在标题中,我想用PYTHON将圆柱体装到一组3D点上。这是一个很好的solution with MATLAB。我们怎样才能用Python做到这一点?
答案 0 :(得分:3)
David Eberly网站"Fitting 3D Data with a Cylinder"上有一篇文章描述了数学基础并展示了伪代码。
您还可以在同一站点的Geometric Tools Engine中引用C ++代码。我认为可以在NymPy中实现一些辅助数学函数,如矩阵逆等。
答案 1 :(得分:2)
使用scipy.optimize.leastsq,我们可以创建一个误差函数,其中观察到的圆柱半径和建模半径之间的差异被最小化。以下是安装垂直圆柱的示例
import numpy as np
from scipy.optimize import leastsq
def cylinderFitting(xyz,p,th):
"""
This is a fitting for a vertical cylinder fitting
Reference:
http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XXXIX-B5/169/2012/isprsarchives-XXXIX-B5-169-2012.pdf
xyz is a matrix contain at least 5 rows, and each row stores x y z of a cylindrical surface
p is initial values of the parameter;
p[0] = Xc, x coordinate of the cylinder centre
P[1] = Yc, y coordinate of the cylinder centre
P[2] = alpha, rotation angle (radian) about the x-axis
P[3] = beta, rotation angle (radian) about the y-axis
P[4] = r, radius of the cylinder
th, threshold for the convergence of the least squares
"""
x = xyz[:,0]
y = xyz[:,1]
z = xyz[:,2]
fitfunc = lambda p, x, y, z: (- np.cos(p[3])*(p[0] - x) - z*np.cos(p[2])*np.sin(p[3]) - np.sin(p[2])*np.sin(p[3])*(p[1] - y))**2 + (z*np.sin(p[2]) - np.cos(p[2])*(p[1] - y))**2 #fit function
errfunc = lambda p, x, y, z: fitfunc(p, x, y, z) - p[4]**2 #error function
est_p , success = leastsq(errfunc, p, args=(x, y, z), maxfev=1000)
return est_p
if __name__=="__main__":
np.set_printoptions(suppress=True)
xyz = np.loadtxt('cylinder11.xyz')
#print xyz
print "Initial Parameters: "
p = np.array([-13.79,-8.45,0,0,0.3])
print p
print " "
print "Performing Cylinder Fitting ... "
est_p = cylinderFitting(xyz,p,0.00001)
print "Fitting Done!"
print " "
print "Estimated Parameters: "
print est_p
答案 2 :(得分:1)
我遇到过类似的情况,通过几个点拟合圆柱体。我们使用间隙传感器在几个点测量了两个圆柱体之间的间隙,我必须想象与圆柱体相比间隙是如何变化的。
我使用了 ax.plot_surface(x, y, z, alpha=0.5) 其中 x , y, z 是所有点的 3D 位置的 numpy 数组。看看下面的图片。
代码片段,
# Extract X,Y,Z values from the sensor data
for i in range(num_of_sensors):
ax.scatter(x[:,i], y[:,i], z[:,i], color = "k", marker=".", s=5, cmap='hot')
ax.text(x[0,i]+ 10, y[0,i] + 10, z[0,i]+100, '%s' % (idx[i]), size=5, zorder=1, color='b')
# plot the surface
ax.plot_surface(x, y, z, alpha=0.5)