Membranes and tubules are part of the same family!
These 3D shape textures optimize curvature functionals that generalize the traditional Willmore and Helfrich energies.
arxiv.org/abs/2103.04856
Curvatubes generates a continuum of 3D shape textures, from simple tubes to structured networks. This is especially relevant to my work on bone marrow vessels @TheCrick.
To visualize the space of 3D shape textures, we combine UMAP with the optimal transport distance on 2D curvature diagrams. @leland_mcinnes@gabrielpeyre