One kind is based on the circularity assess method of MATLAB

Summary: The assess of circularity and computation, it is the definition according to circularity essentially function of travel of tectonic function model, reentry optimizes the course that seeks solution. Offer a kind of circularity assess means that is based on MATLAB, use MATLAB to optimize kit, to use most the law mixes the zonule round law, least square round law, smallest circumscribed circle the biggest inside the assess of circularity of implementation of the law that receive a circle offerred new alternative. 1 foreword is at present in manufacturing practice, the measurement of circularity the instrument basically has circularity appearance, 3 coordinate to measure machine, and the assess of circularity and computation are to pass circularity appearance, 3 coordinate to measure the computational course that the accurate instrument such as machine takes oneself to finish. Because the architect keeps secret strictly to the program and these programs mostly the price does not poor, accordingly, the person that use hopes to develop more, more convenient circularity assess method. Actually, circularity assess and calculative process are the process that according to circularity criterion for evaluation tectonic function prototype has one optimizing begging solving. As MATLAB software function increasingly perfect, at present MATLAB already had function of operation of maths of the practicable in 600 many projects, the algorithm that uses in these function regards scientific research and project calculative as newest research achievement, reach fault tolerance to handle through all sorts of optimizing, use rise have very tall rash club sex and reliability. When undertaking optimizing computation, need to press the function model with tectonic and correct requirement only, call the optimizes function to be able to get satisfaction computation result of MATLAB next: In the meantime, what still can achieve the result that seek solution conveniently through transferring the interpolation function of MATLAB and visible function is visible. Accordingly, introduce MATLAB software circularity assess, the implementation that will be circularity assess offers new alternative. In GB7234-87 " circularity measures term, definition and parameter " in, does the assess method of circularity error have: ? Flood dragon of plutonium ∏  predicts ā ⒆ plutonium "  cough predicts glair of Tun of ⊥ of ā ⒆ plutonium to predict an ancient wind instrument of ê appropriate the She nationality to censure glair predicts flood dragon of  of ∏ of ā W plutonium to predict ㄊ and the method that ZC of Bing of flood dragon of  of the ∏ that slaughter plutonium regards assess as fiducial circle, in getting circularity error to be worth type of ZZ=Rmax-Rmin(1) of Δ of Δ ZZ by this method: Rmax, Rmin -- each measure a place opposite most the the biggest, smallest deviate of zonule round MZC is worth Ri -- each measure a place opposite most the deviate of zonule circle MZC is worth (in most the side outside zonule circle MZC is taken be worth, inside takes negative worth) manage together, respectively least square circle (the LSC) , smallest circumscribed circle (MCC) and the biggest inside receive a circle (MIC) regards assess as basic circle can get Zc of Zq of circularity error Δ , Δ and Δ Zi respectively. Model of maths of 2 circularity assess 2.

1 most the standard equation of circle of basis of zonule round law, with most derivation of zonule round law gives computational formula. Hypothesis circle is in XOY plane or go up at the plane of XOY in parallel, criterion most the general equation of zonule circle is (X-xc)2+(y-yc)2=Rc2(2) is measured this are roundly the N(n>3) on contour line dot, each bits of coordinate is Xi, Yi(I=1, ... , n) , the distance that nods this circle the centre of a circle each is Ri= √ (Xi-xc)2+(yi-yc)2(3) is pressed most zonule law is tectonic and the following function, the essence of this function is to seek solution the optimization problem about Xc of coordinate of the centre of a circle, Yc, xc* of the result that seek solution, Yc* is namely most the value of coordinate of the centre of a circle of zonule circle: F(xc, in Yc)=[Ri]max-[Ri]min=min(4) type: [Ri]max, [Ri]min -- the maximum that is apart from distance of assess round the centre of a circle at each o'clock and the least value 2.

The standard equation of least square circle refers to round law of 2 least square type (2) . Measure the N(n>3) on the contour line that get a circle dot, each bits of coordinate is Xi, Yi(i=1, ... , n) , the distance that nods least square circle each is Ri= √ - Rc(xi-xc)2+(yi-yc)2(5) constructs by the least square method function of the following target, the essence of this function is to seek solution the optimization problem about Xc of coordinate of the centre of a circle, Yc and round radius Rc, this function begs solution result Xc* , Yc* , Rc* to be value of coordinate of least square round the centre of a circle and radius namely: F(xc, yc, rc)=nRi2=min Σ I=1(6)2.

