3D Gaussian Splatting (3DGS) has emerged as a promising method for high-quality, real-time 3D reconstruction. To associate 3DGS with mesh representations, existing methods primarily focus on 3DGS-to-mesh reconstruction from multi-view images. In contrast, the problem of converting a mesh into 3DGS has received comparatively less attention. Instead of relying on heuristic strategies that bind 3D Gaussians to the mesh, we propose a novel white-box 3DGS construction framework, termed Mesh2GS, which generates 3DGS directly from mesh geometry based on plenoptic sampling theory, achieving Nyquist-level performance for high-quality global illumination rendering. Firstly, we propose a plenoptic sampling guided 3DGS construction strategy that theoretically derives the minimum sampling rate of the sampled views and the distribution of 3D Gaussians. Second, we propose a novel 3DGS update procedure with albedo--shading decomposition for efficient global-illumination capture. Finally, we introduce a neural illumination enhancement module to handle non-Lambertian effects. Experimental results demonstrate that our method surpasses state-of-the-art baselines and is practically effective for both real-time shared rendering and non-Lambertian effects capturing specular highlights. The project code will be released upon acceptance.

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