Path simplification in Matplotlib - Step-by-Step Execution

Concept Flow - Path simplification

Start with original path points

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Apply simplification algorithm

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Check if points can be reduced

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Remove unnecessary points

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Output simplified path points

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End

The process starts with original path points, applies a simplification algorithm that checks if points can be removed without changing the shape much, then outputs a simpler path.

Execution Sample

Matplotlib

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

path = Path([(0, 0), (1, 0.1), (2, 0.2), (3, 0)])
simplified = path.simplify_threshold(0.15)
print(simplified.vertices)

This code creates a path with points, simplifies it using a threshold, and prints the simplified points.

Execution Table

Step	Action	Current Points	Simplification Check	Points Removed	Resulting Points
1	Start with original points	[(0,0), (1,0.1), (2,0.2), (3,0)]	N/A	0	[(0,0), (1,0.1), (2,0.2), (3,0)]
2	Check if point (1,0.1) can be removed	[(0,0), (1,0.1), (2,0.2), (3,0)]	Distance < 0.15? Yes	1	[(0,0), (2,0.2), (3,0)]
3	Check if point (2,0.2) can be removed	[(0,0), (2,0.2), (3,0)]	Distance < 0.15? No	0	[(0,0), (2,0.2), (3,0)]
4	End simplification	[(0,0), (2,0.2), (3,0)]	N/A	0	[(0,0), (2,0.2), (3,0)]

💡 No more points can be removed without exceeding threshold

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
path.vertices	[(0,0), (1,0.1), (2,0.2), (3,0)]	[(0,0), (2,0.2), (3,0)]	[(0,0), (2,0.2), (3,0)]	[(0,0), (2,0.2), (3,0)]
simplified.vertices	N/A	[(0,0), (2,0.2), (3,0)]	[(0,0), (2,0.2), (3,0)]	[(0,0), (2,0.2), (3,0)]

Key Moments - 2 Insights

Why is the point (1, 0.1) removed but (2, 0.2) is kept?

Because the simplification checks if removing a point keeps the path within the threshold distance. At step 2, (1, 0.1) is close enough to the line between (0,0) and (2,0.2) to be removed. At step 3, removing (2,0.2) would change the shape too much, so it is kept.

Does simplification always remove points?

No. Simplification only removes points if the path shape stays close enough to the original. If removing a point changes the path beyond the threshold, it is kept, as shown in step 3.

Visual Quiz - 3 Questions

Look at the execution table, what are the points after step 2?

A [(0,0), (1,0.1), (2,0.2), (3,0)]

B [(0,0), (2,0.2), (3,0)]

C [(0,0), (3,0)]

D [(1,0.1), (2,0.2), (3,0)]

💡 Hint

Check the 'Resulting Points' column at step 2 in the execution table.

At which step does the simplification decide not to remove a point?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Points Removed' column and see where it is zero after a check.

If the threshold was smaller, what would happen to the number of points removed?

A More points would be removed

B No points would be removed

C Fewer points would be removed

D All points would be removed

💡 Hint

A smaller threshold means stricter rules for removing points, so fewer points qualify.

Concept Snapshot

Path simplification reduces points in a path while keeping its shape.
Use a threshold to control how much change is allowed.
Points closer than threshold to a line segment can be removed.
Simplify with path.simplify_threshold(threshold).
Result is a simpler path with fewer points.

Full Transcript

Path simplification starts with a set of points defining a path. The algorithm checks each point to see if it can be removed without changing the path shape beyond a set threshold. Points that are close enough to the line between their neighbors are removed. This process repeats until no more points can be removed. The final output is a simpler path with fewer points but a similar shape. In the example, the point (1, 0.1) was removed because it was close to the line between (0,0) and (2,0.2), but (2,0.2) was kept because removing it would change the shape too much.