[求助]请问怎么拟和一个圆

zhzhiwei · 发表于 2004-6-13 23:36:30

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>各位大师:
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> 小弟有一题目解不出来(我只是一个初学者,情有可愿!~Q~),,,,想请各位帮我解一下,,谢谢啦,,,,,最好是在6月15日之后解出来,,,,,因为这是一道高校选拔赛试题的一个小点,,,,6.14是交卷的日子,,,,,,我想在交卷之后才知道答案,,,,,,谢谢!!!!
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已知圆的36个点,,,请拟合并画出该圆及计算出它的半径:
圆A
X=[27.3560 26.2780 22.3160 17.0170 12.2370 8.6070 7.3770 8.8730 12.3880 17.1900 22.4750 26.1630 27.2050 25.3180 21.0770 15.6420 11.0600 8.1180 7.6040 9.6640 13.9490 19.0950 23.7710 26.7940 26.7320 24.1110 18.7400 14.2530 9.9720 7.5270 8.0790 11.1590 15.4390 21.1120 24.8130 27.1490]
Y=[6.4400 10.8310 14.6680 16.0190 14.6230 10.9450 6.2650 0.7850 -2.5280 -3.8300 -2.4160 1.4120 7.6500 12.3050 15.2830 15.8520 13.8750 9.8260 4.0160 -0.1440 -3.2910 -3.7260 -1.5450 3.0270 9.3170 13.5850 15.8850 15.6640 12.7460 8.1820 2.7120 -1.8510 -3.8100 -3.1860 -0.3840 4.0110]
圆B:
X=[ 13.8730 12.6050 8.5370 3.9930 -1.1530 -4.9720 -6.1920 -4.8350 -1.4300 4.1650 8.7760 12.2430 13.6510 11.6710 7.0970 1.9240 -2.8570 -5.3870 -6.0450 -3.9850 0.5330 5.5700 10.0280 13.1470 13.1640 10.3040 5.9030 0.1030 -3.8560 -6.1380 -5.6710 -2.8100 2.4340 6.9360 11.3820 13.5170]
Y=[ -37.3570 -32.3110 -28.3060 -27.1430 -28.5720 -32.5080 -36.8320 -42.1780 -45.5810 -47.1000 -45.7690 -42.4460 -35.0920 -31.0460 -27.6600 -27.4360 -29.7680 -33.4630 -39.2780 -43.2780 -46.7220 -47.1150 -45.1300 -40.7630 -33.4060 -29.4520 -27.3750 -27.9860 -30.7420 -35.6050 -40.2650 -44.5430 -47.0330 -46.7780 -43.7570 -39.2430]<IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0><IMG src="http://www.shumo.org/bbs/Skins/Default/emot/em31.gif" align=middle border=0>

射天狼 · 发表于 2004-6-23 23:19:47

X=[ 13.8730 12.6050 8.5370 3.9930 -1.1530 -4.9720 -6.1920 -4.8350 -1.4300 4.1650 8.7760 12.2430 13.6510 11.6710 7.0970 1.9240 -2.8570 -5.3870 -6.0450 -3.9850 0.5330 5.5700 10.0280 13.1470  13.1640 10.3040 5.9030 0.1030 -3.8560 -6.1380 -5.6710 -2.8100 2.4340 6.9360 11.3820 13.5170]';
Y=[  -37.3570  -32.3110  -28.3060  -27.1430  -28.5720  -32.5080  -36.8320  -42.1780  -45.5810  -47.1000  -45.7690  -42.4460  -35.0920  -31.0460  -27.6600  -27.4360  -29.7680  -33.4630  -39.2780  -43.2780  -46.7220  -47.1150  -45.1300  -40.7630  -33.4060  -29.4520  -27.3750  -27.9860  -30.7420  -35.6050  -40.2650  -44.5430  -47.0330  -46.7780  -43.7570  -39.2430]';
xx=X.*X;
yy=Y.*Y;
xxyy=-xx-yy
B=[X Y ones(36,1)]
a=B\xxyy
xc = -.5*a(1)
yc = -.5*a(2)
R  =  sqrt((a(1)^2+a(2)^2)/4-a(3))
这样做也等得出一样的结果

itmwk · 发表于 2004-6-14 07:47:57

可以拟合,很容易的

zhzhiwei · 发表于 2004-6-14 13:18:19

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>今天早上8--9点钟交卷了,,,,,,嗯,,,,,,请问怎么样拟合呀,,,,,我老是得到复数,,,,,,唉,,,,,晕倒啦!!!<

>我是用 lsqcurvefit 这个函数来拟合的,,,即使我只拟合上半圆,,,,可是得到的圆心坐标,,,,还有半径都是复数的,,,,请问这怎么拟合呀,,,,,还有,,,怎么得到一下复数的实部的值???<

>谢谢[em07][em07]

zhzhiwei · 发表于 2004-6-14 13:28:59

请告诉我吧,,,,,,唉,,,,,,,虽然我交卷很想睡,,,,,,但是没有做好也睡不着呀,,,,,,快点告诉我吧,,,,,让我今天下午能一直睡到明天天大亮,,,,,,,,谢谢谢谢啦,,,,,,不然我总是睡一会醒一会,,,,不爽呀,,,,,已经有4天没有睡好觉啦,,,,,让我睡得香一点吧,,,!!!谢谢啦,,,,

宇游游 · 发表于 2004-6-14 17:41:37

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>我在数模竞赛区发现你发的另外一个重复贴子,回复如下:<

>你究竟在哪方面遇到了困难?<

>是不懂得怎样画图还是不懂得怎样利用这些数字来求得半径?这个圆可以通过matlab画出来,很简单的.你可以自己先试一下,一步步解决.另,以后发贴注意一下贴子题目.只写一个求助大家是不会知道里面有什么东西的.ps,重复贴我给删除了.

zhzhiwei · 发表于 2004-6-14 17:52:21

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>主要是不懂得求半径呀,,,,论文我已经交上去啦,,,,,麻烦你们给我解一解,,,,,我中午想睡个好觉啊!!!![em06][em06]

itmwk · 发表于 2004-6-15 06:56:35

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>function [xc,yc,R,a] = circfit(x,y) 
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>%CIRCFIT Fits a circle in x,y plane 
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>% 
% [XC, YC, R, A] = CIRCFIT(X,Y) 
% Result is center point (yc,xc) and radius R.A is an 
% optional output describing the circle's equation: 
% 
% x^2+y^2+a(1)*x+a(2)*y+a(3)=0 
% by Bucher izhak 25/oct/1991 

n=length(x); xx=x.*x; yy=y.*y; xy=x.*y; 
A=[sum(x) sum(y) n;sum(xy) sum(yy)... 
sum(y);sum(xx) sum(xy) sum(x)]; 
B=[-sum(xx+yy) ; -sum(xx.*y+yy.*y) ; -sum(xx.*x+xy.*y)]; 
a=A\B; 
xc = -.5*a(1); 
yc = -.5*a(2); 
R = sqrt((a(1)^2+a(2)^2)/4-a(3)); 

zhzhiwei,下次注意了,尽量不要一贴多发.
当天我不就已经回复,并且现在在本版内不是已经得到解决了么?
尤其是发到管理区去,很令人反感的!

射天狼 · 发表于 2004-6-23 23:23:00

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>不能算自己做出来的，仅是由itmwk大哥给出的算法演变来的

itmwk · 发表于 2004-6-25 20:13:55

嘻，大家搞懂了是第一位的！：）

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