I am working on an application that flattens 3D meshes into 2D injective maps such as this one:
Essentially, the map is produced by flattening the object, ensuring that it fits within the 2D boundaries in green, and then the distortion of the map is relaxed.
The last point is where I am stuck currently. Ideally, I would like to find a way to relax the deformation of the map by balancing the area and angular distortion. I have already explored some papers that explore this, such as FFM (Garanzha et al., 2021) or IsoTLC (Du et al, 2022).
After dabbling with these methods I however realize that in my case I need to enforce some strict conditions on the produced triangles, mainly ensuring that none of their angles go, say, below 20°. The reason for this is that I want to avoid these long and very thin triangles that one sees near the borders in the image above.
With that being said, I would still need a map that somehow balances area/angular preservation from 3D, even if I'm guessing compromises will have to be taken for the former. Additionally, the map needs to still fit within the green boundaries, as well as keep its injective property.
I'm a bit stuck right now as to where to go from here. Any lead or pointer toward relevant literature would be helpful.