This innovation addresses a critical bottleneck in 3D scene reconstruction by enabling high-fidelity mesh extraction from Neural Radiance Fields (NeRFs). While NeRFs excel at photorealistic view synthesis, their implicit volumetric representation is incompatible with real-time graphics and simulation pipelines that require explicit polygonal meshes. The innovation introduces a Signed Distance Function (SDF) with spatially-varying sharpness control, a key advancement where the surface boundary sharpness parameter (beta) is learned through a neural network rather than fixed, enabling sharper and more accurate surface localization. The method combines grid-based NeRF initialization for geometry and appearance decomposition with differentiable mesh refinement, iteratively optimizing vertex positions and mesh resolution based on rendering errors. The result is a practical bridge between neural implicit fields and conventional mesh-based pipelines, enabling downstream applications in robotics, photogrammetry, extended reality, and physics simulations that depend on precise geometric representation.