3 the smallest circumscribed circle the law manages together, by the smallest circumscribed circle the law constructs the following function, ri refers to type (3) . This function is to seek solution essentially the optimization problem about Xc of coordinate of the centre of a circle, Yc, its beg solution result Xc* , Yc* to be value of coordinate of the centre of a circle of the smallest circumscribed circle namely: F(xc, yc)=[Ri]max=min(7) type [the maximum that Ri]max is apart from assess round the centre of a circle at each o'clock to be apart from 2.

4 the biggest inside the law that receive a circle manages together, press the biggest inside the law that receive a circle is tectonic and the following function, ri refers to type (3) . This function is to seek solution essentially the optimization problem about Xc of coordinate of the centre of a circle, Yc, this function begs solution result Xc* , Yc* to be namely the biggest inside value of coordinate of the centre of a circle that receive a circle: F(xc, in Yc)=[Ri]min=max(8) type: [Ri]min -- the least value that is apart from distance of assess round the centre of a circle at each o'clock the 3 circularity assess that are based on MATLAB 3.

1MATLAB begs solution measure to measure place N(n>3) to nod (each bits of coordinate is Xi, Yi(i=1, ... , in N)) at 3 o'clock P1(x1, y1) , P2(x2, y2) and P3(x3, y3) generation joins group of the following equation, solution gets X0 of initial value of coordinate of the centre of a circle, Y0 and R0:x of radius initial value0=x12(y2-y3)+x22(y3-y1)+x32(y1-y2)-(y1-y2)(y2-y3)(y3-y1)2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]y0=y12(x2-x3)+y22(x3-x1)+y32(x1-x2)-(x1-x2)(x2-x3)(x3-x1)2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]R0= √ (the assess method that X1-x0)2+(y1-y0)2(9) differs according to 4 kinds, press type respectively (4) , type (6) , type (7) , type (F(xc of 8) tectonic function, yc) or function F(xc, yc, rc) : As initial value Y0 or X0, X0, Y0, R0 era enters function F(xc, yc) or function F(xc, yc, rc) undertakes iteration seeks solution, yc* or the solution Xc* that gets satisfaction iteration to beg seeing precision and this function pattern, Xc* , Yc* , Rc* , the coordinate of the centre of a circle that this solution is assess basic circle namely or coordinate of the centre of a circle and radius (note: ? Plutonium of rice of take along sth to sb " blue ㄔ of ㄆ of  new moon is caught benevolence incomplete of the Xia that protect  mires cutting of the feet of  Gan bucket ton Dai 0, Y0, R0 serves as initial value, and method of 3 kinds of assess needs the rest only X0 of coordinate of the centre of a circle, Y0 regards initial value as) . When undertaking iteration seeks solution, use optimize algorithmic Nelder-Mead Simplex Method, this algorithm did not use function derivative information, is the consideration that has case numerical value only. Although its are calculated efficiency, convergent speed not as good as Quasi-NewtonMethod and BFGS Method, but suit to beg Jie Fei linear and discontinuous question very much however. Press type (the distance Ri(i=1 that 3) begs solution to measure each a little bit to be apart from the centre of a circle of assess basic circle, ... , n) . gotten Ri(i=1, ... , n) generation can get circularity error to be worth Z=(Ri)max-(Ri)min(10) of Δ Z Δ to express 1 enumerated data and XY of serial number of circularity assess result into next type most zonule round law least square round way is the smallest circumscribed circle law is the oldest inside the law that receive a circle 149.

99960.

0000-0.

0015-0.

0000-0.

00050.

0014247.

551215.

4503-0.

0027-0.

0014-0.

00180.

0000340.

451029.

3893-0.

00080.

0005-0.

00010.

0017429.

389440.

4511-0.

00070.

0005-0.

00020.

0017515.

450547.

5517-0.

0023-0.

0010-0.

00200.

000060.

000050.

