Unwrapping Mesh Texture to 2D

Hello all,

I am continuing through on a personal project trying to unfold meshes with texture from 3d to 2D inspired by Jarke J. van Wijk’s Unfolding the Earth: Myriahedral Projections

I have figured out all of the geometry processing stuff with help from this post and have moved on to trying to map the globe as a texture on a 3d polygonal mesh, which I am hoping to unfold.

As this a different sort of topic, I thought I might make a new post. I do not have too much experience with texture mapping and meshes but I can map and render it onto the spherical mesh using Human. The trouble comes when I begin to split and unroll the faces while preserving the texture (it does not work at all).

Does anyone have a good way to split and transform meshes while preserving texture? Or is there a better way to go about this? Any help would be greatly appreciated.

This is purely speculative, so take all of it with a grain of salt.

UV-unwrapping is already an unrolling procedure, so chances are that your initial geometry already had a mapping to be able to display the planet earth texture.
When splitting edges with your minimum spanning tree algorithm, you change the mesh by adding vertices, so this UV-mapping probably is now useless.

However, what if you recomputed a spherical UV-mapping for the not yet unrolled, but split mesh?
Since, it’s topology doesn’t really change while unrolling it, you should be able to use that new mapping for texturing.
Since the vertex and thus face positions change when unrolling, it might be that you need to adjust the UV-mapping to these new positions. You have all that information, so it should be feasible with possibly another script.