What are the complexities of the Peeta, Katniss, and Gale triangle from the perspective of Katniss in Catching Fire?
A massively important part of the love triange is the knowledge that President Snow has of it. At this point of the trilogy, at the beginning of the second book, it is clear that the affections of Katniss clearly lean towards Gale more than Peeta in terms of passion. Peeta is clearly a trusted friend--after all, you don't go through something like the Hunger Games together without getting to know the other person very well--but the fact remains that the romance that they had was simulated on the part of Katniss and was designed to garner them sympathy from the audience and support for their cause. When Katniss kissed Gale on her return from the first Hunger Games, she didn't realise that it was recorded or seen, and in Chapter 2, President Snow meets with Katniss in order to threaten her with killing Gale if she does not convince everybody, including himself, that her romance with Peeta is genuine. This becomes the governing directive for Katniss as she travels around the districts. Note how this is reflected in Chapter 3 when she meets Peeta in front of the cameras:
Then I make out Peeta coming through his front door. In my head I hear President Snow's directive, "Convince me." And I know I must.
Katniss therefore loves Gale more but needs to pretend to love Peeta in order to save Gale's life and the lives of her nearest and dearest. This is the main detail of the love triangle from her perspective.