TWISTED RIBBON

Replies to This Discussion

Permalink Reply by David Rutten on March 27, 2010 at 12:23pm

Hi Hana,

there's no Helix component, so you'll have to make a helix from scratch. You should probably generate points on the helix, then interpolate the points. Since the start and end of an interpolated curve often have unwanted wiggles, you should create a longer helix than you actually need, then cut the ends of.

Equations for a Helix are:

x = R * Cos(t)
y = R * Sin(t)
z = S * t

Where x, y and z are the coordinates of the points on the helix. t is a sampling value (the more t's you create the longer your helix, the closer together two t's are, the more accurate your spiral). You can make a collection of t values using a Series component. R is the radius of the helix and S is the vertical speed of the helix.

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Hana Kobe on March 27, 2010 at 12:29pm

Thanks David, I'll try that.

Permalink Reply by Hana Kobe on March 28, 2010 at 9:01am

Hi David,

thx for your previous instructions...

i'm not sure if i got the series bit right but in top view, the helix is not perfectly circular bcos i haven't trimmed the straggly ends yet. you did mention it but why is this? (so i would know how much to trim).

for the next step, i'd like to duplicate the helix but reverse the direction of the spiral. how can i set the negative value? i used subtraction, copied the right half of the script and connected the series output to it. this generated the helix in the negative z direction... :I

cheers,
hana

Permalink Reply by Mårten Nettelbladt on March 27, 2010 at 4:38pm

Hi Hana,
I made some tests with helix ribbons and other bent/twisted ribbon-like shapes:
http://thegeometryofbending.blogspot.com/search/label/twisting
http://thegeometryofbending.blogspot.com
I'm not sure if it's relevant to what you are doing, but I thought I'd mention it.

/Mårten

Permalink Reply by Hana Kobe on March 28, 2010 at 9:07am

thanks Mårten
it looks very intriguing - i am learning gh by experimenting on twisting / spiralling forms; need to develop my models and do iterations later.... maybe i can use some of your research

i like your blog entry dated 2008-11-03 cornu spirals done in gc. would love to try that in gh. possible?

hana

Permalink Reply by Mårten Nettelbladt on March 28, 2010 at 2:14pm

Yes it's definitely possible. Some more of those images here: http://www.omkrets.se/gc/

The reason these curves look the way they do (and I like them too!) is because the definition I used is not a correct Cornu Spiral.

In a Cornu Spiral curvature increases proportionally to the distance along the curve.

But the curve in the image above is slightly different: Imagine a car moving at a constant speed and at the same time you turn the steering wheel at a constant speed (slowly). If there was no limit for how far you could turn the wheel, the car would drive in smaller and smaller circles, like a spiral. Eventually you would reach a turning point and start circling in the other direction - in larger and larger circles. This resembles the Cornu Spiral, but in a true Cornu Spiral you never reach such a turning point.