Scaling trochoid’s and cycloid’s input parameters with the spyrograph scale method

Scaling trochoid’s and cycloid’s input parameters with the spyrograph scale method

In this blog post, we will explore the scale method in the spyrograph package which enables users to easily scale their trochoids and cycloids

Creating a Hypocycloid

First, let’s create a Hypocycloid with 10 cusps to work with:

import numpy as np
from spyrograph import Hypocycloid

hypocycloid = Hypocycloid.n_cusps(
    R=300,
    n=10,
    thetas=np.arange(0, 2*np.pi, .1)
)

Scaling the Hypocycloid with the scale method

Now that we have a Hypocycloid, we can easily scale it using the scale method:

scaled_hypocycloid = hypocycloid.scale(factor=.5)

The scaled_hypocycloid will now have its input parameters (R, r, and d) multiplied by the scaling factor

For example the radius of the big circle R=300 will now be R*.5=150

Using scale to trace a beautiful pattern

Let’s jump into a concrete example of using the scale method in action to trace a gradually smaller set of curves

from spyrograph import Hypocycloid
import numpy as np
import time

screen = None
hypocycloid = Hypocycloid.n_cusps(
    R=200,
    n=20,
    theta_start=0,
    theta_stop=2*3.1415,
    theta_step=.01
)
for i in range(1,40):
    screen = hypocycloid.trace(screen=screen)
    hypocycloid = hypocycloid.scale(factor=((40/(i+40))))
    time.sleep(.1)
turtle.exitonclick()

Conclusion

The scale method in spyrograph provides a convenient way to resize trochoids and cycloids while preserving their shape

With just a single method call and a scaling factor, users can quickly create new shapes with different sizes, making the package even more versatile for artists, educators, and developers alike

Don’t forget to experiment with different scaling factors and shapes to create stunning patterns and visuals!