An accurate representation of three-dimensional (3D) object orientation is essential for interacting with the environment. Where and how the brain visually encodes 3D object orientation remains unknown, but prior studies suggest the caudal intraparietal area (CIP) may be involved. Here, we develop rigorous analytical methods for quantifying 3D orientation tuning curves, and use these tools to the study the neural coding of surface orientation. Specifically, we show that single neurons in area CIP of the rhesus macaque jointly encode the slant and tilt of a planar surface, and that across the population, the distribution of preferred slant-tilts is not statistically different from uniform. This suggests that all slant-tilt combinations are equally represented in area CIP. Furthermore, some CIP neurons are found to also represent the third rotational degree of freedom that determines the orientation of the image pattern on the planar surface. Together, the present results suggest that CIP is a critical neural locus for the encoding of all three rotational degrees of freedom specifying an object's 3D spatial orientation.
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