We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology.