Parametric interpolation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of parametric spline interpolation

What is the output of this code snippet that uses scipy.interpolate.splprep and splev to interpolate a parametric curve?

SciPy

import numpy as np
from scipy.interpolate import splprep, splev

# Define points
x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 0, 1, 0])

# Parametric spline interpolation
(tck, u) = splprep([x, y], s=0)
# Evaluate spline at 5 points
new_points = splev(np.linspace(0, 1, 5), tck)
print(np.round(new_points[0], 2))

A [0. 0.5 1.5 2.5 4. ]

B [0. 1. 1.5 2.5 4. ]

C [0. 1. 2. 3. 4. ]

D [0. 0.84 1.68 2.52 4. ]

💡 Hint

Remember that splev evaluates the spline at given parameter values between 0 and 1.

The spline is constructed to pass through the original x points exactly because smoothing factor s=0. Evaluating at 5 points spaced evenly from 0 to 1 returns the spline evaluated x values, which are not exactly the original x values but smoothed.

❓ data_output

intermediate

Number of points in parametric interpolation output

Given this code using scipy.interpolate.splprep and splev, how many points are in the resulting interpolated curve?

SciPy

import numpy as np
from scipy.interpolate import splprep, splev

x = np.linspace(0, 10, 6)
y = np.sin(x)

(tck, u) = splprep([x, y], s=0)
new_points = splev(np.linspace(0, 1, 50), tck)
print(len(new_points[0]))

A 6

B 50

C 100

D 2

💡 Hint

The number of points returned matches the number of parameter values passed to splev.

The splev function returns points evaluated at the parameter values given. Since 50 points are requested, the output arrays have length 50.

🔧 Debug

advanced

Identify the error in parametric interpolation code

What error does this code raise when trying to perform parametric interpolation with scipy.interpolate.splprep?

SciPy

import numpy as np
from scipy.interpolate import splprep

x = np.array([0, 1, 2])
y = np.array([0, 1])

(tck, u) = splprep([x, y], s=0)

A ValueError: x and y arrays must have the same length

B No error, code runs successfully

C IndexError: index out of range

D TypeError: unsupported operand type(s) for +: 'int' and 'str'

💡 Hint

Check if the input arrays have matching lengths.

The splprep function requires all input coordinate arrays to have the same length. Here, x has length 3 but y has length 2, causing a ValueError.

🚀 Application

advanced

Choosing smoothing factor for noisy data interpolation

You have noisy 2D data points and want to create a smooth parametric curve using scipy.interpolate.splprep. Which smoothing factor s value is best to reduce noise but keep the curve close to data?

A s = 0 (no smoothing, curve passes exactly through points)

B s = very large (curve ignores data and becomes almost a straight line)

C s = moderate positive value (balances smoothness and closeness to data)

D s = negative value (forces curve to oscillate wildly)

💡 Hint

Smoothing factor controls trade-off between fitting data exactly and smoothness.

A moderate positive smoothing factor lets the spline smooth out noise while still following the general shape of the data. Zero smoothing fits exactly, large smoothing oversmooths, negative smoothing is invalid.

🧠 Conceptual

expert

Understanding parameterization in parametric interpolation

In parametric interpolation with scipy.interpolate.splprep, what does the parameter u represent?

A The array of parameter values between 0 and 1 representing the position along the curve

B The array of y-coordinates of the input points

C The smoothing factor controlling curve smoothness

D The knot vector used internally by the spline

💡 Hint

Think about how the curve is parameterized in parametric interpolation.

The parameter u is an array of values from 0 to 1 that represent the relative position of each input point along the parametric curve. It is used to evaluate the spline at any point along the curve.