Nerd Sniping

[sliptonic]

Nothing serious here. This is just for fun.

I got distracted and wasted a lot of time learning about Rose Engine Lathes, Guilloche patterns, and Spirographs.

This video is particularly cool:

phpBB [video]

I'd love to be able to engrave patterns like this, maybe on hard drive platters.

A very simple macro generates a raw path:

Code: Select all

#-----------------------------------------------------------------------
# spirograph.py
#-----------------------------------------------------------------------

import sys
import math
import Path

# Accept float command-line arguments R, r, and a.
# Draw a curve formed by rolling a smaller circle of radius r inside
# a larger circle or radius R. If the pen offset of the pen point in
# the moving circle is a, then the equation of the resulting curve
# at time t is
#
# x = (R+r)*cos(t) - (r+a)*cos(((R+r)*t)/r)
# y = (R+r)*sin(t) - (r+a)*sin(((R+r)*t)/r)
 
# Credits: idea suggested by Diego Nehab
# Reference: http://www.math.dartmouth.edu/~dlittle/java/SpiroGraph
# Reference: http://www.wordsmith.org/~anu/java/spirograph.html

sidecount = 96
rosewidth = 30
type = "e"

R = 8.0
r = R/sidecount
#r = 32.0/96.0
#a = 168.0/96.0
a = rosewidth/2

PathList = []
t = 0.0
if type == "h":
    while t <= 10:
        x = (R+r) * math.cos(t) - (r+a) * math.cos(((R+r)*t)/r)
        y = (R+r) * math.sin(t) - (r+a) * math.sin(((R+r)*t)/r)
        degrees = -math.degrees((R+r)/r)*t
        c = Path.Command("G1 X{} Y{}".format(x,y))
        PathList.append(c)
        t += 0.001
else:
    while t <= 10:
        x = (R-r) * math.cos(t) + (r+a) * math.cos(((R-r)*t)/r)
        y = (R-r) * math.sin(t) - (r+a) * math.sin(((R-r)*t)/r)
        degrees = -math.degrees((R+r)/r)*t
        c = Path.Command("G1 X{} Y{}".format(x,y))
        PathList.append(c)
        t += 0.001

p = Path.Path(PathList)
o = App.ActiveDocument.addObject("Path::Feature","mypath")
o.Path = p

There's a more parametric version attached which adds an object to the tree inside an existing Path job.
Unfortunately, I quickly got out of my depth on the math. Anyone want to take a stab at improving this?

Ideally, the user could tweak and adjust a bunch of settings to achieve a satisfying pattern but control the center point and overall diameter explicitly to position it for engraving.


BTW, the title of this post comes from a relevant XKCD comic.

[RatonLaveur]

Trippy...thank you for sharing.

My brain connected it immediately to this:
https://youtu.be/ds0cmAV-Yek

[Kunda1]

There is something very hypnotic/alpha-brainwave inducing about watching the long strokes of the Spirograph machine. Trippy indeed!

[quick61]

That kind of puts me in mind of this - https://jeffeb3.github.io/sandify/ that provides the gcode for something like this -

phpBB [video]