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The key contributions lie in three-fold. We compute the normal of each 3D Gaussian using the shortest eigenvector, with a directional masking scheme forcing accurate normal estimation without external supervision. We adopt an efficient voxel-based indirect illumination tracing scheme that stores direction-aware outgoing radiance in each 3D Gaussian to disentangle secondary illumination for approximating multi-bounce light transport. To further enhance the illumination disentanglement, we represent a high-resolution environmental map with a learnable low-resolution map and a lightweight, fully convolutional network. Our method achieves state-of-the-art performance in both relighting and novel view synthesis tasks among the recently proposed inverse rendering methods while achieving real-time rendering. This substantiates our proposed method's efficacy and broad applicability, highlighting its potential as an influential tool in various real-time interactive graphics applications such as material editing and relighting. 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