 78mm;

The present invention is based on computer vision technique and accurately measure the method for Rectangular Parts size across the visual field, the concrete implementation step of measuring process is as follows.

Step 1: Rectangular Parts A ' B ' C ' D ' to be measured is positioned over to rectangle reference block ABCD upper, makes axis of symmetry O and axis of symmetry O ' be parallel to each other or mutual α at a certain angle, i.e. 0 °≤α<15 °, as shown in Figure 3;

Step 2: check whether any part of Rectangular Parts A ' B ' C ' D ' to be measured exceeds the edge of rectangle reference block ABCD;

This step is divided following three processes:

Process (1): the mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A at the surface level of rectangle reference block ABCD upper surface certain altitude, in mobile process, Vision imaging system is taken four edges edge line AB, BC, the CD of rectangle reference block ABCD, the image of DA continuously, and is stored in computing machine;

Process (2): computing machine is processed by the image of the four edges edge line AB to rectangle reference block ABCD, BC, CD, DA, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process (3): if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, return to step 1; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, enter step 3;

Step 3: the mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface certain altitude, obtain respectively reference line EE ', FF ', GG ', HH ' not by the image of Rectangular Parts A ' B ' C ' D ' to be measured cover part, take altogether 8 width images, shooting process makes in the complete visual field that appears at Vision imaging system of line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H '.Wherein I, I ' are respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' are respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' are respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', and P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4: utilize the line segment length in 8 width images in the accurate detecting step three of Computer Image Processing program set in advance, obtain respectively the length L of line segment EI _eIthe length L of=2.5174mm, line segment I ' E ' _{i ' E '}the length L of=1.5436mm, line segment FJ _fJthe length L of=1.5433mm, line segment J ' F ' _{j ' F '}the length L of=2.5171mm, line segment GK _gKthe length L of=3.2558mm, line segment K ' G ' _{k ' G '}the length L of=4.5354mm, line segment HP _hPthe length L of=4.5356mm, line segment P ' H ' _{p ' H '}=3.2554mm;

Step 5: by the known parameters substitution in above-mentioned steps

find that it meets

(value that is x is 0.01), so calculate the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured according to following formula _{a ' B '}and L _{a ' D '}value:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{\mathrm{EI}}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

$L_{A^{,}{D}^{,}}=L_{K{K}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{\mathrm{GK}}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

Wherein

$\cos \mathrm{\&alpha;}=\frac{L_{\mathrm{JQ}}}{L_{\mathrm{JI}}}=\frac{L_{\mathrm{JQ}}}{\sqrt{L_{\mathrm{JQ}}^2+L_{\mathrm{QI}}^2}}=\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}=\frac{80}{\sqrt{{80}^2+{(2.5174-1.5433)}^2}}=0.999926$

By known parameters substitution L _{a ' B '}and L _{a ' D '}computing formula, obtain L _{a ' B '}=55.9349mm, L _{a ' D '}=112.2005mm.The L calculated _{a ' B '}and L _{a ' D '}the stroke of length and mechanical shift platform is irrelevant, and therefore Rectangular Parts size detecting method provided by the invention can not be subject to the impact of mechanical shift platform kinematic accuracy, can utilize computer vision accurately to measure the size of part.

Claims (3)

1. computer vision technique is accurately measured the method for Rectangular Parts size across visual field, it is characterized in that comprising the following steps:

Step 1, be positioned over rectangle reference block ABCD by Rectangular Parts A ' B ' C ' D ' to be measured upper, makes axis of symmetry O and axis of symmetry O ' be parallel to each other or mutual α at a certain angle, and 0 °≤α<15 °;

Step 2: check any part of Rectangular Parts A ' B ' C ' D ' to be measured, guarantee not exceed the edge of rectangle reference block ABCD;

Step 3, the mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface 2mm～200mm, obtain respectively reference line EE ', FF ', GG ', HH ' not by the image of Rectangular Parts A ' B ' C ' D ' to be measured cover part, take altogether 8 width images, shooting process makes in the complete visual field that appears at Vision imaging system of line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H '; I, I ' are respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' are respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' are respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', and P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4, utilize the line segment length in 8 width images described in the accurate detecting step three of Computer Image Processing program set in advance, and obtains respectively the length L of line segment EI _eI, line segment I ' E ' length L _{i ' E '}, line segment FJ length L _fJ, line segment J ' F ' length L _{j ' F '}, line segment GK length L _gK, line segment K ' G ' length L _{k ' G '}, line segment HP length L _hP, line segment P ' H ' length L _{p ' H '};

Step 5, utilize the length of rectangle reference block ABCD middle conductor EE ', FF ', GG ', HH ', EF, the length of the line segment EI obtained in integrating step four, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H ', calculate the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '}.

2. computer vision technique as claimed in claim 1 is accurately measured the method for Rectangular Parts size across visual field, it is characterized in that described step 2 further is specially:

Process one, the mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A at the surface level of rectangle reference block ABCD upper surface 2mm～200mm, in mobile process, Vision imaging system is taken four edges edge line AB, BC, the CD of rectangle reference block ABCD, the image of DA continuously, and is stored in computing machine;

Process two, computing machine is processed by the image of the four edges edge line AB to rectangle reference block ABCD, BC, CD, DA, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process three, if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, return to step 1; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, enter step 3.

3. computer vision technique as claimed in claim 1 is accurately measured the method for Rectangular Parts size across visual field, it is characterized in that: the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured in described step 5 _{a ' B '}and L _{a ' D '}below minute, two kinds of modes are calculated:

Mode one, when satisfying condition

the time (0.0001<x<0.05), can think that the axis of symmetry O of rectangle reference block ABCD and the axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured are parallel to each other, L _{a ' B '}and L _{a ' D '}computing formula be respectively:

L _A’B’=L _II’=L _EE’-L _EI-L _I’E’

L _A’D’=L _KK’=L _GG’-L _GK-L _K’G’

Mode two, when satisfying condition

when (0.0001<x<0.05), can think the axis of symmetry O of rectangle reference block ABCD and the mutual α at a certain angle of axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured; In order to determine the size of angle α, the J of take makes vertical line and intersects at the Q point with EI as starting point to line segment EI, and α=∠ IJQ, can obtain thus $\cos \mathrm{\&alpha;}=\frac{L_{\mathrm{JQ}}}{L_{\mathrm{JI}}}=\frac{L_{\mathrm{JQ}}}{\sqrt{L_{\mathrm{JQ}}^2+L_{\mathrm{QI}}^2}}=\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}};$ Due to the existence of angle α, make LA ' B ' ≠ LII ', the I of therefore take makes vertical line also as starting point to B ' C ' and B ' C ' intersects at Q ' point, and ∠ Q ' II '=∠ IJQ=α; L _{a ' B '}computing method be:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{\mathrm{EI}}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

In like manner can obtain L _{a ' D '}computing method be:

$L_{A^{,}{D}^{,}}=L_{K{K}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{\mathrm{GK}}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}.$

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