How to ask a, probably angry, PhD supervisor for a letter of recommendation after graduation from uni?
If you were my student, I would fully expect you to take full credit for your work. If I helped you it is good for both of us, but a lot of other people helped your development before we ever met. 

As to the letter of recommendation issue, I would do this in two separate parts, separated by a bit of time. First, make contact and thank him for past help and bring him up to date on your current life/research/whatever. If at all possible, do this in person. I don't know what you mean by a "long way" but a visit back to the university to meet old professors (and thank them) is always fun and worthwhile. If I'm the professor, I will be very happy to see you and hear about your current successes both academic and IRL.

This meeting should give you feedback on his feelings about you, though if you are both a bit awkward, it may be difficult to judge. 

But a bit later, it needn't be long, ask for the letter of recommendation. Your earlier meeting will give you an idea of how formal you need to make the request. Or, if you are completely comfortable in the first meeting, you could do it then, but don't force it. 

As to the answer of aeismail, the video suggestion will work with some people, but not all. If he is a frequent user already then it should be fine. But that, or even a phone call, won't work with everyone (me, for example). In person is best. The more formal the person is, the more important to meet face-to-face, I think. For a generally informal person, first name basis, less formal communication is possible.