Parametric interpolation in SciPy - Mini Project: Build & Apply

Parametric Interpolation with SciPy

📖 Scenario: You are working with a set of 2D points representing a path on a map. You want to create a smooth curve that passes through these points to better visualize the route.

🎯 Goal: Build a parametric interpolation using SciPy to create smooth x and y coordinates from given points, then plot the smooth curve.

📋 What You'll Learn

Create two lists called x_points and y_points with given coordinates

Create a parameter array t for the points

Use scipy.interpolate.interp1d to create interpolation functions for x and y

Generate new parameter values t_new for smooth interpolation

Calculate interpolated x and y values using the interpolation functions

Print the interpolated x and y arrays

💡 Why This Matters

🌍 Real World

Parametric interpolation is used in mapping, animation, and robotics to create smooth paths from discrete points.

💼 Career

Data scientists and engineers use interpolation to fill missing data, smooth signals, and model continuous phenomena from samples.

1

Create the original points

Create two lists called x_points and y_points with these exact values: x_points = [0, 1, 2, 3, 4] and y_points = [0, 1, 0, 1, 0].

SciPy

# Create x_points and y_points lists with given values
# Your code here

Need a hint?

Use square brackets to create lists with the exact numbers given.

2

Create the parameter array

Import numpy as np and create a numpy array called t with values from 0 to 4 (inclusive) matching the length of x_points.

SciPy

x_points = [0, 1, 2, 3, 4]
y_points = [0, 1, 0, 1, 0]
# Import numpy and create t array
# Your code here

Need a hint?

Use np.arange(5) to create an array from 0 to 4.

3

Create interpolation functions

Import interp1d from scipy.interpolate. Then create two interpolation functions called interp_x and interp_y using interp1d with t and x_points, and t and y_points respectively. Use kind='cubic' for smooth curves.

SciPy

import numpy as np
x_points = [0, 1, 2, 3, 4]
y_points = [0, 1, 0, 1, 0]
t = np.arange(5)
# Import interp1d and create interp_x and interp_y with cubic kind
# Your code here

Need a hint?

Use interp1d with kind='cubic' to create smooth interpolation functions.

4

Generate smooth points and print

Create a numpy array t_new with 50 evenly spaced values from 0 to 4 using np.linspace. Then calculate x_smooth and y_smooth by passing t_new to interp_x and interp_y. Finally, print x_smooth and y_smooth.

SciPy

import numpy as np
from scipy.interpolate import interp1d
x_points = [0, 1, 2, 3, 4]
y_points = [0, 1, 0, 1, 0]
t = np.arange(5)
interp_x = interp1d(t, x_points, kind='cubic')
interp_y = interp1d(t, y_points, kind='cubic')
# Create t_new, calculate x_smooth and y_smooth, then print them
# Your code here

Need a hint?

Use np.linspace(0, 4, 50) to create t_new. Then call interp_x(t_new) and interp_y(t_new). Finally, print both results.