00120.

00000.

00120.

00000.

00227-15.

451247.

5540-0.

00010.

0011-0.

00040.

00208-29.

389240.

4508-0.

0016-0.

0004-0.

00200.

00059-40.

451129.

3895-0.

0014-0.

0001-0.

00190.

000810-47.

553015.

4509-0.

0017-0.

0003-0.

00230.

000511-49.

99980.

0000-0.

0022-0.

0008-0.

00280.

000212-47.

5535-15.

4511-0.

00140.

0001-0.

00180.

001213-40.

4504-29.

3889-0.

0027-0.

0011-0.

00300.

000014-29.

3905-40.

45260.

00000.

0017-0.

00000.

002915-15.

4508-47.

5527-0.

0022-0.

0005-0.

00190.

0008160.

0000-50.

0001-0.

0018-0.

0001-0.

00130.

00131715.

4512-47.

5538-0.

00080.

0010-0.

00000.

00251829.

3893-40.

4509-0.

00150.

0001-0.

00060.

00171940.

4508-29.

3892-0.

00150.

0001-0.

00050.

00172047.

5520-15.

4506-0.

0021-0.

0006-0.

00100.

Result of 0009 circularity statistic 0.

00270.

00310.

00300.

Bits 0029 error are the biggest 00.

001700.

0029 deviation most bit - 0.

0027-0.

0014-0.

0030 watches 2 computation contrast as a result (Mm) most zonule law least square method is the smallest circumscribed circle law is the oldest inside the law that receive a circle ZZ=0 of this Δ of result of program circularity assess.

0027 Δ Zq=0.

0031 Δ Zc=0.

0030 Δ Zi=0.

ZZ=0 of Δ of result of computation of machine of 0029 3 coordinate.

0027 Δ Zq=0.

0031 Δ Zc=0.

0030 Δ Zi=0.

00293.

The implementation order flow of 2 programs applies MATLAB to realize the order flow of circularity assess. Program interface should each measure in program general flow are compositive in a GUI, can realize data file to load through this GUI, iteration of data editor, circularity begs solution, computation to be saved as a result, data is visible wait for a variety of functions. 4 calculate a validity that for test and verify this program demands solution result actually, to the watch 1 in data is pressed respectively most the law mixes the round law of zonule round law, least square, smallest circumscribed circle the biggest inside circularity of assess of the law that receive a circle, measure assess outcome the computation of machine to undertake contrast as a result with 3 coordinate. Enumerated data and enumerated data of circularity assess result and result of program circularity assess see a table 1. The equation of assess basic circle of 4 kinds of methods is respectively: Most equation of basic circle of assess of zonule round law: (X+0.

0005)2+(y+0.

0004)2=50.

Equation of basic circle of assess of round law of 00162 least square: (X+0.

0005)2+(y+0.

0001)2=50.

00012 the smallest circumscribed circle equation of law assess basic circle: (X+0.

0012)2+(y+0.

0001)2=50.

00132 the biggest inside equation of basic circle of assess of the law that receive a circle: (X+0.

0007)2+(y+0.

0001)2=49.

99892 data are visible most the data of the result of computation of 4 kinds of methods such as zonule round law is visible. The comparison of program assess result and result of computation of 3 coordinate machine is measured with 3 coordinate opportunity is right same data has consideration, with test and verify the validity of result of this program circularity assess. The computational result contrast of two kinds of means sees a table 2. 5 conclusion were based on the circularity assess method of MATLAB to offer new alternative for the assess of circularity. Via computational example test and verify, to same data set, the circularity assess result that uses this method and use 3 coordinate to measure machine calculative result to agree completely. Does this program have: of the following characteristic? Di of Ji of  of farsighted  gauze points to hazel of be ignorant of of Ji A Chinese-style unlined garment Qia falls ATLAB of Man of A Chinese-style unlined garment of banter of ＂ of  of collect of neon  Yan is taken oneself compile implement compile the program DLL file or executable document, do not need MATLAB the support of this one giant platform, make the application of the program more agile. What ③ passes the interpolation function that transfers MATLAB and visible function to still can achieve the result that seek solution conveniently is visible. CNC Milling