Path simplification in Matplotlib - Time & Space Complexity

Time Complexity: Path simplification

O(n)

Understanding Time Complexity

When simplifying a path in a plot, we want to know how the time to simplify grows as the path gets longer.

We ask: How does the work increase when the number of points in the path increases?

Scenario Under Consideration

Analyze the time complexity of the following matplotlib path simplification code.

import matplotlib.pyplot as plt
from matplotlib.path import Path

verts = [(0, 0), (1, 2), (2, 3), (3, 5), (5, 8), (8, 13)]
path = Path(verts)
simplified_path = path.simplify_threshold(1.0)
plt.plot(*zip(*simplified_path.vertices))
plt.show()
    

This code creates a path from points and simplifies it by removing points close to a line within a threshold.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each point against a line segment to decide if it can be removed.
• How many times: Each point is checked, and sometimes recursively checked again during simplification.

How Execution Grows With Input

As the number of points grows, the simplification checks more points and segments.

Input Size (n)	Approx. Operations
10	About 20 checks
100	About 200 checks
1000	About 2000 checks

Pattern observation: The number of operations grows roughly in a straight line with the number of points.

Final Time Complexity

Time Complexity: O(n)

This means the time to simplify grows directly in proportion to the number of points in the path.

Common Mistake

[X] Wrong: "Simplifying a path takes the same time no matter how many points it has."

[OK] Correct: More points mean more checks to decide which points to keep or remove, so time grows with input size.

Interview Connect

Understanding how path simplification scales helps you explain efficiency when working with large datasets or complex plots.

Self-Check

"What if the simplification threshold is changed to a smaller value? How would the time complexity change?"