As an important three-dimensional (3D) display technology, computer-generated holograms (CGHs) have been facing challenges of computational efficiency and realism. The polygon-based method, as the mainstream CGH algorithm, has been widely studied and improved over the past 20 years. However, few comprehensive and high-speed methods have been proposed. In this study, we propose an analytical spectrum method based on the principle of spectral energy concentration, which can achieve a speedup of nearly 30 times and generate high-resolution (8K) holograms with low memory requirements. Based on the Phong illumination model and the sub-triangles method, we propose a shading rendering algorithm to achieve a very smooth and realistic reconstruction with only a small increase in computational effort. Benefiting from the idea of triangular subdivision and octree structures, the proposed original occlusion culling scheme can closely crop the overlapping areas with almost no additional overhead, thus rendering a 3D parallax sense. With this, we built a comprehensive high-speed rendering pipeline of polygon-based holograms capable of computing any complex 3D object. Numerical and optical reconstructions confirmed the generalizability of the pipeline.