Its a rectangular strip when unrolled. Its easy to model something that looks like this, but i have a hard time coming up with something that is accurate, i.e. top and bottom rail should be same length as well as the short sides. Note that if you try this with a physical paperstrip, it bends in a certain way (the sharp nose bends slightly up, also the short segments are slightly bent.
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Hi Mich - In plain Rhino there is no way that I know of to constrain a shape in any way accurately acording to how paper, let alone any particular paper, would behave.
-Pascal
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Here’s how this can be simulated in Kangaroo.
Paper can be treated as having uniform bending stiffness in all directions and very little stretch.
Once we’ve made the right mesh, we can pull the vertices of the parts to be glued together.
However, because it starts flat, if we pull them together straight away it tends to crumple, so here I use the ‘grab’ function to start it bending the right way, then increase the strength of the ‘coincident’ goal which glues the ends:
strip_bending.gh (19.0 KB)
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Honestly I was daydreaming earlier about seeing this demonstrated 
I had a feeling I’d see this happen 
omg GH so amazing 
Speechless!
Thanks Daniel, awesome solution!
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draw a cone
Base Radius * 4 = “shell-ruler”
(not sure if “shell ruler” is the correct term, in german its “Mantel-Linie”)
the unrolled cone is a quater of circle
(_unrollUV)
draw the stripe
_flowAlongSrf
_trim
voila.
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Hi Tom - Nice but I still say that has littlle to do with how paper wouild behave -there is an overlap, for one thing- that is not only a 3d modeling thing but also influences how the paper behaves in bending and so on. Wjhat iks the cone shape, where does that ceom from, etc etc. Perhaps I was taking the question too literally but Mich did say
Its easy to model something that looks like this, but i have a hard time coming up with something that is accurate
-Pascal
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… they are.
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if you really need overlapping area twice - do it with a polysurface.
EDIT:
stripe_01.3dm (184.6 KB)
for my initial post I used _unrollsrfUV
but it seams like _unrollSrf (the initial Cone) gives better result as base surface for FlowAlongSrf.
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I can confirm that Tom’s method works in real life.
First find yourself a cone…I found and used a funnel.
Then cut a strip of paper. Well, while your at it cut several strips of different widths.
Then wrap a paper strip around the cone so that it lies flat on the cone.
For me this seemed to work precisely. I could wrap the strip (any of them) around the cone and the strip lay exactly on the cone with no gaps or wrinkles. The ends of the strip could be made to lie on the cone with the corners of the strip touching as in your picture or with the corners aligned as in the original image. Its just a matter of moving the strip in or out along the axis of the cone so that the (random) length of the strip matches with the (random) shape of the cone.
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@jim
any idea how to model this with a single surface?
with some cheating I manged to draw a cone that is revolved more then 360 degree… but I don t get the trimming in the overlapping area… just a academic question.
(it would be great if rhino would offer _applyCrv with an “use as trim curves” option)
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ok I found a way…
single surface with overlapping area…
(rhino does not like it because of self-intersections and so on… which makes totally sense for everyday modelling.)
stripe_03.3dm (3.3 MB)
it is a bit of tweaking…
_creaseSplitting disable
draw an partially mirrored version of the stripe…
_extrudeCrvToPoint will now allow to build the deformed S-shaped cone.
do the trimming
mirror back the CVs (the trimming just follows)
the construction in the “S-shape-state”
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I should point out that the true shape of a paper strip bent and joined like in the original image, and shaped only by its own internal elastic forces will not lie exactly on a cone (even when idealising it to a zero thickness inextensible sheet with uniform bending resistance).
The width of the strip measured perpendicular to the ruling directions along which it bends varies along the strip. I believe this will result in a slightly larger radius of curvature closer to the join. I’d guess the difference from a cone would be pretty small though.
There was some interesting work a while back on the elastic equilibria of Moebius strips that tackles this issue.
Cone vs Kangaroo:
Its quite different, yet both unroll to the same strip. Cant tell who is more correct:)
I would love to see:
cone
vs
kangaroo
vs
photo of real world paper
vs
3d scanned paper-stripe
and maybe we can motivate @martinsiegrist to do a 3d scan ?
(but please, tomorrow the weather is great and there is enough fresh snow over 2200m…)
wow.
… well we did not discuss the scientific method of when and how to glue it
;-D
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Simulating the clamping is tricky. With the right anchor points, the result is pretty much identical.
The Grasshopper definition has all inputs internalised. The scan, trim surfaces and some curves are in the Rhino file should anyone want to play with it.
paper-strip.3dm (2.8 MB)
paper-strip.gh (29.5 KB)
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