I've created a quad sphere using several different methods (sphere -> subdiv surface; sphere -> subdiv surface -> cast). I then marked 12 seams and tried unwrapping it using several methods. The best result for my purposes I get using the regular "unwrap" method. However, the generated UV islands are slightly rotated. Is there a way to prevent that? I Googled a bit and found that I could "pin" certain nodes. But what I tried, I couldn't get nice UV islands. Below I've added some screenshots of my situation. Does anybody know how I could get a result matching the last screenshot?
I actually solved it myself. I installed the
Add Mesh: Extra Objects extension that comes with Blender. Then I created a new quad sphere by doing
Add -> Round Cube. I expanded the properties dialog that appears in the lower left of Blender and selected
Quadsphere from the
Operator Presets dropdown. When you mark the proper seams (see my opening post) and unwrap it, the UV islands appear straight. I don't know why this differs from my own method, but at least it's working.