Optimizing Graphics Rendering and Illumination Simulation using Enhanced L-BFGS Algorithm

Abstract

In computer graphics, photorealistic lighting simulation and efficient rendering technology have always faced the dual challenges of computational complexity and visual fidelity. Traditional global illumination algorithms rely on many ray sampling and iterative calculations. For example, path tracing needs to emit thousands of rays per pixel to converge. However, joint optimization problems of hundreds of dimensions, such as light source parameters and material reflectivity in dynamic scenes, often cause traditional gradient descent methods to fall into local optimization. The L-BFGS algorithm stores historical gradient information through a limited memory strategy and constructs an iterative model approximating the inverse of the Hessian matrix. While maintaining the fast convergence characteristics of second-order optimization, the memory consumption is reduced to the order of O (mn) (m is the number of memory steps), which provides a new idea for large-scale lighting parameter optimization. Experimental results demonstrate that the L-BFGS optimization achieves convergence of the energy function to 10-6 within 500 iterations in scenes with dynamic light sources and complex materials, reducing computation time by 38% compared to traditional BFGS. When integrated into NeRF training, the hybrid L-BFGS strategy reduces geometric reconstruction error to 0.12 mm, improving accuracy by 52% over pure stochastic gradient descent. In real-time rendering, GPU-accelerated L-BFGS optimizes shadow mapping parameters for 256 virtual point lights per frame, maintaining 60 FPS at 4K resolution with 1.2 GB VRAM usage. For mobile AR, a quantized L-BFGS variant achieves material reflection calibration in 8.3 ms with ±0.5% azimuth accuracy, while the Monte Carlo-L-BFGS framework reduces indirect illumination precomputation from 14.6 hours to 2.3 hours with 98.7% visual fidelity. These technological advances provide a new paradigm for integrating movie-level offline and real-time rasterized rendering pipelines and promote the development of efficient visualization in emerging fields such as digital twins and the metaverse.