Drawing cycloids with a specific number of cusps using spyrograph

Drawing cycloids with a specific number of cusps using spyrograph

Introduction

In this blog post, we will explore a powerful feature of the spyrograph package: the ability to create and draw cycloids with a specified number of cusps

Cycloids are special cases of trochoids where the distance parameter d is equal to the rolling circle radius r

By using the n_cusps class method provided in the Hypocycloid and Epicycloid classes, we can easily create beautiful cycloid shapes with a desired number of cusps

Prerequisite imports

Before we begin, let’s make sure we have the spyrograph package installed:

pip3 install spyrograph

Creating a cycloid with a specified number of cusps

To create a cycloid with a specified number of cusps, we can use the n_cusps class method. Here’s a quick example of how to create a hypocycloid with 5 cusps:

from spyrograph import Hypocycloid
import numpy as np

R = 50
n = 5
thetas = np.arange(0, 2 * np.pi, 0.01)

hypocycloid = Hypocycloid.n_cusps(R=R, n=n, thetas=thetas)

In this example, we set the radius of the fixed circle R to 50 and the desired number of cusps n to 5. The n_cusps method calculates the rolling circle radius r as R/n and instantiates a cycloid object with the provided parameters

Tracing the cycloid with trace

Now that we have created a hypocycloid with 5 cusps, let’s trace it using the trace method provided by the spyrograph package

hypocycloid.trace(exit_on_click=True)

The trace method will display an animation of the cycloid shape being drawn

The exit_on_click argument ensures that the animation window remains open until you click on it

Conclusion

The n_cusps class method in the Hypocycloid class is a powerful and easy-to-use feature for creating and drawing cycloid shapes with a specified number of cusps

By using this method, artists and educators alike can create visually stunning and mathematically precise cycloids in a matter of seconds

Give it a try and unlock your creativity with the spyrograph package today!