Voronoi diagrams in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Voronoi vertices coordinates

What is the output of the following code snippet that computes Voronoi vertices for given points?

SciPy

from scipy.spatial import Voronoi
import numpy as np
points = np.array([[0, 0], [1, 0], [0, 1], [1, 1]])
vor = Voronoi(points)
print(np.round(vor.vertices, 2))

A [[0. 0] [1. 0] [0. 1] [1. 1]]

B [[0.5 0.5] [0. 0. ] [1. 0. ] [0. 1. ] [1. 1. ]]

C [[0.5 0.5] [0.5 0. ] [0. 0.5] [1. 0.5] [0.5 1. ]]

D [[0.5 0.5]]

💡 Hint

Voronoi vertices are points equidistant from the input points, often at the center of the input points' convex hull.

The Voronoi diagram for four points at the corners of a square has a single Voronoi vertex at the center (0.5, 0.5). The other options list either input points or incorrect vertices.

❓ data_output

intermediate

Number of Voronoi regions

Given the following points, how many Voronoi regions does the Voronoi diagram have?

SciPy

from scipy.spatial import Voronoi
import numpy as np
points = np.array([[2, 3], [5, 4], [3, 7], [6, 1], [7, 5]])
vor = Voronoi(points)
print(len(vor.regions))

A 7

B 11

C 5

D 10

💡 Hint

The number of Voronoi regions is related to the number of points but includes some empty or infinite regions.

The Voronoi object stores regions for all vertices including empty and infinite ones. For 5 points, the number of regions is 11.

❓ visualization

advanced

Plotting Voronoi diagram with infinite ridges

Which code snippet correctly plots the Voronoi diagram including infinite ridges extended to a finite distance?

SciPy

from scipy.spatial import Voronoi, voronoi_plot_2d
import matplotlib.pyplot as plt
import numpy as np
points = np.array([[1, 1], [2, 3], [3, 1], [4, 4]])
vor = Voronoi(points)
fig, ax = plt.subplots()
# Fill in the missing code to plot infinite ridges

A

voronoi_plot_2d(vor, ax=ax, show_vertices=False, line_colors='orange')
plt.show()

B

voronoi_plot_2d(vor, ax=ax, show_vertices=True)
plt.show()

C

voronoi_plot_2d(vor, ax=ax, show_vertices=False)
plt.xlim(0,5)
plt.ylim(0,5)
plt.show()

D

voronoi_plot_2d(vor, ax=ax, show_vertices=False)
plt.xlim(0,5)
plt.ylim(0,5)
plt.show()  # Infinite ridges are not extended

💡 Hint

Use the parameter to hide vertices and change line colors to highlight edges.

Option A uses show_vertices=False to hide vertices and changes line colors to orange, which helps visualize infinite ridges clearly. Other options either show vertices or do not highlight infinite ridges.

🔧 Debug

advanced

Identify the error in Voronoi region plotting code

What error does the following code produce when trying to plot Voronoi regions?

SciPy

from scipy.spatial import Voronoi
import matplotlib.pyplot as plt
import numpy as np
points = np.array([[0, 0], [1, 0], [0, 1]])
vor = Voronoi(points)
for region_index in vor.point_region:
    region = vor.regions[region_index]
    polygon = [vor.vertices[i] for i in region]
    plt.fill(*zip(*polygon), alpha=0.4)
plt.show()

A TypeError: 'NoneType' object is not iterable

B ValueError: too many values to unpack (expected 2)

C No error, plots correctly

D IndexError: list index out of range

💡 Hint

Some Voronoi regions can be empty or contain -1 indicating infinite vertices.

The region list can contain -1 which is not a valid index for vertices, causing NoneType or iteration errors when accessing vor.vertices[-1].

🚀 Application

expert

Using Voronoi diagram to find nearest neighbor regions

Given a set of points, which code snippet correctly finds the index of the Voronoi region closest to the point [3, 3]?

SciPy

from scipy.spatial import Voronoi, distance
import numpy as np
points = np.array([[1, 2], [4, 4], [5, 1], [2, 5]])
vor = Voronoi(points)
query_point = np.array([3, 3])
# Fill in code to find closest Voronoi region index

A

distances = [distance.euclidean(query_point, vor.vertices[i]) for i in range(len(vor.vertices))]
closest_index = distances.index(min(distances))
print(closest_index)

B

distances = [distance.euclidean(query_point, points[i]) for i in range(len(points))]
closest_index = distances.index(min(distances))
print(closest_index)

C

closest_index = vor.point_region[np.argmin(np.linalg.norm(points - query_point, axis=1))]
print(closest_index)

D

closest_index = np.argmin(np.linalg.norm(vor.vertices - query_point, axis=1))
print(closest_index)

💡 Hint

Voronoi regions correspond to input points via point_region attribute.

