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python 拟合圓心_如何在python中使用最小二乘拟合找到圓心?

我正在嘗試拟合一些資料點以找到圓的中心.以下所有點都是圍繞圓周的噪聲資料點:

data = [(2.2176383052987667, 4.218574252410221),

(3.3041214516913033, 5.223500807396272),

(4.280815855023374, 6.461487709813785),

(4.946375258539319, 7.606952538212697),

(5.382428804463699, 9.045717060494576),

(5.752578028217334, 10.613667377465823),

(5.547729017414035, 11.92662513852466),

(5.260208374620305, 13.57722448066025),

(4.642126672822957, 14.88238955729078),

(3.820310290976751, 16.10605425390148),

(2.8099420132544024, 17.225880123445773),

(1.5731539516426183, 18.17052077121059),

(0.31752822350872545, 18.75261434891438),

(-1.2408437559671106, 19.119355580780265),

(-2.680901948575409, 19.15018791257732),

(-4.190406775175328, 19.001321726517297),

(-5.533990404926917, 18.64857428377178),

(-6.903383826792998, 17.730112542165955),

(-8.082883753215347, 16.928080323602334),

(-9.138397388219254, 15.84088004983959),

(-9.92610373064812, 14.380575762984085),

(-10.358670204629814, 13.018017342781242),

(-10.600053524240247, 11.387283417089911),

(-10.463673966507077, 10.107554951600699),

(-10.179820255235496, 8.429558128401448),

(-9.572153386953028, 7.1976672709797676),

(-8.641475289758178, 5.8312286526738175),

(-7.665976739804268, 4.782663065707469),

(-6.493033077746997, 3.8549965442534684),

(-5.092340806635571, 3.384419909199452),

(-3.6530364510489073, 2.992272643733981),

(-2.1522365767310796, 3.020780664301393),

(-0.6855406924835704, 3.0767643753777447),

(0.7848958776292426, 3.6196842530995332),

(2.0614188482646947, 4.32795711960546),

(3.2705467984691508, 5.295836809444288),

(4.359297538484424, 6.378324784240816),

(4.981264502955681, 7.823851404553242)]

有例如:

# == METHOD 2 ==

from scipy import optimize

method_2 = "leastsq"

def calc_R(xc, yc):

""" calculate the distance of each 2D points from the center (xc, yc) """

return sqrt((x-xc)**2 + (y-yc)**2)

def f_2(c):

""" calculate the algebraic distance between the data points and the mean circle centered at c=(xc, yc) """

Ri = calc_R(*c)

return Ri - Ri.mean()

center_estimate = x_m, y_m

center_2, ier = optimize.leastsq(f_2, center_estimate)

xc_2, yc_2 = center_2

Ri_2 = calc_R(*center_2)

R_2 = Ri_2.mean()

residu_2 = sum((Ri_2 - R_2)**2)

但這似乎是使用單個xy?有關如何将此功能插入我的資料示例的任何想法?