Efficient Monte Carlo Rendering of Implicit-Shaped Volumetric Emitters

We present a practical and unbiased sampling technique for volumetric light sources defined by signed distance functions (SDFs). SDFs can compactly represent complex procedural shapes and support Boolean operations for flexible composition. However, their use as emitters remains underexplored in photorealistic rendering due to the absence of efficient sampling strategies. Our key insight is to model the interior of an SDF as a uniform volume and to project volumetric samples onto the unit sphere centered at the shading point, yielding a solid angle distribution that captures the emitter's relative spatial layout. We derive the directional probability densities for analytic primitives and generalize the formulation to arbitrary SDFs via Monte Carlo volume estimation. Leveraging robust sphere tracing, our method enables accurate and efficient sampling of SDF emitters without requiring explicit surface parameterization, voxelization, or precomputed tables. Compared to baseline approaches such as uniform directional sampling or surface approximations, our technique achieves significantly lower variance and runtime in next-event estimation, while broadening the expressive power of light sources in rendering.