Path simplification in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of path simplification with default tolerance

What is the output of the following code that plots a path and applies path simplification with default tolerance?

Matplotlib

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

vertices = [(0, 0), (1, 0.1), (2, -0.1), (3, 5), (4, 6), (5, 7)]
codes = [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO, Path.LINETO, Path.LINETO]

path = Path(vertices, codes)
simplified_path = path.simplify()

fig, ax = plt.subplots()
patch = patches.PathPatch(path, facecolor='none', lw=2, label='Original')
patch_s = patches.PathPatch(simplified_path, facecolor='none', lw=2, linestyle='--', label='Simplified')
ax.add_patch(patch)
ax.add_patch(patch_s)
ax.legend()
ax.set_xlim(-1, 6)
ax.set_ylim(-1, 8)
plt.show()

len_original = len(path.vertices)
len_simplified = len(simplified_path.vertices)
(len_original, len_simplified)

A (6, 4)

B (6, 3)

C (6, 6)

D (6, 5)

💡 Hint

Check how many points are removed by default simplification in matplotlib Path.

The original path has 6 points. The simplify() method removes points that are nearly collinear within a default tolerance, reducing the number of points to 4.

❓ data_output

intermediate

Number of vertices after increasing tolerance

Given a path with vertices [(0,0), (1,0.1), (2,-0.1), (3,5), (4,6), (5,7)], what is the number of vertices after simplification with tolerance=1.0?

Matplotlib

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

vertices = [(0, 0), (1, 0.1), (2, -0.1), (3, 5), (4, 6), (5, 7)]
codes = [Path.MOVETO] + [Path.LINETO]*5

path = Path(vertices, codes)
simplified_path = path.simplify(tolerance=1.0)
len(simplified_path.vertices)

A 3

B 4

C 5

D 6

💡 Hint

Higher tolerance removes more points.

With tolerance=1.0, the simplification removes more points, leaving only 3 vertices.

❓ visualization

advanced

Visual difference between low and high tolerance simplification

Which plot correctly shows the original path and two simplified paths with tolerance=0.01 and tolerance=1.0 respectively?

Matplotlib

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

vertices = [(0, 0), (1, 0.1), (2, -0.1), (3, 5), (4, 6), (5, 7)]
codes = [Path.MOVETO] + [Path.LINETO]*5

path = Path(vertices, codes)
simplified_low = path.simplify(tolerance=0.01)
simplified_high = path.simplify(tolerance=1.0)

fig, ax = plt.subplots()
ax.plot(*zip(*vertices), 'o-', label='Original')
ax.plot(*zip(*simplified_low.vertices), 's--', label='Simplified tol=0.01')
ax.plot(*zip(*simplified_high.vertices), 'd-.', label='Simplified tol=1.0')
ax.legend()
plt.show()

A Plot with original path missing, only simplified paths shown with same number of points.

B Plot with original path as solid line with circles, low tolerance simplification as dashed line with squares close to original, and high tolerance simplification as dash-dot line with diamonds with fewer points.

C Plot with original path and both simplifications overlapping exactly with no visible difference.

D Plot with original path as dashed line, low tolerance simplification as solid line, and high tolerance simplification as dotted line, all with same number of points.

💡 Hint

Higher tolerance removes more points, so the path looks simpler.

The plot with original path as solid circles, low tolerance simplification close to original with squares, and high tolerance simplification with fewer points as diamonds matches the expected behavior.

🧠 Conceptual

advanced

Effect of tolerance parameter in Path.simplify()

What is the effect of increasing the tolerance parameter in matplotlib's Path.simplify() method?

A It reverses the order of vertices in the path.

B It adds more points to the path, making it more detailed.

C It changes the color of the path when plotted.

D It removes more points, resulting in a simpler path with fewer vertices.

💡 Hint

Think about what simplification means in terms of points.

Increasing tolerance allows the simplification algorithm to remove points that deviate less from a straight line, thus reducing the number of vertices.

🔧 Debug

expert

Identify the error in path simplification code

What error does the following code raise? import matplotlib.pyplot as plt from matplotlib.path import Path vertices = [(0, 0), (1, 1), (2, 2)] codes = [Path.MOVETO, Path.LINETO] path = Path(vertices, codes) simplified = path.simplify() print(len(simplified.vertices))

A TypeError: unsupported operand type(s) for +: 'int' and 'str'

B AttributeError: 'Path' object has no attribute 'simplify'

C ValueError: codes and vertices must be the same length

D No error, prints 3

💡 Hint

Check the length of codes and vertices lists.

The codes list has length 2 but vertices has length 3, causing a ValueError when creating the Path object.