This paper introduces a novel ray-tracing methodology for various gradient-index materials, particularly plasmas. The proposed approach utilizes adaptive-step Runge-Kutta integration to compute ray trajectories while incorporating an innovative rasterization step for ray energy deposition. By removing the requirement for rays to terminate at cell interfaces—a limitation inherent in earlier cell-confined approaches—the numerical formulation of ray motion becomes independent of specific domain geometries. This facilitates a unified and concise tracing method compatible with all commonly used curvilinear coordinate systems in laser-plasma simulations, which were previously unsupported or prohibitively complex under cell-confined frameworks. Numerical experiments demonstrate the algorithm's stability and versatility in capturing diverse ray physics across reduced-dimensional planar, cylindrical, and spherical coordinate systems. We anticipate that the rasterization-based approach will pave the way for the development of a generalized ray-tracing toolkit applicable to a broad range of fluid simulations and synthetic optical diagnostics.