Python Matplotlib | Filled Polygon | Koch Snowflake

Introduction

In this lab, we will learn how to create a filled polygon using Matplotlib in Python. We will use the Koch snowflake as an example polygon.

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Import Libraries

Before we start, let's import the necessary libraries.

import matplotlib.pyplot as plt
import numpy as np

Define the Koch Snowflake Function

Next, we will define a function to generate the Koch snowflake. The function takes two parameters: the recursion depth and the scale factor.

def koch_snowflake(order, scale=10):
    """
    Return two lists x, y of point coordinates of the Koch snowflake.

    Parameters
    ----------
    order : int
        The recursion depth.
    scale : float
        The extent of the snowflake (edge length of the base triangle).
    """
    def _koch_snowflake_complex(order):
        if order == 0:
            ## initial triangle
            angles = np.array([0, 120, 240]) + 90
            return scale / np.sqrt(3) * np.exp(np.deg2rad(angles) * 1j)
        else:
            ZR = 0.5 - 0.5j * np.sqrt(3) / 3

            p1 = _koch_snowflake_complex(order - 1)  ## start points
            p2 = np.roll(p1, shift=-1)  ## end points
            dp = p2 - p1  ## connection vectors

            new_points = np.empty(len(p1) * 4, dtype=np.complex128)
            new_points[::4] = p1
            new_points[1::4] = p1 + dp / 3
            new_points[2::4] = p1 + dp * ZR
            new_points[3::4] = p1 + dp / 3 * 2
            return new_points

    points = _koch_snowflake_complex(order)
    x, y = points.real, points.imag
    return x, y

Generate a Filled Polygon

Now, we can generate a filled polygon using the fill() function. We will use the Koch snowflake function to generate the coordinates for the polygon.

x, y = koch_snowflake(order=5)

plt.figure(figsize=(8, 8))
plt.axis('equal')
plt.fill(x, y)
plt.show()

Customize the Polygon

We can customize the colors and linewidth of the polygon using keyword arguments in the fill() function.

x, y = koch_snowflake(order=2)

fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(9, 3),
                                    subplot_kw={'aspect': 'equal'})
ax1.fill(x, y)
ax2.fill(x, y, facecolor='lightsalmon', edgecolor='orangered', linewidth=3)
ax3.fill(x, y, facecolor='none', edgecolor='purple', linewidth=3)

plt.show()

Summary

In this lab, we learned how to create a filled polygon using Matplotlib in Python. We used the Koch snowflake as an example polygon and demonstrated how to customize the polygon with different colors and linewidths.

Create Filled Polygon with Matplotlib