Option C correctly finds the input point closest to query_point and then gets its Voronoi region index using point_region. Other options either use vertices or do not map to regions correctly.

Practice

1. What does a Voronoi diagram represent in data science?

easy

A. It reduces data dimensions for visualization

B. It divides space into regions closest to given points

C. It predicts future data points using regression

D. It clusters data points into groups based on similarity

Solution

1. Step 1: Understand Voronoi diagram concept

   A Voronoi diagram splits space so each region contains points closest to one seed point.

2. Step 2: Compare options with definition

   Only It divides space into regions closest to given points describes this splitting of space by proximity to points.

3. Final Answer:

   It divides space into regions closest to given points -> Option B

4. Quick Check:

   Voronoi = space division by closest points [OK]

Hint: Voronoi = closest region per point [OK]

Common Mistakes:

• Confusing Voronoi with clustering
• Thinking it predicts or reduces data
• Mixing with regression or PCA

2. Which is the correct way to create a Voronoi diagram using scipy for points stored in variable points?

easy

A. vor = Voronoi(points)

B. vor = scipy.Voronoi(points)

C. vor = spatial.Voronoi(points)

D. vor = scipy.spatial.Voronoi(points)

Solution

1. Step 1: Recall scipy Voronoi syntax

   The Voronoi class is in scipy.spatial module, so full call is scipy.spatial.Voronoi(points).

2. Step 2: Check options for correct import and usage

   Only vor = scipy.spatial.Voronoi(points) uses full correct path. Others miss module or import.

3. Final Answer:

   vor = scipy.spatial.Voronoi(points) -> Option D

4. Quick Check:

   Use scipy.spatial.Voronoi for Voronoi diagrams [OK]

Hint: Use full module path: scipy.spatial.Voronoi(points) [OK]

Common Mistakes:

• Omitting 'spatial' module
• Using incomplete import paths
• Calling Voronoi without module prefix

3. What will be the output of the following code snippet?

import numpy as np
from scipy.spatial import Voronoi
points = np.array([[0, 0], [1, 0], [0, 1]])
vor = Voronoi(points)
print(len(vor.regions))

medium

A. 3

B. 4

C. 7

D. 5

Solution

1. Step 1: Understand Voronoi regions attribute

   vor.regions is a list of all Voronoi regions, including empty and infinite ones, not just one per input point.

2. Step 2: Check typical region count for 3 points

   For 3 points forming a triangle, scipy returns 7 regions (including empty and infinite regions).

3. Final Answer:

   7 -> Option C

4. Quick Check:

   Voronoi regions count includes empty and infinite regions [OK]

Hint: Regions count includes empty and infinite regions [OK]

Common Mistakes:

• Thinking regions count == points count
• Ignoring empty or infinite regions
• Confusing regions with vertices

4. Identify the error in this code that tries to create a Voronoi diagram:

from scipy.spatial import Voronoi
points = np.array([[0, 0], [1, 1], [1, 0]])
vor = Voronoi(points)
print(vor.vertices)

medium

A. Missing import for numpy

B. Voronoi requires 3D points, not 2D

C. points must be a numpy array, not a list

D. Voronoi class does not have vertices attribute

Solution

1. Step 1: Check input type for Voronoi

   np.array is used without importing numpy as np.

2. Step 2: Identify error cause

   Missing import numpy as np causes NameError: name 'np' is not defined.

3. Final Answer:

   Missing import for numpy -> Option A

4. Quick Check:

   Import numpy as np before np.array [OK]

Hint: import numpy as np before using np.array [OK]

Common Mistakes:

• Missing import for numpy
• Assuming 3D points required
• Thinking vertices attribute missing

5. You have 2D points representing store locations. You want to find the area closest to each store using scipy Voronoi. Which approach correctly calculates the polygon area for each Voronoi region?

hard

A. Use vor.regions to get indices, then vor.vertices to get polygon points, and calculate polygon area

B. Calculate distance between points and sum them for area

C. Use vor.points directly as polygon vertices for area

D. Sum the lengths of edges in vor.ridge_vertices for area

Solution

1. Step 1: Understand Voronoi region structure

   Each region is defined by indices in vor.regions pointing to vor.vertices coordinates forming polygons.

2. Step 2: Calculate polygon area from vertices

   Extract vertices for each region polygon and compute area using polygon area formula.

3. Final Answer:

   Use vor.regions indices with vor.vertices to get polygons and calculate area -> Option A

4. Quick Check:

   Regions + vertices = polygon area calculation [OK]

Hint: Use vor.regions and vor.vertices to get polygons [OK]

Common Mistakes:

• Using points instead of vertices for polygons
• Summing distances instead of area
• Using ridge lengths as area