Voronoi diagrams in SciPy - Step-by-Step Execution

Concept Flow - Voronoi diagrams

Input points

↓

Compute Voronoi

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Find edges and vertices

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Plot Voronoi cells

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Visualize regions

Start with points, compute Voronoi regions dividing space, then plot edges and vertices to visualize.

Execution Sample

SciPy

from scipy.spatial import Voronoi, voronoi_plot_2d
import matplotlib.pyplot as plt
points = [[1,1], [2,3], [3,1], [5,4]]
vor = Voronoi(points)
voronoi_plot_2d(vor)
plt.show()

This code creates Voronoi regions from 4 points and plots the diagram.

Execution Table

Step	Action	Input	Output	Notes
1	Input points	[[1,1],[2,3],[3,1],[5,4]]	Points array	Points to build Voronoi from
2	Compute Voronoi	Points array	Voronoi object	Calculates edges, vertices, regions
3	Extract vertices	Voronoi object	Vertices array	Coordinates of Voronoi vertices
4	Extract ridge vertices	Voronoi object	Pairs of vertex indices	Edges between vertices
5	Plot Voronoi	Voronoi object	Plot on matplotlib	Visualizes cells and edges
6	Show plot	Plot	Window with diagram	Displays Voronoi diagram
7	End	N/A	N/A	Execution complete

💡 All points processed and Voronoi diagram displayed

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
points	[[1,1],[2,3],[3,1],[5,4]]	[[1,1],[2,3],[3,1],[5,4]]	[[1,1],[2,3],[3,1],[5,4]]	[[1,1],[2,3],[3,1],[5,4]]	[[1,1],[2,3],[3,1],[5,4]]
vor	N/A	Voronoi object	Voronoi object	Voronoi object	Voronoi object
vertices	N/A	N/A	[array of vertex coords]	[array of vertex coords]	[array of vertex coords]
ridge_vertices	N/A	N/A	N/A	[list of vertex index pairs]	[list of vertex index pairs]

Key Moments - 2 Insights

Why do some Voronoi vertices have coordinates outside the range of input points?

Voronoi vertices can lie outside the convex hull of input points because the diagram extends infinitely; see execution_table step 3 where vertices include points beyond inputs.

What does a ridge vertex pair of [-1, 2] mean in the Voronoi object?

A -1 index means the edge extends to infinity in that direction; this is shown in execution_table step 4 where ridge vertices include -1 for infinite edges.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is stored in 'vertices'?

A Coordinates of Voronoi vertices

B Input points

C Pairs of ridge vertices

D Plot object

💡 Hint

Check the 'Output' column in step 3 of execution_table

At which step does the code calculate edges between Voronoi vertices?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look for 'Extract ridge vertices' in execution_table step 4

If we add more points, how will the 'vertices' variable change after step 3?

A It will have fewer vertices

B It will have more vertices

C It will stay the same

D It will become empty

💡 Hint

More points create more Voronoi regions and vertices, see variable_tracker for 'vertices'

Concept Snapshot

Voronoi diagrams split space by closest points.
Use scipy.spatial.Voronoi(points) to compute.
Vertices are intersection points of edges.
Edges can be finite or infinite (-1 index).
Plot with voronoi_plot_2d(vor) and plt.show().

Full Transcript

Voronoi diagrams divide space into regions closest to each input point. We start by giving a list of points. Then, scipy's Voronoi function calculates the edges and vertices that form these regions. Some vertices can be outside the input points range because the diagram extends infinitely. Edges are pairs of vertices; if an edge extends infinitely, one vertex index is -1. Finally, we plot the diagram using voronoi_plot_2d and show it with matplotlib. This process helps visualize how space is split by proximity to points.