Possible to UV unwrap with zero stretch?

All, I am thinking of making a lamp-shade sort of thing, fairly large (~1m across maybe) using blender for most of the design.

My plan is to create a shape with ~100 faces (probably spheroid with some interesting deviations) and then create connector pieces for each vertex that will hold metal rods in place, forming the mesh. The connectors will be 3D-printed and should be fairly easy to make (if not keep track of). The faces of the mesh will be made of paper.

The remaining question I have for this design process is how to get the paper faces in the correct size. What I need is for every edge length to be exactly correct and un-distorted. I would print out templates on pieces of paper and then cut them out… then glue them to the frame.

Anyway, long story short: Is there any way to take all the faces of a mesh and lay them out flat (UV-unwrapping or otherwise) without changing any of the edge lengths?

Is there any way to take all the faces of a mesh and lay them out flat (UV-unwrapping or otherwise) without changing any of the edge lengths?
Yes, UV unwrapping in blender can do this. It is dependant on the shape of the object you want to unwrap and whether you want to have the unwrap as a single island or multiple islands.

A cube you can unwrap easily as a single island with zero distortion, Suzanne you most likely can’t

Most meshes that people make don’t have perfectly flat faces. Look at your own models and you will probably find some that are bowed one way or another, if not almost triangulated by being folded across opposing vertices. This means that even if you put a seam on every edge and just laid the faces themselves out flat, there would still be some stretching.

Even if that were not the case, you usually do not want to separate faces so much that you can get a perfectly flat, zero-stretch layout. You want islands to remain somewhat recognizable, and you want to minimize the number of seams to avoid having those seams show in the final textures. This will require some stretching, as Richard has already pointed out.

Yes, as long as they are triangles and as you describe the process you don’t care if each one is connected to the next. Edge select mode, Select all, mark seam, Unwrap. You can specify how much room between each island and every face will be its own island. Export the UVmap and print from whatever application you want, and the scale - well that might be a little trial and error…

As soon as you have polygons of more than three sides non planarity becomes possible and laying them flat on a piece of paper becomes impossible. If you do have quads etc I believe Blender now will find non planar faces for you of course it will split them but you can see where they are. But tis next to impossible to edit a mesh to make nonplanar faces flat without making some neighboring face nonplanar in turn.

Thanks all, these are good explanations. I think I can make everything a triangle for this project, so it should be possible. I will try the techniques described.

there is a script to do paper model unwrap


happy bl

Not blender but here’s a program specifically made for what you want.