B-spline Curve Fitting Example in Python

    B-spline or basis spline is a curve approximation method based on given coefficients. B-spline requires the parameters such as knots, spline coefficients, and degree of a spline. The SciPy API provides BSpline class to implement the B-spline fitting for a given dataset.
   In this tutorial, you'll learn how to implement B-spline interpolation by using a BSpline class in Python. The tutorial covers:

  1. B-spline interpolation
  2. Source code listing

 We'll start by loading the required libraries.

 
from scipy import interpolate
import matplotlib.pyplot as plt
import numpy as np 
 
 
 
B-spline interpolation
 
    B-spline constructs a curve for given data points and it is useful function to smooth a curve or surface data. Here, we'll see how B-spline can help us to smooth a given curve data. 
   We'll prepare dataset for this tutorial and visualize it in a plot. The target data contains x and y components of curve data. You may apply the same method for your target data.
 

y = [0,1,3,4,3,5,7,5,2,3,4,8,9,8,7]
n = len(y)
x = range(0, n) 
 
 
    Next, we'll visualize the data and linear interpolation on a graph. Linear interpolation in a graph is simply connecting data points linearly.
 
 
plt.plot(x, y, 'ro', label="original")
plt.plot(x, y, 'b', label="linear interpolation")
plt.title("Target data")
plt.legend(loc='best', fancybox=True, shadow=True)
plt.grid()
plt.show() 

    To represent B-spline interpolation, we need to provide required coefficients. We can take them by using the 'splrep' function. The 'splrep' function returns t, c, k tuple containing  the vector of knots, the B-spline coefficients, and the degree of the spline.

 
tck = interpolate.splrep(x, y, s=0, k=3
 

    Next, we'll create new x data with more sample number to make smoother curve. Then build the B-splne curve on this data.
 
 
x_new = np.linspace(min(x), max(x), 100)
y_fit = interpolate.BSpline(*tck)(x_new)
 
 
    Finally, we can visualize the constructed B-spline curve on a graph.
 
 
plt.title("BSpline curve fitting")
plt.plot(x, y, 'ro', label="original")
plt.plot(x_new, y_fit, '-c', label="B-spline")
plt.legend(loc='best', fancybox=True, shadow=True)
plt.grid()
plt.show() 
 
   
 

    In this tutorial, we've briefly learned how to implement B-spline interpolation by using SciPy API's BSpline class in Python. The full source code is listed below. 
 
 
Source code listing

 
from scipy import interpolate
import matplotlib.pyplot as plt
import numpy as np

y = [0,1,3,4,3,5,7,5,2,3,4,8,9,8,7]
n = len(y)
x = range(0, n)

plt.plot(x, y, 'ro', label="original")
plt.plot(x, y, 'b', label="linear interpolation")
plt.title("Target data")
plt.legend(loc='best', fancybox=True, shadow=True)
plt.grid()
plt.show()

tck = interpolate.splrep(x, y, s=0, k=3)
x_new = np.linspace(min(x), max(x), 100)
y_fit = interpolate.BSpline(*tck)(x_new)

plt.title("BSpline curve fitting")
plt.plot(x, y, 'ro', label="original")
plt.plot(x_new, y_fit, '-c', label="B-spline")
plt.legend(loc='best', fancybox=True, shadow=True)
plt.grid()
plt.show() 
  
 
References:

No comments:

Post a Comment