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?
Here's my result. As you can see the islands are slightly rotated:
Here are the seams I have defined:
And here's the result I'd like to get. This UV I got from an already properly unwrapped triangle-based model I got from the internet: