Abstract. We present a mathematical framework for analysis and design of highperformance structured light (SL) coding schemes. Using this framework, we design Hamiltonian SL coding, a novel family of SL coding schemes that can recover 3D shape with high precision, with only a small number (as few as three) of images. We establish structural similarity between popular discrete (binary) SL coding methods, and Hamiltonian coding, which is a continuous coding approach. Based on this similarity, and by leveraging design principles from several different SL coding families, we propose a general recipe for designing Hamiltonian coding patterns with specific desirable properties, such as patterns with high spatial frequencies for dealing with global illumination. We perform several experiments to evaluate the proposed approach, and demonstrate that Hamiltonian coding based SL approaches outperform existing methods in challenging scenarios, including scenes with dark albedos, strong ambient light, and interreflections