matlab最小二乘法拟合圆程序

%% x,y为题目中数据

plot(x, y, '*')

hold on

A = [x y ones(size(x))]

abc = -(A*A')\sum(A*[x'.^2 y'.^2], 2)

ox = -abc(1)/2

oy = -abc(2)/2

R = sqrt(ox^2+oy^2-abc(3))

plot(ox, oy, 'or')

t = linspace(0, 2*pi, 100)

plot(ox+R*cos(t), oy+R*sin(t))

点击按钮分别按照提示输入6个点的X和Y坐标 如果显示溢出的话应该是无法生成圆 因为运算中有一步会变成除以0出错的

给你一组测试数据

(1,7)

(2,6)

(5,8)

(7,7)

(9,5)

(3,7)

以上都是整数 当然你也可以输入小数

Private Sub Command1_Click()

Dim i As Integer

Dim X(0 To 5) As Double

Dim Y(0 To 5) As Double

For i = 0 To 5

X(i) = InputBox("输入第" &Str(i + 1) &"点的X值")

Y(i) = InputBox("输入第" &Str(i + 1) &"点的Y值")

Next

Dim x1, y1, x2, y2, x3, y3, x1y1, x1y2, x2y1 As Double

For i = 0 To 5

x1 = x1 + X(i)

y1 = y1 + Y(i)

x2 = x2 + X(i) * X(i)

y2 = y2 + Y(i) * Y(i)

x3 = x3 + X(i) * X(i) * X(i)

y3 = y3 + Y(i) * Y(i) * Y(i)

x1y1 = x1y1 + X(i) * Y(i)

x1y2 = x1y2 + X(i) * Y(i) * Y(i)

x2y1 = x2y1 + X(i) * X(i) * Y(i)

Next

Dim C, D, E, G, H, N As Double

N = 6

C = N * x2 - x1 * x1

D = N * x1y1 - x1 * y1

E = N * x3 + N * x1y2 - (x2 + y2) * x1

G = N * y2 - y1 * y1

H = N * x2y1 + N * y3 - (x2 + y2) * y1

Dim thea, theb, thec As Double

thea = (H * D - E * G) / (C * G - D * D)

theb = (H * C - E * D) / (D * D - G * C)

thec = -(thea * x1 + theb * y1 + x2 + y2) / N

Dim resultA, resultB, resultR As Double

resultA = thea / (-2)

resultB = theb / (-2)

resultR = (thea * thea + theb * theb - 4 * thec) ^ 0.5 / 2

MsgBox ("最小二乘法拟合圆为:(" &Str(resultA) &"," &Str(resultB) &") 半径为:" &Str(resultR))

End Sub

第一步，提供一组【X，Y】已知点

第二步，根据已知点拟合圆的一般式方程，利用公式求出圆心和半径。即 用圆的基本方程x^2+y^2+Dx+Ey+F=0，来拟合出其系数D、E、F，求出圆心（-D/2，-E/2），半径0.5√（D^2+-E^2-4F）

第三步，根据圆的参数方程，求出x，y的点，描点plot(x,y,'r-')，得到拟合圆的图形

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