将 3d 坐标拟合成抛物线

如何解决将 3d 坐标拟合成抛物线

我想通过将球的 3d 坐标拟合成抛物线来预测球的轨迹。下面是我的代码。但不是抛物线，我得到了一条直线。如果您对此有任何线索，请告诉我。谢谢！

# draw scatter coordiante 
fig = plt.figure()
ax = plt.axes(projection = '3d')
x_list = []
y_list = []
z_list = []
for x in rm_list:
    x_list.append(x[0][0])
    y_list.append(x[0][1])
    z_list.append(x[0][2])
x = np.array(x_list)
y = np.array(y_list)
z = np.array(z_list)
ax.scatter(x,y,z)

# curve fit
def func(x,a,b,c,d):
    return a * x[0]**2 + b * x[1]**2 + c * x[0] * x[1] + d

data = np.column_stack([x_list,y_list,z_list])
popt,_ = curve_fit(func,data[:,:2].T,ydata=data[:,2])
a,d = popt
print('y= %.5f * x ^ 2 + %.5f * y ^ 2 + %.5f * x * y + %.5f' %(a,d))
x1 = np.linspace(0.3,0.4,100)
y1 = np.linspace(0.02,0.06,100)
z1 = a * x1 ** 2 + b * y1 ** 2 + c * x1 * y1 + d
ax.plot(x1,y1,z1,color='green')

plt.show()

更新 1 将 func 更改为 ax^2 + by^2 + cxy + dx + ey + f 后，我得到了一条抛物线，但不适合坐标。

解决方法

您拥有基础时间戳数据使拟合过程更容易：

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
from numpy.polynomial import Polynomial

# test data generation with some noise
# here read in your data
np.random.seed(123)
n = 40
x_param = [ 1,21,-1]
y_param = [12,-3,0]
z_param = [-3,-2]
px = Polynomial(x_param)
py = Polynomial(y_param)
pz = Polynomial(z_param)
t = np.random.choice(np.linspace (-3000,2000,1000)/500,n)
x = px(t) + np.random.random(n)
y = py(t) + np.random.random(n)
z = pz(t) + np.random.random(n)


# here start the real calculations 
# draw scatter coordinates of raw data
fig = plt.figure()
ax = plt.axes(projection = '3d')
ax.scatter(x,y,z,label="raw data")

# curve fit function
def func(t,x2,x1,x0,y2,y1,y0,z2,z1,z0):
    Px=Polynomial([x2,x0])
    Py=Polynomial([y2,y0])
    Pz=Polynomial([z2,z0])
    return np.concatenate([Px(t),Py(t),Pz(t)])


# curve fit
# start values are not necessary for this example 
# but make it your rule to always provide start values for curve_fit 
start_vals = [ 1,10,1,-1,-1]
xyz = np.concatenate([x,z])
popt,_ = curve_fit(func,t,xyz,p0=start_vals)
print(popt)
#[ 1.58003630e+00  2.10059868e+01 -1.00401965e+00  
#  1.25895591e+01 -2.97374035e+00 -3.23358241e-03 
# -2.44293562e+00  3.96407428e-02 -1.99671092e+00]

# regularly spaced fit data
t_fit = np.linspace(min(t),max(t),100)
xyz_fit = func(t_fit,*popt).reshape(3,-1)    
ax.plot(xyz_fit[0,:],xyz_fit[1,xyz_fit[2,color="green",label="fitted data")

ax.legend()
plt.show()

示例输出：