Flat pattern overlayed onto 3d objects without deformation of original pattern?

If I have a flat pattern comprising of equilateral triangles and squares, how would I go about overlaying it onto waved surfaces/3D objects without deforming the original pattern?

An example being if I had a 3d donut shape and wanted to wrap said pattern on top of it and have the pattern react as if if was really comprised of unbendable tiles as opposed to what would occur if I used a command such as "flow along surface."

I think this is pretty self-explanatory, but am able to add examples if it would help.

Does anyone know how to accomplish this aesthetic?

Thanks for at the very least reading this, guys (and gals)!

Replies to This Discussion

Permalink Reply by Joseph Oster on December 7, 2015 at 11:15am

Not quite as "self-explanatory" as you may think... Based on your first sentence, I would have suggested 'Project' on a "waved surface" but that won't work on a 3D donut shape. 'Pull' might be helpful but again, it won't work from a 2D pattern to a 3D surface.

Mapping 2D patterns to 3D surfaces comes up again and again here - many examples including "How to make a 2d map into a 3d globe":

http://www.grasshopper3d.com/forum/topics/how-to-make-a-2d-map-into...

Find and study more examples. And yes, of course, providing an example (in GH!) is always good.

Permalink Reply by Chris Beffa on December 7, 2015 at 11:59am

Thanks for the feedback Joseph!

I seem to think I write clearer and more concisely than I apparently do.

Imagine lasercutting equilateral triangles and squares out of a material such as wood and gluing each of the pieces on a fabric background to form a specific pattern. The edges of the pattern would be flexible allowing you to roughly mold it to any shape beneath it, right? Now imagine draping this pattern on any three-dimensional object--a cube, a donut, a contour architectural model, anything. It would roughly give you the same shape as the object below the pattern, but it would now be using the shapes of that pattern to translate the shape of the object beneath.

That's basically what I'm trying to do here, but on Rhino using Grasshopper.

Here's an image that is close to what I am going for aside from the fact that I'll be using a different pattern and won't be bunching it up like this guy did. Again, think of how it would appear draped over an architectural contour model and pressed down as much as possible to really fit the model:

Permalink Reply by Joseph Oster on December 7, 2015 at 12:19pm

Yeah, I see nothing at all simple about your assumptions on this! "overlaying", "wrap", "draping", etc... Again, this is a challenge that comes up frequently here. There are MANY examples available and no single best solution, as far as I know. The scale of your pattern elements relative to the surface/object you are draping is just one factor that complicates a general solution.

Do you have a practical objective? Pattern and drape shape? Not that I want to get into this, mind you. I believe you can learn a lot about this by searching this forum and reading code.

Just out of the blue, here's one way to think about it:

Get the centroids (from 'Area') for all the pattern shapes.
'Project' those points down onto the drape shape (some will miss it, right?)
For those projected points that land on the drape shape, re-orient the corresponding patterns to the surface normals for each point.

Of course, flat shapes in the pattern won't match curved surfaces so...?

Permalink Reply by Chris Beffa on December 7, 2015 at 12:33pm

Apologies again, I must really suck at explaining things, but am honestly at a loss as to how to better explain it. I genuinely thank you for trying, though.

Here are some more images of what I am trying to accomplish within Rhino/Grasshopper:

Also, I've been searching all week for solutions to this, so I didn't start here if that's what you're thinking.

Permalink Reply by Joseph Oster on December 7, 2015 at 12:44pm

I find it hard to believe that there is nothing like this on this forum. I just used the words "drape pattern" in the "Search Grasshopper" box and see four pages of results but I'm not going to read them or find the answer for you, sorry.

And post your pattern and drape object here. It's not your explanation, it's your expectation that this can be done without distorting the pattern elements at all that I question. Good luck and share your results when you figure it out!

Permalink Reply by Chris Beffa on December 7, 2015 at 1:00pm

Yep, looked at all those already. Although informative, none of them seem to suit my needs. Again, I've been at this for a week now, but am considering waving the white flag. Although doable manually, I plan on toying around with thousands of compositions and the time it would take me to do it manually simply isn't a realistic option.

You're right that I thought it could be done, though (perhaps not as complicated as the top design, but surely something akin to the bottom one which is almost exactly what I am going for). I guess I'll keep this open for another couple days and see what comes of it, though.

Thanks once more, Joseph!

Permalink Reply by Chris Beffa on December 7, 2015 at 1:18pm