Convex hull computation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Convex Hull vertices indices

What is the output of this code snippet that computes the convex hull of a set of 2D points using scipy?

SciPy

import numpy as np
from scipy.spatial import ConvexHull
points = np.array([[0, 0], [1, 1], [1, 0], [0, 1], [0.5, 0.5]])
hull = ConvexHull(points)
print(list(hull.vertices))

A [0, 2, 1, 3]

B [0, 1, 2, 3, 4]

C [4, 2, 1]

D [1, 2, 3]

💡 Hint

The convex hull vertices are the outermost points forming the polygon around all points.

The points at indices 0, 2, 1, and 3 form the convex polygon enclosing all points. The point at index 4 lies inside and is not part of the hull vertices.

❓ data_output

intermediate

Number of simplices in 3D convex hull

Given a set of 3D points, how many simplices (triangular faces) does the convex hull have?

SciPy

import numpy as np
from scipy.spatial import ConvexHull
points = np.random.rand(10, 3)
hull = ConvexHull(points)
print(len(hull.simplices))

A 8

B 10

C 20

D 16

💡 Hint

The number of simplices depends on the shape formed by the points, but for 10 random points in 3D, it is usually around 16.

For 10 random points in 3D, the convex hull typically has 16 triangular faces (simplices).

🔧 Debug

advanced

Identify the error in convex hull computation

What error does this code raise when trying to compute the convex hull of a single point?

SciPy

import numpy as np
from scipy.spatial import ConvexHull
points = np.array([[0, 0]])
hull = ConvexHull(points)

A IndexError: list index out of range

B QhullError: input must contain at least 3 points

C TypeError: unsupported operand type(s)

D No error, returns empty hull

💡 Hint

Convex hull requires at least 3 points in 2D to form a polygon.

The ConvexHull function raises a QhullError because the input has fewer than 3 points, which is insufficient to form a hull in 2D.

❓ visualization

advanced

Visualizing convex hull edges in 2D

Which option correctly plots the convex hull edges for a set of 2D points using matplotlib and scipy?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import ConvexHull
points = np.random.rand(15, 2)
hull = ConvexHull(points)
plt.plot(points[:,0], points[:,1], 'o')
for simplex in hull.simplices:
    plt.plot(points[simplex, 0], points[simplex, 1], 'r-')
plt.show()

A Plots points and blue lines connecting all points, not just hull edges.

B Plots points but no lines connecting hull edges.

C Plots points and red lines connecting hull edges correctly.

D Raises an error due to incorrect indexing.

💡 Hint

The hull.simplices attribute contains pairs of indices for edges of the hull.

The code plots the points and draws red lines between points that form the convex hull edges, correctly visualizing the hull.

🚀 Application

expert

Using convex hull to filter outliers in 2D data

You have 2D data points with some outliers far from the main cluster. Which approach uses the convex hull to identify and remove outliers?

A Compute the convex hull of the main cluster only, then remove points outside this hull.

B Compute the convex hull of all points, then remove points inside the hull polygon.

C Compute the convex hull of all points, then remove points that are vertices of the hull.

D Compute the convex hull of all points, then remove points outside the hull's polygon.

💡 Hint

Outliers lie outside the main cluster's convex hull.

To remove outliers, first identify the main cluster, compute its convex hull, and remove points outside this hull. Removing hull vertices or points inside the hull does not remove outliers.