This work studies the geometry of affective representations in large language models as a setting where latent structure can be compared with established psychological models of emotion. Using geometric data analysis, it shows that LLM representations of affective concepts align with valence-arousal structure, exhibit nonlinear geometry that is still well approximated by linear representations, and can be used to quantify uncertainty in emotion-processing tasks. These findings connect model representations to human emotion models and suggest applications for interpretability and AI safety.