We need to create a flat pattern (sketch) to properly design a label or fabric for a spherical surface. We've tried to use sheet metal but as far as we can tell its not possible to create sphere with this method. Any ideas on how to translate spherical shapes into flat patterns?
Deepak, I don't think this is what Andrew means.This only flattens curvature in one direction. Roland is correct you can't flatten a spherical surface
without stretching or splitting it.
Very nice link, Deepak. Developing surfaces for decals on fancy blue computerw is what compelled me to learn about Gaussian curvature and what kind of surfaces can be flattened. Sometimes it's possible to come up with a series of approximations that passes muster.
Flattenable surface can be developed using a combination of portions of the following:
•planes
•cylinders
•cones
•extruded surfaces
You can connect them in any way along straight tangent edges.
Thanks guys! I'm not sure about lofted bend. How is is possible to create a sphere with a loft?
The method I've been using is trial/error and little math. I create a flat part and then use the flex tool to flex in two directions. This gives me the sphere shape. I can then line it up with my spherical part to see if its a fit. If not I tweak it. The problem is that flex is not always accurate. Its also really slow even on my new workstation
I think I'll try Deepak's idea and see what happens.
You could try applying FEA to deform the label or fabric. This will be sensitive to Poisson's ratio. There are also commercial codes to do this for fabric in composite design. Check out fibersim. It is probably overkill for your application though. I hope this helps.
Rob Stupplebeen
One thing I've done in the past when needing to design a label/sticker/etc. onto a part with compound curvature is to model the area where the label goes such that it only curves in one direction. This is important to ensure that the sticker or label will seat completely and properly. Unless a sticker is very stretchable, it's virtually impossible to get a flat sticker/label to stay un-puckered for very long on a surface with compound curvature.
In the picture below, the grey part has compound curvature throughout the top surfaces, but the recessed area that contains the user interface label is cylindrical. This lets the sticker mate properly, without puckering or stretching.
This also lets you drive the sticker design with the recessed surface, which allows the "unfolding" of the sticker so you can get a true flat pattern.
Not sure if this trick lends itself to your particular situation, but it might be something for one to consider.
i WAS INTERESTED IN A SIMILAR PROBLEM ONLY MY SHAPE IS A TRUNCATED CONE.
I searched google for "flat surface fit on a sphere". The very first hit was a PDFh paper dealing with the practical problem of creating joined "petals" on a flat sheet, which petals could be 'crinkled' to cover a spherical chocolate candy. (1) The problem is claimed to be insoluble in a perfect mapping, however when the crinkling of a foil is allowed, the problem of the least amount of foil to be crinkled to cover a sphere is claimed to be solved.
(1) "Wrapping Spheres with Flat Paper", Erik Demaine
If you make the shape from a lofted bend SW will try to flatten it.
Keep in mind that a flat pattern of a spherical surface patch is a geometric impossibility. Can't go from flat to sphere without considerable stretching or shrinking. The best you can do is an approximation. Look at basketballs, soccer balls (futbols), and baseballs.