Hi, I dont know exactly how to describe the transformation I'm looking for, and I have a hard way figuring out how to do it...

I want to transform a regular triangle into one third of a circle as shown in the image below:

https://www.dropbox.com/s/nm69mk4qr1arv4k/rozetteTransform.svg
(better still: I want to transform three of those triangles to make the full circle...)

I made the example image above by hand, no transformation was involved, so the curved lines are just estimated. I want to add a more complex vector drawing on the faces of the triangles and also transform them to the circle, but haven't found any clues in inkscape nor in the forum as how to acheive this...
Anyone has a clue how this kind of transformation would be called, and if there are any tools available?

Thanks!

Your example reminds me of transformations needed for printed globes, where common geography maps are adjusted for spherical representation. Still, you have much simpler shapes and it should be equally simpler.

Try with gnomonic projection, stereographic projection, Spherical triangle...

Hi.

As far as I know there is no such thing inside inkscape, maybe some python gurus could write an extension for that.
What else could be used?

Gimp has a distortion filter, the polar coordinates.
By having large sized raster images for the start, the result could be traced well back in inkscape.

A bit more complex solution that you could use, is with blender. It would produce a raster image for the output too.
For example that pattern could be rendered as a topview of a cone, having the triangle on the left as a texture .
To unwrap the mesh you can use cilindrical projection, then use that layout for mapping the texture.

On your sketch of the problem, the estimated curves are Archimedean spirals.
Polar coordinates can construct the same thing.
But the projection used could lead to heavy distortion of the base pattern, if more rows of triangles are involved.
To overcome that, blender is much handier, as you can render other solid of revolution than a simple cone, like http://www.math.tamu.edu/~tkiffe/calc3/revolution2/images/revolution2c1.jpeg.

Thanks for your quick replies.

Maestral, I guess the difference is that I'm looking for a transformation (2D triangle -> 2D 1/3 circle), whereas your suggestions are projections (3D sphere -> 2D whatever).
But maybe you were thinking of the transformations between the resulting 2D whatevers...

Anyway, I already doubted there was a possibility to attach a vector drawing to a mesh for transformation in Inkscape.
I'm trying the Blender thing, although a bit overkill for this
I'm mapping an image to a cone of height zero with a camera exactly above it. Problem is that the image of my triangle is a square image mapped to the cone. I guess I need to study the UV mapping to first select the triangle out of the square image?

Thanks, we're getting there.
If anyone has an all-vector solution, that would still be awesome!

Oh I forgot.

You can use the envelope extension to make a rectangular texture from the triangle shape -sort of.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Extensions-ModifyPath.html#Extensions-Envelope
The top would need some part to be cut off, so it's more of a trapezoid.
I will check for that.

Mate, your spirit conquers all difficulties!
Keep chearing us up and we`ll be glad to help your dreams come true!!!

p.s.
What happened with your initial example?!

Hmm it's not my day, isn't it?
I couldn't work with either my suggestions.
Anyway.

Modelled a solution in blender, and unwrapped it in a different way.
The model and a quick auto-trace of a rendering is presented
here.

Note that it could be improved largely if there was no overlapping of the objects in the original texture image
-thus making separate textures from each of the tile's elements, rendering them separately would lead to a cleaner result.

Thanks Lazur, I had already done something similar as well.
Find my results here: https://www.dropbox.com/s/ln2s62jwv3zcaxl/transformation_forum.zip. I used UV mapping of the triangles to the surface of the cone.

For the stroked image, I had to manipulate the thickness of the strokes in the original pattern to get a somewhat uniform thickness in the circular result.
Just for the record I have to ask if someone would know how to solve this in a proper manner?

Thanks for all suggestions!