Subject:
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Re: Spirograph Formulas??
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Newsgroups:
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lugnet.robotics
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Date:
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Thu, 18 May 2000 23:17:22 GMT
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Original-From:
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brett <BRETT@spamlessMADHOUSE.ORG>
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Viewed:
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630 times
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I wrote a director program once to graph those equations and made it into
a shockwave movie. Ill see if i can't dig it up.
b
-----------------------------------------------
brett wagner | brett@madhouse.org
get committed! | http://www.madhouse.org
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On Thu, 18 May 2000, Doug Weathers wrote:
> in article 3923F01F.2834EA50@idt.net, Dan Novy at lego-robotics@crynwr.com
> wrote on 5/18/00 6:29 AM:
>
> > Hi, all! My daughter and I have built a robot that holds a piece
> > of sidewalk chalk and draws "spirograph-like" patterns on the side
> > walk. No sensors, it really just executes a repeated path with an off
> > set.
>
> Cool! Any pictures available on the web somewhere?
>
> > Then I remembered an old math teacher had a set of the spirographs
> > that he used as an extra credit assignment. That was so long ago I
> > can't remember what the assignment actually was, but I remember it had
> > something to do with predicting and graphing the patterns a spirogear
> > WOULD make given certain variables. Does this sound vaguely familiar to
> > anyone? My question is, are there basic formulas (or at least an area
> > of research) governing the spirograph patterns that I could translate
> > into code for the RCX.
>
> I typed "spirograph" into my favorite search engine (www.google.com) and
> came up with several good hits. These two are way too math-intensive for me
> to comprehend:
>
> http://www.csm.astate.edu/spirotest/spirotest.html
> http://www.geom.umn.edu/docs/reference/CRC-formulas/node34.html
>
> This one has a much simpler set of formulas, plus a cool applet for drawing
> the curves.
>
> http://www.wordsmith.org/~anu/java/spirograph.html
>
> From the above page:
> ==
> What is a Spirograph?
>
> A Spirograph is formed by rolling a circle inside or outside of another
> circle. The pen is placed at any point on the rolling circle. If the radius
> of fixed circle is R, the radius of moving circle is r, and the offset of
> the pen point in the moving circle is O, then the equation of the resulting
> curve is defined by:
>
> x = (R+r)*cos(t) - (r+O)*cos(((R+r)/r)*t)
> y = (R+r)*sin(t) - (r+O)*sin(((R+r)/r)*t)
> ==
> The applet lets you change the parameters but doesn't display the actual
> numbers, darn it.
>
> I don't have any handy tools to use to graph these equations, which I
> believe are parametric. Pacific Tech makes a commercial version of the
> Graphing Calculator that comes free with the Mac OS, and version 2 does
> parametric equations and works with Mac or Windows. It's about $40, and
> it's a severely cool piece of software. Check them out and download a demo
> at http://www.pacifict.com.
>
> It's not immediately obvious to me how to convert these equations into a
> piece of RCX code. Perhaps someone else can help, or find more appropriate
> equations.
>
> > Right now we're having fun guessing and
> > adjusting different variables to get different patterns, but it would
> > also be fun to generate a pattern on paper with our real spirograph and
> > then have the RCX duplicate the same pattern only much larger in the
> > sidewalk chalk. If you have no idea what a spirograph toy is, I'm sure
> > many of us would be willing to explain. It was, and is, one of my all
> > time favorite toys.
>
> Mine's still in the closet, much the worse for wear. I loved it too, but
> instead of a Lego Dark Ages I went into a Spirograph Dark Ages :)
>
> >
> > --
> > Dan Novy
> > Visual Effects Technical Supervisor
> > Flash Film Works
> > dan@flashfilmworks.com
> >
> > /////////////////////////////////////
> >
> > Simia anaticulam caseis defricavit.
> >
> > /////////////////////////////////////
> >
> >
> >
>
> --
> Doug Weathers, http://www.rdrop.com/~dougw
> Portland, Oregon, USA
> Don't spam me - I know how to use http://www.spamcop.net
> "On a clear disk you can seek forever"
>
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Message is in Reply To:
 | | Re: Spirograph Formulas??
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| in article 3923F01F.2834EA50@idt.net, Dan Novy at lego-robotics@crynwr.com wrote on 5/18/00 6:29 AM: (...) Cool! Any pictures available on the web somewhere? (...) I typed "spirograph" into my favorite search engine (www.google.com) and came up with (...) (24 years ago, 18-May-00, to lugnet.robotics)
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