The advent of Artificial General Intelligence (AGI) promises to revolutionize affective computing. However, current research lacks a systematic framework that accounts for the inherently cross-space nature of human emotion, where physiological states (physical space), cultural norms (social space), cognitive processes (thinking space), and digital data (cyberspace) continuously interact and shape each other. To address this gap, this paper starts by repositioning affective computing within the theory of Cyber-Physical-Social-Thinking (CPST) space, conceptualizing it as a dynamic process of cross-space transformation rather than an isolated function. AGI capabilities of perception, learning, reasoning, memory, generalization, and generation serve as the computational engines that enable these cross-space transformations. We then systematically map AGI techniques (e.g., causal modeling, chain-of-thought, diffusion models) to specific affective computing tasks, showing how each technique supports their realization. By integrating CPST as a theoretical backbone and AGI as an enabling technology, this paper provides a systematic roadmap for next-generation affective computing. Potential applications and future directions are also discussed, highlighting how this framework advances human-level affective intelligence toward genuine empathy and contextual awareness.