Voronoi diagrams in SciPy - Mini Project: Build & Apply

Voronoi Diagrams with SciPy

📖 Scenario: Imagine you are working for a city planning team. You want to divide a park into areas closest to each of several fountains. This helps decide where to place benches and signs so visitors are near a water source.

🎯 Goal: You will create a set of points representing fountains, configure a boundary size, compute the Voronoi diagram using SciPy, and finally display the Voronoi regions.

📋 What You'll Learn

Create a list of fountain coordinates as tuples

Set a boundary size variable for the park area

Use SciPy's Voronoi function to compute the diagram

Plot the Voronoi diagram using matplotlib

💡 Why This Matters

🌍 Real World

Voronoi diagrams help divide spaces based on proximity, useful in city planning, resource allocation, and biology.

💼 Career

Data scientists and GIS specialists use Voronoi diagrams to analyze spatial data and optimize locations.

1

Create fountain coordinates

Create a list called fountains with these exact tuples: (2, 3), (5, 5), (1, 8), (7, 2), and (6, 6).

SciPy

# Create the list of fountain coordinates
# Your code here

Hint

Use a Python list with tuples for each fountain's (x, y) position.

2

Set park boundary size

Create a variable called boundary_size and set it to 10 to represent the park's width and height.

SciPy

fountains = [(2, 3), (5, 5), (1, 8), (7, 2), (6, 6)]
# Set the boundary size of the park
# Your code here

Hint

This variable will help later when plotting the park area.

3

Compute the Voronoi diagram

Import Voronoi from scipy.spatial. Then create a variable called vor by passing fountains to Voronoi().

SciPy

fountains = [(2, 3), (5, 5), (1, 8), (7, 2), (6, 6)]
boundary_size = 10
# Import Voronoi and compute the diagram
# Your code here

Hint

Use from scipy.spatial import Voronoi and then call Voronoi(fountains).

4

Plot the Voronoi diagram

Import matplotlib.pyplot as plt. Use plt.figure() to create a figure. Then use scipy.spatial.voronoi_plot_2d(vor) to plot the diagram. Finally, set the x and y limits to 0 and boundary_size and call plt.show() to display.

SciPy

from scipy.spatial import Voronoi

fountains = [(2, 3), (5, 5), (1, 8), (7, 2), (6, 6)]
boundary_size = 10

vor = Voronoi(fountains)
# Import matplotlib and plot the Voronoi diagram
# Your code here

Hint

Use voronoi_plot_2d(vor) to draw the diagram and plt.show() to display it.

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