Improved rapid algorithm for continuous shading based on the fully analytical polygon-based method

The fully analytical polygon-based algorithm is an efficient and precise method for generating holograms. However, the method cannot directly incorporate rendering information. We adopt the framework of the fully analytical polygon-based algorithm and introduce an improved self-similar subdivision model to simplify the computation of pixel normal vectors in the Blinn-Phong lighting model. By decoupling the specular reflection component from the spectrum, the method elegantly avoids the issue of non-integrable exponents in the specular reflection term. Building upon previous research, we propose a new segmentation method that combines square and triangular segments to compute continuous shading. By reducing the number of segments, the proposed method can nearly double the computational efficiency while generating lighting effects for realistic scenes with specular highlights, thus reconstructing realistic 3D scenes. The effectiveness of the proposed method is validated through numerical simulations and optical reconstructions.