Methods, systems, and non-transitory computer readable storage media are disclosed for generating enriched light sources by utilizing surface-centric representations of three-dimensional surfaces. Specifically, the disclosed system utilizes a surface-centric re-parameterization that combines geometric and algebraic components of a sphere to model different light source types in a continuous range of lighting configurations. The disclosed systems utilize a set of intuitive parameters to determine a shape and emission parameters for generating an enriched light source. Additionally, the disclosed system provides a set of interactive light source controls to modify a position, orientation, shape, emittance, and lighting attenuation over distance of a light source within a three-dimensional environment. The disclosed system determines the light source controls based on sets of three-dimensional interaction primitives to control one or more parameters of the light source. The disclosed system provides the light source controls for consistently modifying various light source types within the three-dimensional environment.