How to draw the largest polygon from a set of points in matplotlib?

To draw the largest polygon from a set of points in matplotlib, we need to find the convex hull of the points and then create a polygon patch. The convex hull gives us the outermost boundary that encloses all points, forming the largest possible polygon.

Understanding Convex Hull

A convex hull is the smallest convex polygon that contains all given points. Think of it as stretching a rubber band around all the points − the shape it forms is the convex hull.

Finding the Largest Polygon

We'll use scipy's ConvexHull to find the largest polygon from a set of points ?

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
from scipy.spatial import ConvexHull

# Set figure size
plt.rcParams["figure.figsize"] = [8.00, 6.00]
plt.rcParams["figure.autolayout"] = True

# Create a set of random points
points = np.array([[1, 1], [0.5, 1.5], [2, 1], [1, 2], [2, 2], 
                   [1.5, 0.5], [0.8, 2.2], [2.5, 1.8], [0.3, 1.2]])

# Find the convex hull (largest polygon)
hull = ConvexHull(points)
hull_points = points[hull.vertices]

# Create the polygon
polygon = Polygon(hull_points, facecolor='lightblue', 
                 edgecolor='blue', alpha=0.7, linewidth=2)

# Create figure and plot
fig, ax = plt.subplots()

# Add the polygon patch
ax.add_patch(polygon)

# Plot all points
ax.scatter(points[:, 0], points[:, 1], color='red', s=50, zorder=5)

# Plot hull vertices
ax.scatter(hull_points[:, 0], hull_points[:, 1], color='blue', s=80, zorder=6)

# Set axis limits
ax.set_xlim([0, 3])
ax.set_ylim([0, 3])
ax.set_xlabel('X coordinate')
ax.set_ylabel('Y coordinate')
ax.set_title('Largest Polygon (Convex Hull) from Set of Points')
ax.grid(True, alpha=0.3)

plt.show()

The plot displays:
- A light blue polygon representing the convex hull
- Red dots showing all input points
- Blue dots highlighting the vertices of the largest polygon
- Grid lines for better visualization

Simple Polygon Without Convex Hull

If you want to create a polygon directly from specific points without finding the convex hull ?

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon

# Define polygon vertices in order
vertices = np.array([[1, 1], [0.5, 1.5], [1, 2], [2, 2], [2, 1]])

# Create polygon patch
polygon = Polygon(vertices, facecolor='lightgreen', 
                 edgecolor='darkgreen', alpha=0.8, linewidth=2)

# Create figure
fig, ax = plt.subplots(figsize=(7, 5))

# Add polygon to plot
ax.add_patch(polygon)

# Plot vertices
ax.scatter(vertices[:, 0], vertices[:, 1], color='red', s=60, zorder=5)

# Annotate vertices
for i, (x, y) in enumerate(vertices):
    ax.annotate(f'P{i+1}', (x, y), xytext=(5, 5), 
               textcoords='offset points', fontsize=10)

ax.set_xlim([0, 3])
ax.set_ylim([0, 3])
ax.set_xlabel('X coordinate')
ax.set_ylabel('Y coordinate')
ax.set_title('Custom Polygon from Ordered Points')
ax.grid(True, alpha=0.3)

plt.show()

Displays a green polygon with:
- Vertices marked as red dots
- Labels P1, P2, etc. for each point
- Grid for reference

Key Parameters

• facecolor − Interior color of the polygon
• edgecolor − Border color of the polygon
• alpha − Transparency level (0−1)
• linewidth − Thickness of the polygon border

Conclusion

Use scipy's ConvexHull to find the largest polygon from scattered points. For predefined shapes, create a Polygon patch directly with ordered vertices. Both approaches allow customization of colors, transparency, and styling.