Voronoi diagrams in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Voronoi class from scipy.spatial.

SciPy

from scipy.spatial import [1]

points = [[1, 2], [3, 4], [5, 6]]
vor = Voronoi(points)

Drag options to blanks, or click blank then click option'

AConvexHull

BVoronoi

CDelaunay

DKDTree

Attempts:

3 left

💡 Hint

Common Mistakes

Importing Delaunay instead of Voronoi

Using ConvexHull which is for a different geometry

Trying to import from the wrong module

The Voronoi class is used to create Voronoi diagrams from points.

2fill in blank

medium

Complete the code to create a Voronoi diagram from the points list.

SciPy

points = [[0, 0], [1, 0], [0, 1], [1, 1]]
vor = [1](points)

Drag options to blanks, or click blank then click option'

ADelaunay

BKDTree

CConvexHull

DVoronoi

Attempts:

3 left

💡 Hint

Common Mistakes

Using Delaunay instead of Voronoi

Calling a function that does not exist

Passing points to the wrong class

We use Voronoi(points) to create the Voronoi diagram from the points.

3fill in blank

hard

Fix the error in accessing the Voronoi vertices attribute.

SciPy

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

Drag options to blanks, or click blank then click option'

Avertices

Bridge_points

Cpoints

Dregions

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'points' which are the input points

Using 'regions' which are indices of vertices

Using 'ridge_points' which are pairs of points

The Voronoi vertices are stored in the vertices attribute of the Voronoi object.

4fill in blank

hard

Fill both blanks to create a dictionary of region indices to their vertex coordinates.

SciPy

regions = {i: [vor.[1][v] for v in region] for i, region in enumerate(vor.[2]) if -1 not in region}

Drag options to blanks, or click blank then click option'

Avertices

Bregions

Cridge_vertices

Dridge_points

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up ridge_vertices and regions

Using ridge_points which are pairs of input points

Using vertices where indices are expected

The regions attribute contains lists of vertex indices for each region. We use vertices to get the coordinates of those vertices.

5fill in blank

hard

Fill all three blanks to create a list of ridge vertex pairs for edges between points.

SciPy

ridge_list = [[vor.[1][0], vor.[1][1]] for vor.[2] in vor.[3] if -1 not in vor.[1]]

Drag options to blanks, or click blank then click option'

Aridge_vertices

Bridge_points

Cregions

Dvertices

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing ridge_vertices with regions

Using vertices instead of ridge_vertices for edges

Using regions which are not pairs

The ridge_vertices attribute contains pairs of vertex indices for edges. The ridge_points attribute contains pairs of input points that share those edges.

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