We have developed a full analytical method with texture mapping for polygon-based computer-generated holography. A parallel planar projection mapping for holographic rendering along with affine transformation and self-similar segmentation is derived. Based on this method, we further propose a parallelogram-approximation to reduce the number of polygons used in the polygon-based technique. We demonstrate that the overall method can reduce the computational effort by 50% as compared to an existing method without sacrificing the reconstruction quality based on high precision rendering of complex textures. Numerical and optical reconstructions have shown the effectiveness of the overall scheme.