Douglas-Peucker line simplification

Simplifies a wiggly coastline-like curve at several tolerances. Larger tolerances keep fewer vertices, and every discarded vertex stays within the tolerance of the simplified line.

import matplotlib.pyplot as plt
import numpy as np

from mathematicskit.geometry import douglas_peucker

A rough curve and its simplifications

rng = np.random.default_rng(2)
x = np.linspace(0, 10, 2000)
y = np.sin(x) + 0.3 * np.sin(5 * x) + 0.05 * np.cumsum(rng.normal(size=x.size)) / np.sqrt(x.size) * 10
line = np.column_stack([x, y])

fig, ax = plt.subplots(figsize=(9, 4))
ax.plot(*line.T, color="0.7", lw=3, label=f"original ({len(line)} points)")
for eps, color in ((0.05, "tab:blue"), (0.2, "tab:green"), (0.6, "tab:red")):
    simple = douglas_peucker(line, eps)
    ax.plot(*simple.T, "o-", color=color, ms=3, lw=1, label=f"epsilon = {eps}: {len(simple)} points")
ax.legend()
ax.set_title("Douglas-Peucker (1973)")

Text(0.5, 1.0, 'Douglas-Peucker (1973)')