The massive increase in the number of choices the encoder has to make (and correspondingly, the decoder to follow) is the main reason why H.265 requires so much more processing power than H.264, and H.264 compared to previous standards as well. The intra prediction modes (33 directions!) are a good example of this.

That said, if you actually get the standard and look at the section on the intra prediction modes, how to compute them is spelled out in very detailed pseudocode.